Entropic manifestations of topological order in three dimensions

NASA Astrophysics Data System (ADS)

Bullivant, Alex; Pachos, Jiannis K.

2016-03-01

We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological properties is richer than the two-dimensional case. In addition to the reduction of the entropy caused by a nonzero vacuum expectation value of contractible loop operators, a topological invariant emerges that increases the entropy if the model consists of nontrivially braiding anyons. As a result the three-dimensional topological entanglement entropy provides only partial information about the two entropic topological invariants.

Reparametrization-based estimation of genetic parameters in multi-trait animal model using Integrated Nested Laplace Approximation.

PubMed

Mathew, Boby; Holand, Anna Marie; Koistinen, Petri; Léon, Jens; Sillanpää, Mikko J

2016-02-01

A novel reparametrization-based INLA approach as a fast alternative to MCMC for the Bayesian estimation of genetic parameters in multivariate animal model is presented. Multi-trait genetic parameter estimation is a relevant topic in animal and plant breeding programs because multi-trait analysis can take into account the genetic correlation between different traits and that significantly improves the accuracy of the genetic parameter estimates. Generally, multi-trait analysis is computationally demanding and requires initial estimates of genetic and residual correlations among the traits, while those are difficult to obtain. In this study, we illustrate how to reparametrize covariance matrices of a multivariate animal model/animal models using modified Cholesky decompositions. This reparametrization-based approach is used in the Integrated Nested Laplace Approximation (INLA) methodology to estimate genetic parameters of multivariate animal model. Immediate benefits are: (1) to avoid difficulties of finding good starting values for analysis which can be a problem, for example in Restricted Maximum Likelihood (REML); (2) Bayesian estimation of (co)variance components using INLA is faster to execute than using Markov Chain Monte Carlo (MCMC) especially when realized relationship matrices are dense. The slight drawback is that priors for covariance matrices are assigned for elements of the Cholesky factor but not directly to the covariance matrix elements as in MCMC. Additionally, we illustrate the concordance of the INLA results with the traditional methods like MCMC and REML approaches. We also present results obtained from simulated data sets with replicates and field data in rice.

A Phase-Locked Loop Epilepsy Network Emulator

PubMed Central

Watson, P.D.; Horecka, K. M.; Cohen, N.J.; Ratnam, R.

2015-01-01

Most seizure forecasting employs statistical learning techniques that lack a representation of the network interactions that give rise to seizures. We present an epilepsy network emulator (ENE) that uses a network of interconnected phase-locked loops (PLLs) to model synchronous, circuit-level oscillations between electrocorticography (ECoG) electrodes. Using ECoG data from a canine-epilepsy model (Davis et al. 2011) and a physiological entropy measure (approximate entropy or ApEn, Pincus 1995), we demonstrate the entropy of the emulator phases increases dramatically during ictal periods across all ECoG recording sites and across all animals in the sample. Further, this increase precedes the observable voltage spikes that characterize seizure activity in the ECoG data. These results suggest that the ENE is sensitive to phase-domain information in the neural circuits measured by ECoG and that an increase in the entropy of this measure coincides with increasing likelihood of seizure activity. Understanding this unpredictable phase-domain electrical activity present in ECoG recordings may provide a target for seizure detection and feedback control. PMID:26664133

Fine-grained state counting for black holes in loop quantum gravity.

PubMed

Ghosh, A; Mitra, P

2009-04-10

A state of a black hole in loop quantum gravity is given by a distribution of spins on punctures on the horizon. The distribution is of the Boltzmann type, with the area playing the role of the energy. In investigations where the total area was kept approximately constant, there was a kind of thermal equilibrium between the spins which have the same analogue temperature and the entropy was proportional to the area. If the area is precisely fixed, however, multiple constraints appear, different spins have different analogue temperatures and the entropy is not strictly linear in the area, but is bounded by a linear rise.

Entanglement entropy of ABJM theory and entropy of topological black hole

NASA Astrophysics Data System (ADS)

Nian, Jun; Zhang, Xinyu

2017-07-01

In this paper we discuss the supersymmetric localization of the 4D N = 2 offshell gauged supergravity on the background of the AdS4 neutral topological black hole, which is the gravity dual of the ABJM theory defined on the boundary {S}^1× H^2 . We compute the large- N expansion of the supergravity partition function. The result gives the black hole entropy with the logarithmic correction, which matches the previous result of the entanglement entropy of the ABJM theory up to some stringy effects. Our result is consistent with the previous on-shell one-loop computation of the logarithmic correction to black hole entropy. It provides an explicit example of the identification of the entanglement entropy of the boundary conformal field theory with the bulk black hole entropy beyond the leading order given by the classical Bekenstein-Hawking formula, which consequently tests the AdS/CFT correspondence at the subleading order.

Covariance in self-dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems

NASA Astrophysics Data System (ADS)

Ben Achour, Jibril; Brahma, Suddhasattwa

2018-06-01

When applying the techniques of loop quantum gravity (LQG) to symmetry-reduced gravitational systems, one first regularizes the scalar constraint using holonomy corrections, prior to quantization. In inhomogeneous system, where a residual spatial diffeomorphism symmetry survives, such modification of the gauge generator generating time reparametrization can potentially lead to deformations or anomalies in the modified algebra of first-class constraints. When working with self-dual variables, it has already been shown that, for spherically symmetric geometry coupled to a scalar field, the holonomy-modified constraints do not generate any modifications to general covariance, as one faces in the real variables formulation, and can thus accommodate local degrees of freedom in such inhomogeneous models. In this paper, we extend this result to Gowdy cosmologies in the self-dual Ashtekar formulation. Furthermore, we show that the introduction of a μ ¯-scheme in midisuperspace models, as is required in the "improved dynamics" of LQG, is possible in the self-dual formalism while being out of reach in the current effective models using real-valued Ashtekar-Barbero variables. Our results indicate the advantages of using the self-dual variables to obtain a covariant loop regularization prior to quantization in inhomogeneous symmetry-reduced polymer models, additionally implementing the crucial μ ¯-scheme, and thus a consistent semiclassical limit.

Oliver E. Buckley Condensed Matter Prize: Emergent gravity from interacting Majorana modes

NASA Astrophysics Data System (ADS)

Kitaev, Alexei

I will describe a concrete many-body Hamiltonian that exhibits some features of a quantum black hole. The Sachdev-Ye-Kitaev model is a system of N >> 1 Majorana modes that are all coupled by random 4-th order terms. The problem admits an approximate dynamic mean field solution. At low temperatures, there is a fluctuating collective mode that corresponds to reparametrization of time. The effective action for this mode is equivalent to dilaton gravity in two space-time dimensions. Some important questions are how to quantize the reparametrization mode in Lorentzian time, include dissipative effects, and understand this system from the quantum information perspective. Supported by the Simons Foundation, Award Number 376205.

Effects of temperature on the irradiation responses of Al 0.1 CoCrFeNi high entropy alloy

DOE PAGES

Yang, Tengfei; Xia, Songqin; Guo, Wei; ...

2017-09-29

Structural damage and chemical segregation in Al 0.1CoCrFeNi high entropy alloy irradiated at elevated temperatures are studied using transmission electron microscopy (TEM) and atom probe tomography (APT). Irradiation-induced defects include dislocation loops, long dislocations and stacking-fault tetrahedra, but no voids can be observed. Furthermore, as irradiation temperature increases, defect density is decreased but defect size is increased, which is induced by increasing defect mobility. Finally, APT characterization reveals that ion irradiation at elevated temperatures can induce an enrichment of Ni and Co as well as a depletion of Fe and Cr at defect clusters, mainly including dislocation loops and longmore » dislocations.« less

Effects of temperature on the irradiation responses of Al 0.1 CoCrFeNi high entropy alloy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Tengfei; Xia, Songqin; Guo, Wei

Structural damage and chemical segregation in Al 0.1CoCrFeNi high entropy alloy irradiated at elevated temperatures are studied using transmission electron microscopy (TEM) and atom probe tomography (APT). Irradiation-induced defects include dislocation loops, long dislocations and stacking-fault tetrahedra, but no voids can be observed. Furthermore, as irradiation temperature increases, defect density is decreased but defect size is increased, which is induced by increasing defect mobility. Finally, APT characterization reveals that ion irradiation at elevated temperatures can induce an enrichment of Ni and Co as well as a depletion of Fe and Cr at defect clusters, mainly including dislocation loops and longmore » dislocations.« less

Holographic calculation for large interval Rényi entropy at high temperature

NASA Astrophysics Data System (ADS)

Chen, Bin; Wu, Jie-qiang

2015-11-01

In this paper, we study the holographic Rényi entropy of a large interval on a circle at high temperature for the two-dimensional conformal field theory (CFT) dual to pure AdS3 gravity. In the field theory, the Rényi entropy is encoded in the CFT partition function on n -sheeted torus connected with each other by a large branch cut. As proposed by Chen and Wu [Large interval limit of Rényi entropy at high temperature, arXiv:1412.0763], the effective way to read the entropy in the large interval limit is to insert a complete set of state bases of the twist sector at the branch cut. Then the calculation transforms into an expansion of four-point functions in the twist sector with respect to e-2/π T R n . By using the operator product expansion of the twist operators at the branch points, we read the first few terms of the Rényi entropy, including the leading and next-to-leading contributions in the large central charge limit. Moreover, we show that the leading contribution is actually captured by the twist vacuum module. In this case by the Ward identity the four-point functions can be derived from the correlation function of four twist operators, which is related to double interval entanglement entropy. Holographically, we apply the recipe in [T. Faulkner, The entanglement Rényi entropies of disjoint intervals in AdS/CFT, arXiv:1303.7221] and [T. Barrella et al., Holographic entanglement beyond classical gravity, J. High Energy Phys. 09 (2013) 109] to compute the classical Rényi entropy and its one-loop quantum correction, after imposing a new set of monodromy conditions. The holographic classical result matches exactly with the leading contribution in the field theory up to e-4 π T R and l6, while the holographical one-loop contribution is in exact agreement with next-to-leading results in field theory up to e-6/π T R n and l4 as well.

Energetics analysis of interstitial loops in single-phase concentrated solid-solution alloys

NASA Astrophysics Data System (ADS)

Wang, Xin-Xin; Niu, Liang-Liang; Wang, Shaoqing

2018-04-01

Systematic energetics analysis on the shape preference, relative stability and radiation-induced segregation of interstitial loops in nickel-containing single-phase concentrated solid-solution alloys have been conducted using atomistic simulations. It is shown that the perfect loops prefer rhombus shape for its low potential energy, while the Frank faulted loops favor ellipse for its low potential energy and the possible large configurational entropy. The decrease of stacking fault energy with increasing compositional complexity provides the energetic driving force for the formation of faulted loops, which, in conjunction with the kinetic factors, explains the experimental observation that the fraction of faulted loops rises with increasing compositional complexity. Notably, the kinetics is primarily responsible for the absence of faulted loops in nickel-cobalt with a very low stacking fault energy. We further demonstrate that the simultaneous nickel enrichment and iron/chromium depletion on interstitial loops can be fully accounted for by their energetics.

Predicting RNA pseudoknot folding thermodynamics

PubMed Central

Cao, Song; Chen, Shi-Jie

2006-01-01

Based on the experimentally determined atomic coordinates for RNA helices and the self-avoiding walks of the P (phosphate) and C4 (carbon) atoms in the diamond lattice for the polynucleotide loop conformations, we derive a set of conformational entropy parameters for RNA pseudoknots. Based on the entropy parameters, we develop a folding thermodynamics model that enables us to compute the sequence-specific RNA pseudoknot folding free energy landscape and thermodynamics. The model is validated through extensive experimental tests both for the native structures and for the folding thermodynamics. The model predicts strong sequence-dependent helix-loop competitions in the pseudoknot stability and the resultant conformational switches between different hairpin and pseudoknot structures. For instance, for the pseudoknot domain of human telomerase RNA, a native-like and a misfolded hairpin intermediates are found to coexist on the (equilibrium) folding pathways, and the interplay between the stabilities of these intermediates causes the conformational switch that may underlie a human telomerase disease. PMID:16709732

Systems analysis of a closed loop ECLSS using the ASPEN simulation tool. Thermodynamic efficiency analysis of ECLSS components. M.S. Thesis

NASA Technical Reports Server (NTRS)

Chatterjee, Sharmista

1993-01-01

Our first goal in this project was to perform a systems analysis of a closed loop Environmental Control Life Support System (ECLSS). This pertains to the development of a model of an existing real system from which to assess the state or performance of the existing system. Systems analysis is applied to conceptual models obtained from a system design effort. For our modelling purposes we used a simulator tool called ASPEN (Advanced System for Process Engineering). Our second goal was to evaluate the thermodynamic efficiency of the different components comprising an ECLSS. Use is made of the second law of thermodynamics to determine the amount of irreversibility of energy loss of each component. This will aid design scientists in selecting the components generating the least entropy, as our penultimate goal is to keep the entropy generation of the whole system at a minimum.

Large reversible entropy change at the inverse magnetocaloric effect in Ni-Co-Mn-Ga-In magnetic shape memory alloys

NASA Astrophysics Data System (ADS)

Emre, Baris; Yüce, Süheyla; Stern-Taulats, Enric; Planes, Antoni; Fabbrici, Simone; Albertini, Franca; Mañosa, Lluís

2013-06-01

Calorimetry under magnetic field has been used to study the inverse magnetocaloric effect in Ni-Co-Mn-Ga-In magnetic shape memory alloys. It is shown that the energy dissipated during a complete transformation loop only represents a small fraction (5% to 7%) of the latent heat of the martensitic transition. It is found that the entropy values obtained from isofield temperature scans agree well with those obtained from isothermal magnetic field scans. The reproducibility of the magnetocaloric effect has been studied from isothermal measurements. Reproducible entropy values under field cycling have been found within a temperature interval bounded by the start temperature of the forward transition at zero field and the start temperature of the reverse transition under applied field. Large reversible entropy changes around 11 J/kg K have been found for fields up to 6 T.

Structure and Dynamics Analysis on Plexin-B1 Rho GTPase Binding Domain as a Monomer and Dimer

PubMed Central

2015-01-01

Plexin-B1 is a single-pass transmembrane receptor. Its Rho GTPase binding domain (RBD) can associate with small Rho GTPases and can also self-bind to form a dimer. In total, more than 400 ns of NAMD molecular dynamics simulations were performed on RBD monomer and dimer. Different analysis methods, such as root mean squared fluctuation (RMSF), order parameters (S2), dihedral angle correlation, transfer entropy, principal component analysis, and dynamical network analysis, were carried out to characterize the motions seen in the trajectories. RMSF results show that after binding, the L4 loop becomes more rigid, but the L2 loop and a number of residues in other regions become slightly more flexible. Calculating order parameters (S2) for CH, NH, and CO bonds on both backbone and side chain shows that the L4 loop becomes essentially rigid after binding, but part of the L1 loop becomes slightly more flexible. Backbone dihedral angle cross-correlation results show that loop regions such as the L1 loop including residues Q25 and G26, the L2 loop including residue R61, and the L4 loop including residues L89–R91, are highly correlated compared to other regions in the monomer form. Analysis of the correlated motions at these residues, such as Q25 and R61, indicate two signal pathways. Transfer entropy calculations on the RBD monomer and dimer forms suggest that the binding process should be driven by the L4 loop and C-terminal. However, after binding, the L4 loop functions as the motion responder. The signal pathways in RBD were predicted based on a dynamical network analysis method using the pathways predicted from the dihedral angle cross-correlation calculations as input. It is found that the shortest pathways predicted from both inputs can overlap, but signal pathway 2 (from F90 to R61) is more dominant and overlaps all of the routes of pathway 1 (from F90 to P111). This project confirms the allosteric mechanism in signal transmission inside the RBD network, which was in part proposed in the previous experimental study. PMID:24901636

Looping and clustering model for the organization of protein-DNA complexes on the bacterial genome

NASA Astrophysics Data System (ADS)

Walter, Jean-Charles; Walliser, Nils-Ole; David, Gabriel; Dorignac, Jérôme; Geniet, Frédéric; Palmeri, John; Parmeggiani, Andrea; Wingreen, Ned S.; Broedersz, Chase P.

2018-03-01

The bacterial genome is organized by a variety of associated proteins inside a structure called the nucleoid. These proteins can form complexes on DNA that play a central role in various biological processes, including chromosome segregation. A prominent example is the large ParB-DNA complex, which forms an essential component of the segregation machinery in many bacteria. ChIP-Seq experiments show that ParB proteins localize around centromere-like parS sites on the DNA to which ParB binds specifically, and spreads from there over large sections of the chromosome. Recent theoretical and experimental studies suggest that DNA-bound ParB proteins can interact with each other to condense into a coherent 3D complex on the DNA. However, the structural organization of this protein-DNA complex remains unclear, and a predictive quantitative theory for the distribution of ParB proteins on DNA is lacking. Here, we propose the looping and clustering model, which employs a statistical physics approach to describe protein-DNA complexes. The looping and clustering model accounts for the extrusion of DNA loops from a cluster of interacting DNA-bound proteins that is organized around a single high-affinity binding site. Conceptually, the structure of the protein-DNA complex is determined by a competition between attractive protein interactions and loop closure entropy of this protein-DNA cluster on the one hand, and the positional entropy for placing loops within the cluster on the other. Indeed, we show that the protein interaction strength determines the ‘tightness’ of the loopy protein-DNA complex. Thus, our model provides a theoretical framework for quantitatively computing the binding profiles of ParB-like proteins around a cognate (parS) binding site.

Effect of urea and alkylureas on the stability and structural fluctuation of the M80-containing Ω-loop of horse cytochrome c.

PubMed

Kumar, Sandeep; Sharma, Deepak; Kumar, Rajesh

2014-03-01

The effect of denaturants on the structural fluctuation of M80-containing Ω-loop of ferrocytochrome c was determined by measuring the rate coefficient of CO-association with ferrocytochrome c under varying concentrations of urea and alkylureas (methylurea (MU), N,N'-dimethylurea (DMU), ethylurea (EU), tetramethylurea (TMU)) at pH7.0, 25°C. As denaturant concentration is increased within the subdenaturing limit, the CO-association reaction is decelerated indicating that subdenaturing concentrations of denaturant reduce the structural fluctuation of the Ω-loop. Structural fluctuation of the Ω-loop is reduced more for urea and least for TMU. Intermolecular docking between horse cytochrome c and denaturant molecule (urea, MU, DMU, EU and TMU) reveals that polyfunctional interactions between the denaturant and different groups of Ω-loop and other part of protein decrease with an increase of alkyl group on urea molecule, which suggests that the decrease in the extent of restricted dynamics of Ω-loop with a corresponding increase of alkyl groups on urea molecule is due to the decrease of denaturant-mediated cross-linking interactions. These denaturant-mediated interactions are expected to reduce the conformational entropy of protein. Analysis of rate-temperature data shows a progressive decrease in conformational entropy of protein in the native to subdenaturing region. Thermodynamic analysis of denaturant (urea, MU, DMU, EU, TMU) effects on the thermal unfolding of ferrocytochrome c reveals that (i) thermodynamic stability of protein decreases with increasing concentration of denaturant or hydrophobicity of urea derivatives, (ii) water activity plays an important role in stabilization of ferrocytochrome c, and (iii) destabilization of ferrocytochrome c by denaturant occurs through the disturbance of hydrophobic interactions and hydrogen-bonding. Copyright © 2014 Elsevier B.V. All rights reserved.

Remarks on entanglement entropy in string theory

NASA Astrophysics Data System (ADS)

Balasubramanian, Vijay; Parrikar, Onkar

2018-03-01

Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the "space of open string configurations." We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.

Is the catalytic activity of triosephosphate isomerase fully optimized? An investigation based on maximization of entropy production.

PubMed

Bonačić Lošić, Željana; Donđivić, Tomislav; Juretić, Davor

2017-03-01

Triosephosphate isomerase (TIM) is often described as a fully evolved housekeeping enzyme with near-maximal possible reaction rate. The assumption that an enzyme is perfectly evolved has not been easy to confirm or refute. In this paper, we use maximization of entropy production within known constraints to examine this assumption by calculating steady-state cyclic flux, corresponding entropy production, and catalytic activity in a reversible four-state scheme of TIM functional states. The maximal entropy production (MaxEP) requirement for any of the first three transitions between TIM functional states leads to decreased total entropy production. Only the MaxEP requirement for the product (R-glyceraldehyde-3-phosphate) release step led to a 30% increase in enzyme activity, specificity constant k cat /K M , and overall entropy production. The product release step, due to the TIM molecular machine working in the physiological direction of glycolysis, has not been identified before as the rate-limiting step by using irreversible thermodynamics. Together with structural studies, our results open the possibility for finding amino acid substitutions leading to an increased frequency of loop six opening and product release.

Entanglement entropy with a time-dependent Hamiltonian

NASA Astrophysics Data System (ADS)

Sivaramakrishnan, Allic

2018-03-01

The time evolution of entanglement tracks how information propagates in interacting quantum systems. We study entanglement entropy in CFT2 with a time-dependent Hamiltonian. We perturb by operators with time-dependent source functions and use the replica trick to calculate higher-order corrections to entanglement entropy. At first order, we compute the correction due to a metric perturbation in AdS3/CFT2 and find agreement on both sides of the duality. Past first order, we find evidence of a universal structure of entanglement propagation to all orders. The central feature is that interactions entangle unentangled excitations. Entanglement propagates according to "entanglement diagrams," proposed structures that are motivated by accessory spacetime diagrams for real-time perturbation theory. To illustrate the mechanisms involved, we compute higher-order corrections to free fermion entanglement entropy. We identify an unentangled operator, one which does not change the entanglement entropy to any order. Then, we introduce an interaction and find it changes entanglement entropy by entangling the unentangled excitations. The entanglement propagates in line with our conjecture. We compute several entanglement diagrams. We provide tools to simplify the computation of loop entanglement diagrams, which probe UV effects in entanglement propagation in CFT and holography.

Black hole state counting in loop quantum gravity: a number-theoretical approach.

PubMed

Agulló, Iván; Barbero G, J Fernando; Díaz-Polo, Jacobo; Fernández-Borja, Enrique; Villaseñor, Eduardo J S

2008-05-30

We give an efficient method, combining number-theoretic and combinatorial ideas, to exactly compute black hole entropy in the framework of loop quantum gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and explicitly determine the number of solutions to the projection constraint. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum.

Black holes as quantum gravity condensates

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo

2018-03-01

We model spherically symmetric black holes within the group field theory formalism for quantum gravity via generalized condensate states, involving sums over arbitrarily refined graphs (dual to three-dimensional triangulations). The construction relies heavily on both the combinatorial tools of random tensor models and the quantum geometric data of loop quantum gravity, both part of the group field theory formalism. Armed with the detailed microscopic structure, we compute the entropy associated with the black hole horizon, which turns out to be equivalently the Boltzmann entropy of its microscopic degrees of freedom and the entanglement entropy between the inside and outside regions. We recover the area law under very general conditions, as well as the Bekenstein-Hawking formula. The result is also shown to be generically independent of any specific value of the Immirzi parameter.

Possibility-based robust design optimization for the structural-acoustic system with fuzzy parameters

NASA Astrophysics Data System (ADS)

Yin, Hui; Yu, Dejie; Yin, Shengwen; Xia, Baizhan

2018-03-01

The conventional engineering optimization problems considering uncertainties are based on the probabilistic model. However, the probabilistic model may be unavailable because of the lack of sufficient objective information to construct the precise probability distribution of uncertainties. This paper proposes a possibility-based robust design optimization (PBRDO) framework for the uncertain structural-acoustic system based on the fuzzy set model, which can be constructed by expert opinions. The objective of robust design is to optimize the expectation and variability of system performance with respect to uncertainties simultaneously. In the proposed PBRDO, the entropy of the fuzzy system response is used as the variability index; the weighted sum of the entropy and expectation of the fuzzy response is used as the objective function, and the constraints are established in the possibility context. The computations for the constraints and objective function of PBRDO are a triple-loop and a double-loop nested problem, respectively, whose computational costs are considerable. To improve the computational efficiency, the target performance approach is introduced to transform the calculation of the constraints into a double-loop nested problem. To further improve the computational efficiency, a Chebyshev fuzzy method (CFM) based on the Chebyshev polynomials is proposed to estimate the objective function, and the Chebyshev interval method (CIM) is introduced to estimate the constraints, thereby the optimization problem is transformed into a single-loop one. Numerical results on a shell structural-acoustic system verify the effectiveness and feasibility of the proposed methods.

Finite-time braiding exponents

NASA Astrophysics Data System (ADS)

Budišić, Marko; Thiffeault, Jean-Luc

2015-08-01

Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.

Finite-time braiding exponents.

PubMed

Budišić, Marko; Thiffeault, Jean-Luc

2015-08-01

Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.

Information loss in effective field theory: Entanglement and thermal entropies

NASA Astrophysics Data System (ADS)

Boyanovsky, Daniel

2018-03-01

Integrating out high energy degrees of freedom to yield a low energy effective field theory leads to a loss of information with a concomitant increase in entropy. We obtain the effective field theory of a light scalar field interacting with heavy fields after tracing out the heavy degrees of freedom from the time evolved density matrix. The initial density matrix describes the light field in its ground state and the heavy fields in equilibrium at a common temperature T . For T =0 , we obtain the reduced density matrix in a perturbative expansion; it reveals an emergent mixed state as a consequence of the entanglement between light and heavy fields. We obtain the effective action that determines the time evolution of the reduced density matrix for the light field in a nonperturbative Dyson resummation of one-loop correlations of the heavy fields. The Von-Neumann entanglement entropy associated with the reduced density matrix is obtained for the nonresonant and resonant cases in the asymptotic long time limit. In the nonresonant case the reduced density matrix displays an incipient thermalization albeit with a wave-vector, time and coupling dependent effective temperature as a consequence of memory of initial conditions. The entanglement entropy is time independent and is the thermal entropy for this effective, nonequilibrium temperature. In the resonant case the light field fully thermalizes with the heavy fields, the reduced density matrix loses memory of the initial conditions and the entanglement entropy becomes the thermal entropy of the light field. We discuss the relation between the entanglement entropy ultraviolet divergences and renormalization.

Magnetic heat pumping

NASA Technical Reports Server (NTRS)

Brown, G. V. (Inventor)

1978-01-01

A ferromagnetic or ferrimagnetic element is used to control the temperature and applied magnetic field of the element to cause the state of the element as represented on a temperature-magnetic entropy diagram to repeatedly traverse a loop. The loop may have a first portion of concurrent substantially isothermal or constant temperature and increasing applied magnetic field, a second portion of lowering temperature and constant applied magnetic field, a third portion of isothermal and decreasing applied magnetic field, and a fourth portion of increasing temperature and constant applied magnetic field. Other loops may be four-sided, with two isotherms and two adiabats. Preferably, a regenerator is used to enhance desired cooling or heating effects, with varied magnetic fields, or varying temperatures including three-sided figures traversed by the representative point.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jevicki, Antal; Suzuki, Kenta

We continue the study of the Sachdev-Ye-Kitaev model in the Large N limit. Following our formulation in terms of bi-local collective fields with dynamical reparametrization symmetry, we perform perturbative calculations around the conformal IR point. As a result, these are based on an ε expansion which allows for analytical evaluation of correlators and finite temperature quantities.

Cascade control of superheated steam temperature with neuro-PID controller.

PubMed

Zhang, Jianhua; Zhang, Fenfang; Ren, Mifeng; Hou, Guolian; Fang, Fang

2012-11-01

In this paper, an improved cascade control methodology for superheated processes is developed, in which the primary PID controller is implemented by neural networks trained by minimizing error entropy criterion. The entropy of the tracking error can be estimated recursively by utilizing receding horizon window technique. The measurable disturbances in superheated processes are input to the neuro-PID controller besides the sequences of tracking error in outer loop control system, hence, feedback control is combined with feedforward control in the proposed neuro-PID controller. The convergent condition of the neural networks is analyzed. The implementation procedures of the proposed cascade control approach are summarized. Compared with the neuro-PID controller using minimizing squared error criterion, the proposed neuro-PID controller using minimizing error entropy criterion may decrease fluctuations of the superheated steam temperature. A simulation example shows the advantages of the proposed method. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Probing topological order with Rényi entropy

NASA Astrophysics Data System (ADS)

Halász, Gábor B.; Hamma, Alioscia

2012-12-01

We present an analytical study of the quantum phase transition between the topologically ordered toric-code-model ground state and the disordered spin-polarized state. The phase transition is induced by applying an external magnetic field, and the variation in topological order is detected via two nonlocal quantities: the Wilson loop and the topological Rényi entropy of order 2. By exploiting an equivalence with the transverse-field Ising model and considering two different variants of the problem, we investigate the field dependence of these quantities by means of an exact treatment in the exactly solvable variant and complementary perturbation theories around the limits of zero and infinite fields in both variants. We find strong evidence that the phase transition point between topological order and disorder is marked by a discontinuity in the topological Rényi entropy and that the two phases around the phase transition point are characterized by its different constant values. Our results therefore indicate that the topological Rényi entropy is a proper topological invariant: its allowed values are discrete and can be used to distinguish between different phases of matter.

Functional determinants, index theorems, and exact quantum black hole entropy

NASA Astrophysics Data System (ADS)

Murthy, Sameer; Reys, Valentin

2015-12-01

The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the QV operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around Q-invariant off-shell configurations in four-dimensional N=2 supergravity with AdS 2 × S 2 boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in N=2 supergravity. We explain cancellations concerning 1/8 -BPS black holes in N=8 supergravity that were observed in arXiv:1111.1161. We also make comments about the interpretation of a logarithmic term in the topological string partition function in the low energy supergravity theory.

A classical model for closed-loop diagrams of binary liquid mixtures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schnitzler, J.v.; Prausnitz, J.M.

1994-03-01

A classical lattice model for closed-loop temperature-composition phase diagrams has been developed. It considers the effect of specific interactions, such as hydrogen bonding, between dissimilar components. This van Laar-type model includes a Flory-Huggins term for the excess entropy of mixing. It is applied to several liquid-liquid equilibria of nonelectrolytes, where the molecules of the two components differ in size. The model is able to represent the observed data semi-quantitatively, but in most cases it is not flexible enough to predict all parts of the closed loop quantitatively. The ability of the model to represent different binary systems is discussed. Finally,more » attention is given to a correction term, concerning the effect of concentration fluctuations near the upper critical solution temperature.« less

Modified Dispersion Relations: from Black-Hole Entropy to the Cosmological Constant

NASA Astrophysics Data System (ADS)

Garattini, Remo

2012-07-01

Quantum Field Theory is plagued by divergences in the attempt to calculate physical quantities. Standard techniques of regularization and renormalization are used to keep under control such a problem. In this paper we would like to use a different scheme based on Modified Dispersion Relations (MDR) to remove infinities appearing in one loop approximation in contrast to what happens in conventional approaches. In particular, we apply the MDR regularization to the computation of the entropy of a Schwarzschild black hole from one side and the Zero Point Energy (ZPE) of the graviton from the other side. The graviton ZPE is connected to the cosmological constant by means of of the Wheeler-DeWitt equation.

Decoupling of the reparametrization degree of freedom and a generalized probability in quantum cosmology

NASA Astrophysics Data System (ADS)

Dimakis, N.; Terzis, Petros A.; Zampeli, Adamantia; Christodoulakis, T.

2016-09-01

The high degree of symmetry renders the dynamics of cosmological as well as some black hole spacetimes describable by a system of finite degrees of freedom. These systems are generally known as minisuperspace models. One of their important key features is the invariance of the corresponding reduced actions under reparametrizations of the independent variable, a fact that can be seen as the remnant of the general covariance of the full theory. In the case of a system of n degrees of freedom, described by a Lagrangian quadratic in velocities, one can use the lapse by either gauge fixing it or letting it be defined by the constraint and subsequently substitute into the rest of the equations. In the first case, the system of the second-order equations of motion is solvable for all n accelerations and the constraint becomes a restriction among constants of integration. In the second case, the system can be solved for only n -1 accelerations and the "gauge" freedom is transferred to the choice of one of the scalar degrees of freedom. In this paper, we take the second path and express all n -1 scalar degrees of freedom in terms of the remaining one, say q . By considering these n -1 degrees of freedom as arbitrary but given functions of q , we manage to extract a two-dimensional pure gauge system consisting of the lapse N and the arbitrary q : in a way, we decouple the reparametrization invariance from the rest of the equations of motion, which are thus describing the "true" dynamics. The solution of the corresponding quantum two-dimensional system is used for the definition of a generalized probability for every configuration fi(q ), be it classical or not. The main result is that, interestingly enough, this probability attains its extrema on the classical solution of the initial n -dimensional system.

Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space.

PubMed

Ahnert, S E; Fink, T M A

2016-07-01

Network motifs have been studied extensively over the past decade, and certain motifs, such as the feed-forward loop, play an important role in regulatory networks. Recent studies have used Boolean network motifs to explore the link between form and function in gene regulatory networks and have found that the structure of a motif does not strongly determine its function, if this is defined in terms of the gene expression patterns the motif can produce. Here, we offer a different, higher-level definition of the 'function' of a motif, in terms of two fundamental properties of its dynamical state space as a Boolean network. One is the basin entropy, which is a complexity measure of the dynamics of Boolean networks. The other is the diversity of cyclic attractor lengths that a given motif can produce. Using these two measures, we examine all 104 topologically distinct three-node motifs and show that the structural properties of a motif, such as the presence of feedback loops and feed-forward loops, predict fundamental characteristics of its dynamical state space, which in turn determine aspects of its functional versatility. We also show that these higher-level properties have a direct bearing on real regulatory networks, as both basin entropy and cycle length diversity show a close correspondence with the prevalence, in neural and genetic regulatory networks, of the 13 connected motifs without self-interactions that have been studied extensively in the literature. © 2016 The Authors.

Bi-local holography in the SYK model: Perturbations

DOE PAGES

Jevicki, Antal; Suzuki, Kenta

2016-11-08

We continue the study of the Sachdev-Ye-Kitaev model in the Large N limit. Following our formulation in terms of bi-local collective fields with dynamical reparametrization symmetry, we perform perturbative calculations around the conformal IR point. As a result, these are based on an ε expansion which allows for analytical evaluation of correlators and finite temperature quantities.

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

NASA Astrophysics Data System (ADS)

Burnier, Yannis; Rothkopf, Alexander

2013-11-01

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33TC.

Bayesian approach to spectral function reconstruction for Euclidean quantum field theories.

PubMed

Burnier, Yannis; Rothkopf, Alexander

2013-11-01

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33T(C).

Moving heavy quarkonium entropy, effective string tension, and the QCD phase diagram

NASA Astrophysics Data System (ADS)

Chen, Xun; Feng, Sheng-Qin; Shi, Ya-Fei; Zhong, Yang

2018-03-01

The entropy and effective string tension of the moving heavy quark-antiquark pair in the strongly coupled plasmas are calculated by using a deformed an anti-de Sitter/Reissner-Nordström black hole metric. A sharp peak of the heavy-quarkonium entropy around the deconfinement transition can be realized in our model, which is consistent with the lattice QCD result. The effective string tension of the heavy quark-antiquark pair is related to the deconfinement phase transition. Thus, we investigate the deconfinement phase transition by analyzing the characteristics of the effective string tension with different temperatures, chemical potentials, and rapidities. It is found that the results of phase diagram calculated through effective string tension are in agreement with results calculated through a Polyakov loop. We argue that a moving system will reach the phase transition point at a lower temperature and chemical potential than a stationary system. It means that the lifetime of the moving quark-gluon plasma become longer than the static one.

Effect of proline and glycine residues on dynamics and barriers of loop formation in polypeptide chains.

PubMed

Krieger, Florian; Möglich, Andreas; Kiefhaber, Thomas

2005-03-16

Glycine and proline residues are frequently found in turn and loop structures of proteins and are believed to play an important role during chain compaction early in folding. We investigated their effect on the dynamics of intrachain loop formation in various unstructured polypeptide chains. Loop formation is significantly slower around trans prolyl peptide bonds and faster around glycine residues compared to any other amino acid. However, short loops are formed fastest around cis prolyl bonds with a time constant of 6 ns for end-to-end contact formation in a four-residue loop. Formation of short loops encounters activation energies in the range of 15 to 30 kJ/mol. The altered dynamics around glycine and trans prolyl bonds can be mainly ascribed to their effects on the activation energy. The fast dynamics around cis prolyl bonds, in contrast, originate in a higher Arrhenius pre-exponential factor, which compensates for an increased activation energy for loop formation compared to trans isomers. All-atom simulations of proline-containing peptides indicate that the conformational space for cis prolyl isomers is largely restricted compared to trans isomers. This leads to decreased average end-to-end distances and to a smaller loss in conformational entropy upon loop formation in cis isomers. The results further show that glycine and proline residues only influence formation of short loops containing between 2 and 10 residues, which is the typical loop size in native proteins. Formation of larger loops is not affected by the presence of a single glycine or proline residue.

EKF-Based Enhanced Performance Controller Design for Nonlinear Stochastic Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Yuyang; Zhang, Qichun; Wang, Hong

In this paper, a novel control algorithm is presented to enhance the performance of tracking property for a class of non-linear dynamic stochastic systems with unmeasurable variables. To minimize the entropy of tracking errors without changing the existing closed loop with PI controller, the enhanced performance loop is constructed based on the state estimation by extended Kalman Filter and the new controller is designed by full state feedback following this presented control algorithm. Besides, the conditions are obtained for the stability analysis in the mean square sense. In the end, the comparative simulation results are given to illustrate the effectivenessmore » of proposed control algorithm.« less

Toward microstate counting beyond large N in localization and the dual one-loop quantum supergravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, James T.; Pando Zayas, Leopoldo A.; Rathee, Vimal

The topologically twisted index for ABJM theory with gauge group U(N)k × U(N)−k has recently been shown, in the large-N limit, to reproduce the BekensteinHawking entropy of certain magnetically charged asymptotically AdS4 black holes. We numerically study the index beyond the large-N limit and provide evidence that it contains a subleading logarithmic term of the form −1/2 log N. On the holographic side, this term naturally arises from a one-loop computation. However, we find that the contribution coming from the near horizon states does not reproduce the field theory answer. We give some possible reasons for this apparent discrepancy.

First-order irreversible thermodynamic approach to a simple energy converter

NASA Astrophysics Data System (ADS)

Arias-Hernandez, L. A.; Angulo-Brown, F.; Paez-Hernandez, R. T.

2008-01-01

Several authors have shown that dissipative thermal cycle models based on finite-time thermodynamics exhibit loop-shaped curves of power output versus efficiency, such as it occurs with actual dissipative thermal engines. Within the context of first-order irreversible thermodynamics (FOIT), in this work we show that for an energy converter consisting of two coupled fluxes it is also possible to find loop-shaped curves of both power output and the so-called ecological function versus efficiency. In a previous work Stucki [J. W. Stucki, Eur. J. Biochem. 109, 269 (1980)] used a FOIT approach to describe the modes of thermodynamic performance of oxidative phosphorylation involved in adenosine triphosphate (ATP) synthesis within mithochondrias. In that work the author did not use the mentioned loop-shaped curves and he proposed that oxidative phosphorylation operates in a steady state at both minimum entropy production and maximum efficiency simultaneously, by means of a conductance matching condition between extreme states of zero and infinite conductances, respectively. In the present work we show that all Stucki’s results about the oxidative phosphorylation energetics can be obtained without the so-called conductance matching condition. On the other hand, we also show that the minimum entropy production state implies both null power output and efficiency and therefore this state is not fulfilled by the oxidative phosphorylation performance. Our results suggest that actual efficiency values of oxidative phosphorylation performance are better described by a mode of operation consisting of the simultaneous maximization of both the so-called ecological function and the efficiency.

Proline cis-trans isomerization in staphylococcal nuclease: multi-substrate free energy perturbation calculations.

PubMed Central

Hodel, A.; Rice, L. M.; Simonson, T.; Fox, R. O.; Brünger, A. T.

1995-01-01

Staphylococcal nuclease A exists in two folded forms that differ in the isomerization state of the Lys 116-Pro 117 peptide bond. The dominant form (90% occupancy) adopts a cis peptide bond, which is observed in the crystal structure. NMR studies show that the relatively small difference in free energy between the cis and trans forms (delta Gcis-->trans approximately 1.2 kcal/mol) results from large and nearly compensating differences in enthalpy and entropy (delta Hcis-->trans approximately delta TScis-->trans approximately 10 kcal/mol). There is evidence from X-ray crystal structures that the structural differences between the cis and the trans forms of nuclease are confined to the conformation of residues 112-117, a solvated protein loop. Here, we obtain a thermodynamic and structural description of the conformational equilibrium of this protein loop through an exhaustive conformational search that identified several substates followed by free energy simulations between the substrates. By partitioning the search into conformational substates, we overcame the multiple minima problem in this particular case and obtained precise and reproducible free energy values. The protein and water environment was implicitly modeled by appropriately chosen nonbonded terms between the explicitly treated loop and the rest of the protein. These simulations correctly predicted a small free energy difference between the cis and trans forms composed of larger, compensating differences in enthalpy and entropy. The structural predictions of these simulations were qualitatively consistent with known X-ray structures of nuclease variants and yield a model of the unknown minor trans conformation. PMID:7613463

Entropic benefit of a cross-link in protein association.

PubMed

Zaman, Muhammad H; Berry, R Stephen; Sosnick, Tobin R

2002-08-01

We introduce a method to estimate the loss of configurational entropy upon insertion of a cross-link to a dimeric system. First, a clear distinction is established between the loss of entropy upon tethering and binding, two quantities that are often considered to be equivalent. By comparing the probability distribution of the center-to-center distances for untethered and cross-linked versions, we are able to calculate the loss of translational entropy upon cross-linking. The distribution function for the untethered helices is calculated from the probability that a given helix is closer to its partner than to all other helices, the "Nearest Neighbor" method. This method requires no assumptions about the nature of the solvent, and hence resolves difficulties normally associated with calculations for systems in liquids. Analysis of the restriction of angular freedom upon tethering indicates that the loss of rotational entropy is negligible. The method is applied in the context of the folding of a ten turn helical coiled coil with the tether modeled as a Gaussian chain or a flexible amino acid chain. After correcting for loop closure entropy in the docked state, we estimate the introduction of a six-residue tether in the coiled coil results in an effective concentration of the chain to be about 4 or 100 mM, depending upon whether the helices are denatured or pre-folded prior to their association. Thus, tethering results in significant stabilization for systems with millimolar or stronger dissociation constants. Copyright 2002 Wiley-Liss, Inc.

Large deviation analysis of a simple information engine

NASA Astrophysics Data System (ADS)

Maitland, Michael; Grosskinsky, Stefan; Harris, Rosemary J.

2015-11-01

Information thermodynamics provides a framework for studying the effect of feedback loops on entropy production. It has enabled the understanding of novel thermodynamic systems such as the information engine, which can be seen as a modern version of "Maxwell's Dæmon," whereby a feedback controller processes information gained by measurements in order to extract work. Here, we analyze a simple model of such an engine that uses feedback control based on measurements to obtain negative entropy production. We focus on the distribution and fluctuations of the information obtained by the feedback controller. Significantly, our model allows an analytic treatment for a two-state system with exact calculation of the large deviation rate function. These results suggest an approximate technique for larger systems, which is corroborated by simulation data.

Quasithermodynamic Contributions to the Fluctuations of a Protein Nanopore

PubMed Central

2015-01-01

Proteins undergo thermally activated conformational fluctuations among two or more substates, but a quantitative inquiry on their kinetics is persistently challenged by numerous factors, including the complexity and dynamics of various interactions, along with the inability to detect functional substates within a resolvable time scale. Here, we analyzed in detail the current fluctuations of a monomeric β-barrel protein nanopore of known high-resolution X-ray crystal structure. We demonstrated that targeted perturbations of the protein nanopore system, in the form of loop-deletion mutagenesis, accompanying alterations of electrostatic interactions between long extracellular loops, produced modest changes of the differential activation free energies calculated at 25 °C, ΔΔG⧧, in the range near the thermal energy but substantial and correlated modifications of the differential activation enthalpies, ΔΔH⧧, and entropies, ΔΔS⧧. This finding indicates that the local conformational reorganizations of the packing and flexibility of the fluctuating loops lining the central constriction of this protein nanopore were supplemented by changes in the single-channel kinetics. These changes were reflected in the enthalpy–entropy reconversions of the interactions between the loop partners with a compensating temperature, TC, of ∼300 K, and an activation free energy constant of ∼41 kJ/mol. We also determined that temperature has a much greater effect on the energetics of the equilibrium gating fluctuations of a protein nanopore than other environmental parameters, such as the ionic strength of the aqueous phase as well as the applied transmembrane potential, likely due to ample changes in the solvation activation enthalpies. There is no fundamental limitation for applying this approach to other complex, multistate membrane protein systems. Therefore, this methodology has major implications in the area of membrane protein design and dynamics, primarily by revealing a better quantitative assessment on the equilibrium transitions among multiple well-defined and functionally distinct substates of protein channels and pores. PMID:25479108

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vázquez-Báez, V.; Ramírez, C.

We present calculations towards obtaining a wave functions of the universe for the supersymmetric closed string tachyon cosmology. Supersymmetrization, in the superfield formalism, is performed by taking advantage of the time reparametrization invariance of the cosmological action and generalizing the transformations to include grassmannian variables. We calculate the corresponding Hamiltonian, by means of the Dirac formalism, and make use of the superalgebra to find solutions to the Wheeler-DeWitt equations indirectly.

Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential

NASA Astrophysics Data System (ADS)

Andersen, Jens O.; Haque, Najmul; Mustafa, Munshi G.; Strickland, Michael

2016-03-01

In a previous paper [N. Haque et al., J. High Energy Phys. 05 (2014) 27], we calculated the three-loop thermodynamic potential of QCD at finite temperature T and quark chemical potentials μq using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The result allows us to study the thermodynamics of QCD at finite temperature and finite baryon, strangeness, and isospin chemical potentials μB, μS, and μI. We calculate the pressure at nonzero μB and μI with μS=0 , and the energy density, the entropy density, the trace anomaly, and the speed of sound at nonzero μI with μB=μS=0 . The second- and fourth-order isospin susceptibilities are calculated at μB=μS=μI=0 . Our results can be directly compared to lattice QCD without Taylor expansions around μq=0 since QCD has no sign problem at μB=μS=0 and finite isospin chemical potential μI.

Radiation-induced segregation on defect clusters in single-phase concentrated solid-solution alloys

DOE PAGES

Lu, Chenyang; Yang, Taini; Jin, Ke; ...

2017-01-12

A group of single-phase concentrated solid-solution alloys (SP-CSAs), including NiFe, NiCoFe, NiCoFeCr, as well as a high entropy alloy NiCoFeCrMn, was irradiated with 3 MeV Ni 2+ ions at 773 K to a fluence of 5 10 16 ions/cm 2 for the study of radiation response with increasing compositional complexity. Advanced transmission electron microscopy (TEM) with electron energy loss spectroscopy (EELS) was used to characterize the dislocation loop distribution and radiation-induced segregation (RIS) on defect clusters in the SP-CSAs. The results show that a higher fraction of faulted loops exists in the more compositionally complex alloys, which indicate that increasingmore » compositional complexity can extend the incubation period and delay loop growth. The RIS behaviors of each element in the SP-CSAs were observed as follows: Ni and Co tend to enrich, but Cr, Fe and Mn prefer to deplete near the defect clusters. RIS level can be significantly suppressed by increasing compositional complexity due to the sluggish atom diffusion. According to molecular static (MS) simulations, disk like segregations may form near the faulted dislocation loops in the SP-CSAs. Segregated elements tend to distribute around the whole faulted loop as a disk rather than only around the edge of the loop.« less

Spin-Orbit Torque from a Magnetic Heterostructure of High-Entropy Alloy

NASA Astrophysics Data System (ADS)

Chen, Tian-Yue; Chuang, Tsao-Chi; Huang, Ssu-Yen; Yen, Hung-Wei; Pai, Chi-Feng

2017-10-01

High-entropy alloy (HEA) is a family of metallic materials with nearly equal partitions of five or more metals, which might possess mechanical and transport properties that are different from conventional binary or tertiary alloys. In this work, we demonstrate current-induced spin-orbit torque (SOT) magnetization switching in a Ta-Nb-Hf-Zr-Ti HEA-based magnetic heterostructure with perpendicular magnetic anisotropy. The maximum dampinglike SOT efficiency from this particular HEA-based magnetic heterostructure is further determined to be |ζDLHEA | ≈0.033 by hysteresis-loop-shift measurements, while that for the Ta control sample is |ζDLTa | ≈0.04 . Our results indicate that HEA-based magnetic heterostructures can serve as an alternative group of potential candidates for SOT device applications due to the possibility of tuning buffer-layer properties with more than two constituent elements.

BRST-BFV method for nonstationary systems

NASA Astrophysics Data System (ADS)

García, J. Antonio; Vergara, J. David; Urrutia, Luis F.

1995-05-01

Starting from an associated reparametrization-invariant action, the generalization of the BRST-BFV method for the case of nonstationary systems is constructed. The extension of the Batalin-Tyutin conversional approach is also considered in the nonstationary case. In order to illustrate these ideas, the propagator for the time-dependent two-dimensional rotor is calculated by reformulating the problem as a system with only first-class constraints and subsequently using the BRST-BFV prescription previously obtained.

Phage selection of peptide "microantibodies".

PubMed

Fujiwara, Daisuke; Fujii, Ikuo

2013-01-01

A bioactive peptide capable of inhibiting protein-protein interactions has the potential to be a molecular tool for biological studies and a therapeutic by disrupting aberrant interactions involved in diseases. We have developed combinatorial libraries of peptides with helix-loop-helix structure, from which the isolated peptides have the constrained structure to reduce entropy costs in binding, resulting in high binding affinities for target molecules. Previously, we designed a de novo peptide of helix-loop-helix structure that we termed a "microantibody." Using the microantibody as a library scaffold, we have constructed a phage-display library to successfully isolate molecular-targeting peptides against a cytokine receptor (granulocyte colony-stimulating factor receptor), a protein kinase (Aurora-A), and a ganglioside (GM1). Protocols in this article describe a general procedure for the library construction and the library screening.

Thermodynamics of single polyethylene and polybutylene glycols with hydrogen-bonding ends: A transition from looped to open conformations

NASA Astrophysics Data System (ADS)

Lee, Eunsang; Paul, Wolfgang

2018-02-01

A variety of linear polymer precursors with hydrogen bonding motifs at both ends enable us to design supramolecular polymer systems with tailored macroscopic properties including self-healing. In this study, we investigate thermodynamic properties of single polyethylene and polybutylene glycols with hydrogen bonding motifs. In this context, we first build a coarse-grained model of building blocks of the supramolecular polymer system based on all-atom molecular structures. The density of states of the single precursor is obtained using the stochastic approximation Monte Carlo method. Constructing canonical partition functions from the density of states, we find the transition from looped to open conformations at transition temperatures which are non-monotonously changing with an increasing degree of polymerization due to the competition between chain stiffness and loop-forming entropy penalty. In the complete range of chain length under investigation, a coexistence of the looped and open morphologies at the transition temperature is shown regardless of whether the transition is first-order-like or continuous. Polyethylene and polybutylene glycols show similar behavior in all the thermodynamic properties but the transition temperature of the more flexible polybutylene glycol is shown to change more gradually.

One-Loop Test of Quantum Black Holes in anti–de Sitter Space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, James T.; Pando Zayas, Leopoldo A.; Rathee, Vimal

Within 11-dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS4 black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes.

One-Loop Test of Quantum Black Holes in anti–de Sitter Space

DOE PAGES

Liu, James T.; Pando Zayas, Leopoldo A.; Rathee, Vimal; ...

2018-06-01

Within 11-dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS4 black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes.

One-Loop Test of Quantum Black Holes in anti-de Sitter Space

NASA Astrophysics Data System (ADS)

Liu, James T.; Pando Zayas, Leopoldo A.; Rathee, Vimal; Zhao, Wenli

2018-06-01

Within 11-dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS4 black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes.

One-Loop Test of Quantum Black Holes in anti-de Sitter Space.

PubMed

Liu, James T; Pando Zayas, Leopoldo A; Rathee, Vimal; Zhao, Wenli

2018-06-01

Within 11-dimensional supergravity we compute the logarithmic correction to the entropy of magnetically charged asymptotically AdS_{4} black holes with arbitrary horizon topology. We find perfect agreement with the expected microscopic result arising from the dual field theory computation of the topologically twisted index. Our result relies crucially on a particular limit to the extremal black hole case and clarifies some aspects of quantum corrections in asymptotically AdS spacetimes.

Homological Order in Three and Four dimensions: Wilson Algebra, Entanglement Entropy and Twist Defects

NASA Astrophysics Data System (ADS)

Roy, Abhishek; Chen, Xiao; Teo, Jeffrey

2013-03-01

We investigate homological orders in two, three and four dimensions by studying Zk toric code models on simplicial, cellular or in general differential complexes. The ground state degeneracy is obtained from Wilson loop and surface operators, and the homological intersection form. We compute these for a series of closed 3 and 4 dimensional manifolds and study the projective representations of mapping class groups (modular transformations). Braiding statistics between point and string excitations in (3+1)-dimensions or between dual string excitations in (4+1)-dimensions are topologically determined by the higher dimensional linking number, and can be understood by an effective topological field theory. An algorithm for calculating entanglemnent entropy of any bipartition of closed manifolds is presented, and its topological signature is completely characterized homologically. Extrinsic twist defects (or disclinations) are studied in 2,3 and 4 dimensions and are shown to carry exotic fusion and braiding properties. Simons Fellowship

The Size of the Internal Loop in DNA Hairpins Influences Their Targeting with Partially Complementary Strands

PubMed Central

2015-01-01

Targeting of noncanonical DNA structures, such as hairpin loops, may have significant diagnostic and therapeutic potential. Oligonucleotides can be used for binding to mRNA, forming a DNA/RNA hybrid duplex that inhibits translation. This kind of modulation of gene expression is called the antisense approach. In order to determine the best strategy to target a common structural motif in mRNA, we have designed a set of stem-loop DNA molecules with sequence: d(GCGCTnGTAAT5GTTACTnGCGC), where n = 1, 3, or 5, “T5” is an end loop of five thymines. We used a combination of calorimetric and spectroscopy techniques to determine the thermodynamics for the reaction of a set of hairpins containing internal loops with their respective partially complementary strands. Our aim was to determine if internal- and end-loops are promising regions for targeting with their corresponding complementary strands. Indeed, all targeting reactions were accompanied by negative changes in free energy, indicating that reactions proceed spontaneously. Further investigation showed that these negative free energy terms result from a net balance of unfavorable entropy and favorable enthalpy contributions. In particular, unfolding of hairpins and duplexes is accompanied by positive changes in heat capacity, which may be a result of exposure of hydrophobic groups to the solvent. This study provides a new method for the targeting of mRNA in order to control gene expression. PMID:25486129

Compensation effects and relation between the activation energy of spin transition and the hysteresis loop width for an iron(ii) complex.

PubMed

Bushuev, Mark B; Pishchur, Denis P; Nikolaenkova, Elena B; Krivopalov, Viktor P

2016-06-22

The enthalpy-entropy compensation was observed for the cooperative → spin transition (the phase is a mononuclear complex [FeL2](BF4)2, L is 4-(3,5-dimethyl-1H-pyrazol-1-yl)-2-(pyridin-2-yl)-6-methylpyrimidine). The physical origin of this effect is the fact that the → spin transition is the first order phase transition accompanied by noticeable variations in the Tonset↑, ΔH and ΔS values. Higher ΔH and ΔS values are correlated with higher Tonset↑ values. The higher the enthalpy and entropy of the spin transition, the wider the hysteresis loop. The kinetic compensation effect, i.e. a linear relationship between ln A and Ea, was observed for the → spin transition. Moreover, an isokinetic relationship was detected in this system: the Arrhenius lines (ln k vs. 1/T) obtained from magnetochemical data for different samples of the phase undergoing the → transition show a common point of intersection (Tiso = 490 ± 2 K, ln kiso = -6.0 ± 0.2). The validity of this conclusion was confirmed by the Exner-Linert statistical method. This means that the isokinetic relationship and the kinetic compensation effect (ln A vs. Ea) in this system are true ones. The existence of a true kinetic compensation effect is supported independently by the fact that the hysteresis loop width for the cooperative spin transition ↔ increases with increasing activation barrier height. Estimating the energy of excitations for the phase with Tiso ∼ 490 K yields wavenumbers of ca. 340 cm(-1) corresponding to the frequencies of the stretching vibrations of the Fe(LS)-N bonds, i.e. the bonds directly involved in the mechanism of the spin transition. This is the first observation of the kinetic compensation effect (ln A vs. Ea) and the isokinetic relationship for a cooperative spin crossover system showing thermal hysteresis. Our results provide the first experimental evidence that the higher the activation barrier for the spin transition, the wider the hysteresis loop for a series of related spin crossover systems.

Predicting loop–helix tertiary structural contacts in RNA pseudoknots

PubMed Central

Cao, Song; Giedroc, David P.; Chen, Shi-Jie

2010-01-01

Tertiary interactions between loops and helical stems play critical roles in the biological function of many RNA pseudoknots. However, quantitative predictions for RNA tertiary interactions remain elusive. Here we report a statistical mechanical model for the prediction of noncanonical loop–stem base-pairing interactions in RNA pseudoknots. Central to the model is the evaluation of the conformational entropy for the pseudoknotted folds with defined loop–stem tertiary structural contacts. We develop an RNA virtual bond-based conformational model (Vfold model), which permits a rigorous computation of the conformational entropy for a given fold that contains loop–stem tertiary contacts. With the entropy parameters predicted from the Vfold model and the energy parameters for the tertiary contacts as inserted parameters, we can then predict the RNA folding thermodynamics, from which we can extract the tertiary contact thermodynamic parameters from theory–experimental comparisons. These comparisons reveal a contact enthalpy (ΔH) of −14 kcal/mol and a contact entropy (ΔS) of −38 cal/mol/K for a protonated C+•(G–C) base triple at pH 7.0, and (ΔH = −7 kcal/mol, ΔS = −19 cal/mol/K) for an unprotonated base triple. Tests of the model for a series of pseudoknots show good theory–experiment agreement. Based on the extracted energy parameters for the tertiary structural contacts, the model enables predictions for the structure, stability, and folding pathways for RNA pseudoknots with known or postulated loop–stem tertiary contacts from the nucleotide sequence alone. PMID:20100813

Effects of ordinary and superconducting cosmic strings on primordial nucleosynthesis

NASA Technical Reports Server (NTRS)

Hodges, Hardy M.; Turner, Michael S.

1988-01-01

A precise calculation is done of the primordial nucleosynthesis constraint on the energy per length of ordinary and superconducting cosmic strings. A general formula is provided for the constraint on the string tension for ordinary strings. Using the current values for the various parameters that describe the evolution of loops, the constraint for ordinary strings is G mu less than 2.2 x 10 to the minus 5 power. Our constraint is weaker than previously quoted limits by a factor of approximately 5. For superconducting loops, with currents generated by primordial magnetic fields, the constraint can be less or more stringent than this limit, depending on the strength of the magnetic field. It is also found in this case that there is a negligible amount of entropy production if the electromagnetic radiation from strings thermalizes with the radiation background.

Area law from loop quantum gravity

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Hung, Ling-Yan; Marcianò, Antonino; Zhang, Mingyi

2018-03-01

We explore the constraints following from requiring the area law in the entanglement entropy in the context of loop quantum gravity. We find a unique solution to the single-link wave function in the large j limit, believed to be appropriate in the semiclassical limit. We then generalize our considerations to multilink coherent states, and find that the area law is preserved very generically using our single-link wave function as a building block. Finally, we develop the framework that generates families of multilink states that preserve the area law while avoiding macroscopic entanglement, the space-time analogue of "Schrödinger's cat." We note that these states, defined on a given set of graphs, are the ground states of some local Hamiltonian that can be constructed explicitly. This can potentially shed light on the construction of the appropriate Hamiltonian constraints in the LQG framework.

Fluorescence Competition Assay Measurements of Free Energy Changes for RNA Pseudoknots†

PubMed Central

2009-01-01

RNA pseudoknots have important functions, and thermodynamic stability is a key to predicting pseudoknots in RNA sequences and to understanding their functions. Traditional methods, such as UV melting and differential scanning calorimetry, for measuring RNA thermodynamics are restricted to temperature ranges around the melting temperature for a pseudoknot. Here, we report RNA pseudoknot free energy changes at 37 °C measured by fluorescence competition assays. Sequence-dependent studies for the loop 1−stem 2 region reveal (1) the individual nearest-neighbor hydrogen bonding (INN-HB) model provides a reasonable estimate for the free energy change when a Watson−Crick base pair in stem 2 is changed, (2) the loop entropy can be estimated by a statistical polymer model, although some penalty for certain loop sequences is necessary, and (3) tertiary interactions can significantly stabilize pseudoknots and extending the length of stem 2 may alter tertiary interactions such that the INN-HB model does not predict the net effect of adding a base pair. The results can inform writing of algorithms for predicting and/or designing RNA secondary structures. PMID:19921809

Entanglement in Nonunitary Quantum Critical Spin Chains

NASA Astrophysics Data System (ADS)

Couvreur, Romain; Jacobsen, Jesper Lykke; Saleur, Hubert

2017-07-01

Entanglement entropy has proven invaluable to our understanding of quantum criticality. It is natural to try to extend the concept to "nonunitary quantum mechanics," which has seen growing interest from areas as diverse as open quantum systems, noninteracting electronic disordered systems, or nonunitary conformal field theory (CFT). We propose and investigate such an extension here, by focusing on the case of one-dimensional quantum group symmetric or supergroup symmetric spin chains. We show that the consideration of left and right eigenstates combined with appropriate definitions of the trace leads to a natural definition of Rényi entropies in a large variety of models. We interpret this definition geometrically in terms of related loop models and calculate the corresponding scaling in the conformal case. This allows us to distinguish the role of the central charge and effective central charge in rational minimal models of CFT, and to define an effective central charge in other, less well-understood cases. The example of the s l (2 |1 ) alternating spin chain for percolation is discussed in detail.

System Mass Variation and Entropy Generation in 100k We Closed-Brayton-Cycle Space Power Systems

NASA Technical Reports Server (NTRS)

Barrett, Michael J.; Reid, Bryan M.

2004-01-01

State-of-the-art closed-Brayton-cycle (CBC) space power systems were modeled to study performance trends in a trade space characteristic of interplanetary orbiters. For working-fluid molar masses of 48.6, 39.9, and 11.9 kg/kmol, peak system pressures of 1.38 and 3.0 MPa and compressor pressure ratios ranging from 1.6 to 2.4, total system masses were estimated. System mass increased as peak operating pressure increased for all compressor pressure ratios and molar mass values examined. Minimum mass point comparison between 72 percent He at 1.38 MPa peak and 94 percent He at 3.0 MPa peak showed an increase in system mass of 14 percent. Converter flow loop entropy generation rates were calculated for 1.38 and 3.0 MPa peak pressure cases. Physical system behavior was approximated using a pedigreed NASA Glenn modeling code, Closed Cycle Engine Program (CCEP), which included realistic performance prediction for heat exchangers, radiators and turbomachinery.

System Mass Variation and Entropy Generation in 100-kWe Closed-Brayton-Cycle Space Power Systems

NASA Technical Reports Server (NTRS)

Barrett, Michael J.; Reid, Bryan M.

2004-01-01

State-of-the-art closed-Brayton-cycle (CBC) space power systems were modeled to study performance trends in a trade space characteristic of interplanetary orbiters. For working-fluid molar masses of 48.6, 39.9, and 11.9 kg/kmol, peak system pressures of 1.38 and 3.0 MPa and compressor pressure ratios ranging from 1.6 to 2.4, total system masses were estimated. System mass increased as peak operating pressure increased for all compressor pressure ratios and molar mass values examined. Minimum mass point comparison between 72 percent He at 1.38 MPa peak and 94 percent He at 3.0 MPa peak showed an increase in system mass of 14 percent. Converter flow loop entropy generation rates were calculated for 1.38 and 3.0 MPa peak pressure cases. Physical system behavior was approximated using a pedigreed NASA Glenn modeling code, Closed Cycle Engine Program (CCEP), which included realistic performance prediction for heat exchangers, radiators and turbomachinery.

Second Law of Thermodynamics Applied to Metabolic Networks

NASA Technical Reports Server (NTRS)

Nigam, R.; Liang, S.

2003-01-01

We present a simple algorithm based on linear programming, that combines Kirchoff's flux and potential laws and applies them to metabolic networks to predict thermodynamically feasible reaction fluxes. These law's represent mass conservation and energy feasibility that are widely used in electrical circuit analysis. Formulating the Kirchoff's potential law around a reaction loop in terms of the null space of the stoichiometric matrix leads to a simple representation of the law of entropy that can be readily incorporated into the traditional flux balance analysis without resorting to non-linear optimization. Our technique is new as it can easily check the fluxes got by applying flux balance analysis for thermodynamic feasibility and modify them if they are infeasible so that they satisfy the law of entropy. We illustrate our method by applying it to the network dealing with the central metabolism of Escherichia coli. Due to its simplicity this algorithm will be useful in studying large scale complex metabolic networks in the cell of different organisms.

Path-integral representation for the relativistic particle propagators and BFV quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fradkin, E.S.; Gitman, D.M.

1991-11-15

The path-integral representations for the propagators of scalar and spinor fields in an external electromagnetic field are derived. The Hamiltonian form of such expressions can be interpreted in the sense of Batalin-Fradkin-Vilkovisky quantization of one-particle theory. The Lagrangian representation as derived allows one to extract in a natural way the expressions for the corresponding gauge-invariant (reparametrization- and supergauge-invariant) actions for pointlike scalar and spinning particles. At the same time, the measure and ranges of integrations, admissible gauge conditions, and boundary conditions can be exactly established.

Stability properties of a general class of nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Gléria, I. M.; Figueiredo, A.; Rocha Filho, T. M.

2001-05-01

We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format.

Vfold: a web server for RNA structure and folding thermodynamics prediction.

PubMed

Xu, Xiaojun; Zhao, Peinan; Chen, Shi-Jie

2014-01-01

The ever increasing discovery of non-coding RNAs leads to unprecedented demand for the accurate modeling of RNA folding, including the predictions of two-dimensional (base pair) and three-dimensional all-atom structures and folding stabilities. Accurate modeling of RNA structure and stability has far-reaching impact on our understanding of RNA functions in human health and our ability to design RNA-based therapeutic strategies. The Vfold server offers a web interface to predict (a) RNA two-dimensional structure from the nucleotide sequence, (b) three-dimensional structure from the two-dimensional structure and the sequence, and (c) folding thermodynamics (heat capacity melting curve) from the sequence. To predict the two-dimensional structure (base pairs), the server generates an ensemble of structures, including loop structures with the different intra-loop mismatches, and evaluates the free energies using the experimental parameters for the base stacks and the loop entropy parameters given by a coarse-grained RNA folding model (the Vfold model) for the loops. To predict the three-dimensional structure, the server assembles the motif scaffolds using structure templates extracted from the known PDB structures and refines the structure using all-atom energy minimization. The Vfold-based web server provides a user friendly tool for the prediction of RNA structure and stability. The web server and the source codes are freely accessible for public use at "http://rna.physics.missouri.edu".

Methods for calculating the absolute entropy and free energy of biological systems based on ideas from polymer physics.

PubMed

Meirovitch, Hagai

2010-01-01

The commonly used simulation techniques, Metropolis Monte Carlo (MC) and molecular dynamics (MD) are of a dynamical type which enables one to sample system configurations i correctly with the Boltzmann probability, P(i)(B), while the value of P(i)(B) is not provided directly; therefore, it is difficult to obtain the absolute entropy, S approximately -ln P(i)(B), and the Helmholtz free energy, F. With a different simulation approach developed in polymer physics, a chain is grown step-by-step with transition probabilities (TPs), and thus their product is the value of the construction probability; therefore, the entropy is known. Because all exact simulation methods are equivalent, i.e. they lead to the same averages and fluctuations of physical properties, one can treat an MC or MD sample as if its members have rather been generated step-by-step. Thus, each configuration i of the sample can be reconstructed (from nothing) by calculating the TPs with which it could have been constructed. This idea applies also to bulk systems such as fluids or magnets. This approach has led earlier to the "local states" (LS) and the "hypothetical scanning" (HS) methods, which are approximate in nature. A recent development is the hypothetical scanning Monte Carlo (HSMC) (or molecular dynamics, HSMD) method which is based on stochastic TPs where all interactions are taken into account. In this respect, HSMC(D) can be viewed as exact and the only approximation involved is due to insufficient MC(MD) sampling for calculating the TPs. The validity of HSMC has been established by applying it first to liquid argon, TIP3P water, self-avoiding walks (SAW), and polyglycine models, where the results for F were found to agree with those obtained by other methods. Subsequently, HSMD was applied to mobile loops of the enzymes porcine pancreatic alpha-amylase and acetylcholinesterase in explicit water, where the difference in F between the bound and free states of the loop was calculated. Currently, HSMD is being extended for calculating the absolute and relative free energies of ligand-enzyme binding. We describe the whole approach and discuss future directions. 2009 John Wiley & Sons, Ltd.

Mrst '96: Current Ideas in Theoretical Physics - Proceedings of the Eighteenth Annual Montréal-Rochester-Syracuse-Toronto Meeting

NASA Astrophysics Data System (ADS)

O'Donnell, Patrick J.; Smith, Brian Hendee

1996-11-01

The Table of Contents for the full book PDF is as follows: * Preface * Roberto Mendel, An Appreciaton * The Infamous Coulomb Gauge * Renormalized Path Integral in Quantum Mechanics * New Analysis of the Divergence of Perturbation Theory * The Last of the Soluble Two Dimensional Field Theories? * Rb and Heavy Quark Mixing * Rb Problem: Loop Contributions and Supersymmetry * QCD Radiative Effects in Inclusive Hadronic B Decays * CP-Violating Dipole Moments of Quarks in the Kobayashi-Maskawa Model * Hints of Dynamical Symmetry Breaking? * Pi Pi Scattering in an Effective Chiral Lagrangian * Pion-Resonance Parameters from QCD Sum Rules * Higgs Theorem, Effective Action, and its Gauge Invariance * SUSY and the Decay H_2^0 to gg * Effective Higgs-to-Light Quark Coupling Induced by Heavy Quark Loops * Heavy Charged Lepton Production in Superstring Inspired E6 Models * The Elastic Properties of a Flat Crystalline Membrane * Gauge Dependence of Topological Observables in Chern-Simons Theory * Entanglement Entropy From Edge States * A Simple General Treatment of Flavor Oscillations * From Schrödinger to Maupertuis: Least Action Principles from Quantum Mechanics * The Matrix Method for Multi-Loop Feynman Integrals * Simplification in QCD and Electroweak Calculations * Programme * List of Participants

Thermodynamics of BTZ black holes in gravity’s rainbow

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa

2017-05-01

In this paper, we deform the thermodynamics of a BTZ black hole from rainbow functions in gravity’s rainbow. The rainbow functions will be motivated from the results in loop quantum gravity and noncommutative geometry. It will be observed that the thermodynamics gets deformed due to these rainbow functions, indicating the existence of a remnant. However, the Gibbs free energy does not get deformed due to these rainbow functions, and so the critical behavior from Gibbs does not change by this deformation. This is because the deformation in the entropy cancels out the temperature deformation.

Image Science Research for Speckle-based LADAR (Speckle Research for 3D Imaging LADAR)

DTIC Science & Technology

2008-04-03

INVARIANT + FERGUS, TORRALBA, AND FREEMAN. MIT-CSAIL-TR-2006-058 MAP DETECTOR PATTERN FOR EACH POINT IN OBJECT SPACE DEBLURRING PROBLEM IMPULSE RESPONSE...GENERALIZED THEORY FOR THE LOGARITHMIC ASPHERE ( )( ) it e φ ρρ −= IMPULSE RESPONSE (PSF) 2 2 2 2 0 0 22 2( ) 2 2 0 2 2 2 2 2 2 0 0 2 ( ; ) 2 ( ) i s i i t R...ascent; γ=1, Burch, Skilling, Gull; Loops needed Noise deviation Area of PSF New parameter L σ A γ COMPARISON OF MAXIMUM ENTROPY METHODS † † W. CHI

Multiscale Persistent Functions for Biomolecular Structure Characterization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, Kelin; Li, Zhiming; Mu, Lin

Here in this paper, we introduce multiscale persistent functions for biomolecular structure characterization. The essential idea is to combine our multiscale rigidity functions (MRFs) with persistent homology analysis, so as to construct a series of multiscale persistent functions, particularly multiscale persistent entropies, for structure characterization. To clarify the fundamental idea of our method, the multiscale persistent entropy (MPE) model is discussed in great detail. Mathematically, unlike the previous persistent entropy (Chintakunta et al. in Pattern Recognit 48(2):391–401, 2015; Merelli et al. in Entropy 17(10):6872–6892, 2015; Rucco et al. in: Proceedings of ECCS 2014, Springer, pp 117–128, 2016), a special resolutionmore » parameter is incorporated into our model. Various scales can be achieved by tuning its value. Physically, our MPE can be used in conformational entropy evaluation. More specifically, it is found that our method incorporates in it a natural classification scheme. This is achieved through a density filtration of an MRF built from angular distributions. To further validate our model, a systematical comparison with the traditional entropy evaluation model is done. Additionally, it is found that our model is able to preserve the intrinsic topological features of biomolecular data much better than traditional approaches, particularly for resolutions in the intermediate range. Moreover, by comparing with traditional entropies from various grid sizes, bond angle-based methods and a persistent homology-based support vector machine method (Cang et al. in Mol Based Math Biol 3:140–162, 2015), we find that our MPE method gives the best results in terms of average true positive rate in a classic protein structure classification test. More interestingly, all-alpha and all-beta protein classes can be clearly separated from each other with zero error only in our model. Finally, a special protein structure index (PSI) is proposed, for the first time, to describe the “regularity” of protein structures. Basically, a protein structure is deemed as regular if it has a consistent and orderly configuration. Our PSI model is tested on a database of 110 proteins; we find that structures with larger portions of loops and intrinsically disorder regions are always associated with larger PSI, meaning an irregular configuration, while proteins with larger portions of secondary structures, i.e., alpha-helix or beta-sheet, have smaller PSI. Essentially, PSI can be used to describe the “regularity” information in any systems.« less

Universality of Generalized Parton Distributions in Light-Front Holographic QCD

NASA Astrophysics Data System (ADS)

de Téramond, Guy F.; Liu, Tianbo; Sufian, Raza Sabbir; Dosch, Hans Günter; Brodsky, Stanley J.; Deur, Alexandre; Hlfhs Collaboration

2018-05-01

The structure of generalized parton distributions is determined from light-front holographic QCD up to a universal reparametrization function w (x ) which incorporates Regge behavior at small x and inclusive counting rules at x →1 . A simple ansatz for w (x ) that fulfills these physics constraints with a single-parameter results in precise descriptions of both the nucleon and the pion quark distribution functions in comparison with global fits. The analytic structure of the amplitudes leads to a connection with the Veneziano model and hence to a nontrivial connection with Regge theory and the hadron spectrum.

Universality of Generalized Parton Distributions in Light-Front Holographic QCD.

PubMed

de Téramond, Guy F; Liu, Tianbo; Sufian, Raza Sabbir; Dosch, Hans Günter; Brodsky, Stanley J; Deur, Alexandre

2018-05-04

The structure of generalized parton distributions is determined from light-front holographic QCD up to a universal reparametrization function w(x) which incorporates Regge behavior at small x and inclusive counting rules at x→1. A simple ansatz for w(x) that fulfills these physics constraints with a single-parameter results in precise descriptions of both the nucleon and the pion quark distribution functions in comparison with global fits. The analytic structure of the amplitudes leads to a connection with the Veneziano model and hence to a nontrivial connection with Regge theory and the hadron spectrum.

Experimental validation of the predicted binding site of Escherichia coli K1 outer membrane protein A to human brain microvascular endothelial cells: identification of critical mutations that prevent E. coli meningitis.

PubMed

Pascal, Tod A; Abrol, Ravinder; Mittal, Rahul; Wang, Ying; Prasadarao, Nemani V; Goddard, William A

2010-11-26

Escherichia coli K1, the most common cause of meningitis in neonates, has been shown to interact with GlcNAc1-4GlcNAc epitopes of Ecgp96 on human brain microvascular endothelial cells (HBMECs) via OmpA (outer membrane protein A). However, the precise domains of extracellular loops of OmpA interacting with the chitobiose epitopes have not been elucidated. We report the loop-barrel model of these OmpA interactions with the carbohydrate moieties of Ecgp96 predicted from molecular modeling. To test this model experimentally, we generated E. coli K1 strains expressing OmpA with mutations of residues predicted to be critical for interaction with the HBMEC and tested E. coli invasion efficiency. For these same mutations, we predicted the interaction free energies (including explicit calculation of the entropy) from molecular dynamics (MD), finding excellent correlation (R(2) = 90%) with experimental invasion efficiency. Particularly important is that mutating specific residues in loops 1, 2, and 4 to alanines resulted in significant inhibition of E. coli K1 invasion in HBMECs, which is consistent with the complete lack of binding found in the MD simulations for these two cases. These studies suggest that inhibition of the interactions of these residues of Loop 1, 2, and 4 with Ecgp96 could provide a therapeutic strategy to prevent neonatal meningitis due to E. coli K1.

BOOK REVIEW: Modern Canonical Quantum General Relativity

NASA Astrophysics Data System (ADS)

Kiefer, Claus

2008-06-01

The open problem of constructing a consistent and experimentally tested quantum theory of the gravitational field has its place at the heart of fundamental physics. The main approaches can be roughly divided into two classes: either one seeks a unified quantum framework of all interactions or one starts with a direct quantization of general relativity. In the first class, string theory (M-theory) is the only known example. In the second class, one can make an additional methodological distinction: while covariant approaches such as path-integral quantization use the four-dimensional metric as an essential ingredient of their formalism, canonical approaches start with a foliation of spacetime into spacelike hypersurfaces in order to arrive at a Hamiltonian formulation. The present book is devoted to one of the canonical approaches—loop quantum gravity. It is named modern canonical quantum general relativity by the author because it uses connections and holonomies as central variables, which are analogous to the variables used in Yang Mills theories. In fact, the canonically conjugate variables are a holonomy of a connection and the flux of a non-Abelian electric field. This has to be contrasted with the older geometrodynamical approach in which the metric of three-dimensional space and the second fundamental form are the fundamental entities, an approach which is still actively being pursued. It is the author's ambition to present loop quantum gravity in a way in which every step is formulated in a mathematically rigorous form. In his own words: 'loop quantum gravity is an attempt to construct a mathematically rigorous, background-independent, non-perturbative quantum field theory of Lorentzian general relativity and all known matter in four spacetime dimensions, not more and not less'. The formal Leitmotiv of loop quantum gravity is background independence. Non-gravitational theories are usually quantized on a given non-dynamical background. In contrast, due to the geometrical nature of gravity, no such background exists in quantum gravity. Instead, the notion of a background is supposed to emerge a posteriori as an approximate notion from quantum states of geometry. As a consequence, the standard ultraviolet divergences of quantum field theory do not show up because there is no limit of Δx → 0 to be taken in a given spacetime. On the other hand, it is open whether the theory is free of any type of divergences and anomalies. A central feature of any canonical approach, independent of the choice of variables, is the existence of constraints. In geometrodynamics, these are the Hamiltonian and diffeomorphism constraints. They also hold in loop quantum gravity, but are supplemented there by the Gauss constraint, which emerges due to the use of triads in the formalism. These constraints capture all the physics of the quantum theory because no spacetime is present anymore (analogous to the absence of trajectories in quantum mechanics), so no additional equations of motion are needed. This book presents a careful and comprehensive discussion of these constraints. In particular, the constraint algebra is calculated in a transparent and explicit way. The author makes the important assumption that a Hilbert-space structure is still needed on the fundamental level of quantum gravity. In ordinary quantum theory, such a structure is needed for the probability interpretation, in particular for the conservation of probability with respect to external time. It is thus interesting to see how far this concept can be extrapolated into the timeless realm of quantum gravity. On the kinematical level, that is, before the constraints are imposed, an essentially unique Hilbert space can be constructed in terms of spin-network states. Potentially problematic features are the implementation of the diffeomorphism and Hamiltonian constraints. The Hilbert space Hdiff defined on the diffeomorphism subspace can throw states out of the kinematical Hilbert space and is thus not contained in it. Moreover, the Hamiltonian constraint does not seem to preserve Hdiff, so its implementation remains open. To avoid some of these problems, the author proposes his 'master constraint programme' in which the infinitely many local Hamiltonian constraints are combined into one master constraint. This is a subject of his current research. With regard to this situation, it is not surprising that the main results in loop quantum gravity are found on the kinematical level. An especially important feature are the discrete spectra of geometric operators such as the area operator. This quantifies the earlier heuristic ideas about a discreteness at the Planck scale. The hope is that these results survive the consistent implementation of all constraints. The status of loop quantum gravity is concisely and competently summarized in this volume, whose author is himself one of the pioneers of this approach. What is the relation of this book to the other monograph on loop quantum gravity, written by Carlo Rovelli and published in 2004 under the title Quantum Gravity with the same company? In the words of the present author: 'the two books are complementary in the sense that they can be regarded almost as volume I ('introduction and conceptual framework') and volume II ('mathematical framework and applications') of a general presentation of quantum general relativity in general and loop quantum gravity in particular'. In fact, the present volume gives a complete and self-contained presentation of the required mathematics, especially on the approximately 200 pages of chapters 18 33. As for the physical applications, the main topic is the microscopic derivation of the black-hole entropy. This is presented in a clear and detailed form. Employing the concept of an isolated horizon (a local generalization of an event horizon), the counting of surface states gives an entropy proportional to the horizon area. It also contains the Barbero Immirzi parameter β, which is a free parameter of the theory. Demanding, on the other hand, that the entropy be equal to the Bekenstein Hawking entropy would fix this parameter. Other applications such as loop quantum cosmology are only briefly touched upon. Since loop quantum gravity is a very active field of research, the author warns that the present book can at best be seen as a snapshot. Part of the overall picture may thus in the future be subject to modifications. For example, recent work by the author using a concept of dust time is not yet covered here. Nevertheless, I expect that this volume will continue to serve as a valuable introduction and reference book. It is essential reading for everyone working on loop quantum gravity.

Normal Mode Analysis in Zeolites: Toward an Efficient Calculation of Adsorption Entropies.

PubMed

De Moor, Bart A; Ghysels, An; Reyniers, Marie-Françoise; Van Speybroeck, Veronique; Waroquier, Michel; Marin, Guy B

2011-04-12

An efficient procedure for normal-mode analysis of extended systems, such as zeolites, is developed and illustrated for the physisorption and chemisorption of n-octane and isobutene in H-ZSM-22 and H-FAU using periodic DFT calculations employing the Vienna Ab Initio Simulation Package. Physisorption and chemisorption entropies resulting from partial Hessian vibrational analysis (PHVA) differ at most 10 J mol(-1) K(-1) from those resulting from full Hessian vibrational analysis, even for PHVA schemes in which only a very limited number of atoms are considered free. To acquire a well-conditioned Hessian, much tighter optimization criteria than commonly used for electronic energy calculations in zeolites are required, i.e., at least an energy cutoff of 400 eV, maximum force of 0.02 eV/Å, and self-consistent field loop convergence criteria of 10(-8) eV. For loosely bonded complexes the mobile adsorbate method is applied, in which frequency contributions originating from translational or rotational motions of the adsorbate are removed from the total partition function and replaced by free translational and/or rotational contributions. The frequencies corresponding with these translational and rotational modes can be selected unambiguously based on a mobile block Hessian-PHVA calculation, allowing the prediction of physisorption entropies within an accuracy of 10-15 J mol(-1) K(-1) as compared to experimental values. The approach presented in this study is useful for studies on other extended catalytic systems.

Relative stability of the open and closed conformations of the active site loop of streptavidin

NASA Astrophysics Data System (ADS)

Ignacio J., General; Meirovitch, Hagai

2011-01-01

The eight-residue surface loop, 45-52 (Ser, Ala, Val, Gly, Asn, Ala, Glu, Ser), of the homotetrameric protein streptavidin has a "closed" conformation in the streptavidin-biotin complex, where the corresponding binding affinity is one of the strongest found in nature (ΔG ˜ -18 kcal/mol). However, in most of the crystal structures of apo (unbound) streptavidin, the loop conformation is "open" and typically exhibits partial disorder and high B-factors. Thus, it is plausible to assume that the loop structure is changed from open to closed upon binding of biotin, and the corresponding difference in free energy, ΔF = Fopen - Fclosed in the unbound protein, should therefore be considered in the total absolute free energy of binding. ΔF (which has generally been neglected) is calculated here using our "hypothetical scanning molecular-dynamics" (HSMD) method. We use a protein model in which only the atoms closest to the loop are considered (the "template") and they are fixed in the x-ray coordinates of the free protein; the x-ray conformation of the closed loop is attached to the same (unbound) template and both systems are capped with the same sphere of TIP3P water. Using the force field of the assisted model building with energy refinement (AMBER), we carry out two separate MD simulations (at temperature T = 300 K), starting from the open and closed conformations, where only the atoms of the loop and water are allowed to move (the template-water and template-loop interactions are considered). The absolute Fopen and Fclosed (of loop + water) are calculated from these trajectories, where the loop and water contributions are obtained by HSMD and a thermodynamic integration (TI) process, respectively. The combined HSMD-TI procedure leads to total (loop + water) ΔF = -27.1 ± 2.0 kcal/mol, where the entropy TΔS constitutes 34% of ΔF, meaning that the effect of S is significant and should not be ignored. Also, ΔS is positive, in accord with the high flexibility of the open loop observed in crystal structures, while the energy ΔE is unexpectedly negative, thus also adding to the stability of the open loop. The loop and the 250 capped water molecules are the largest system studied thus far, which constitutes a test for the efficiency of HSMD-TI; this efficiency and technical issues related to the implementation of the method are also discussed. Finally, the result for ΔF is a prediction that will be considered in the calculation of the absolute free energy of binding of biotin to streptavidin, which constitutes our next project.

Book Review:

NASA Astrophysics Data System (ADS)

Kiefer, C.

2005-10-01

The most difficult unsolved problem in fundamental theoretical physics is the consistent implementation of the gravitational interaction into a quantum framework, which would lead to a theory of quantum gravity. Although a final answer is still pending, several promising attempts do exist. Despite the general title, this book is about one of them - loop quantum gravity. This approach proceeds from the idea that a direct quantization of Einstein's theory of general relativity is possible. In contrast to string theory, it presupposes that the unification of all interactions is not needed as a prerequisite for quantum gravity. Usually one divides theories of quantum general relativity into covariant and canonical approaches. Covariant theories employ four-dimensional concepts in its formulation, one example being the path integral approach. Canonical theories start from a classical Hamiltonian version of the theory in which spacetime is foliated into spacelike hypersurfaces. Loop quantum gravity is a variant of the canonical approach, the oldest being quantum geometrodynamics where the fundamental configuration variable is the three-metric. Loop quantum gravity has developed from a new choice of canonical variables introduced by Abhay Ashtekar in 1986, the new configuration variable being a connection defined on a three-manifold. Instead of the connection itself, the loop approach employs a non-local version in which the connection is integrated over closed loops. This is similar to the Wilson loops used in gauge theories. Carlo Rovelli is one of the pioneers of loop quantum gravity which he started to develop with Lee Smolin in two papers written in 1988 and 1990. In his book, he presents a comprehensive and competent overview of this approach and provides at the same time the necessary technical background in order to make the treatment self-contained. In fact, half of the book is devoted to 'preparations' giving a detailed account of Hamiltonian mechanics, quantum mechanics, general relativity and other topics. According to the level of the reader, this part can be skipped or studied as interesting material on its own. The penetrating theme of the whole book (its leitmotiv) is background independence. In non-gravitational theories, dynamical fields are formulated on a fixed background spacetime that plays the role of an absolute structure in the theory. In general relativity, on the other hand, there is no background structure - all fields are dynamical. This was a confusing point already during the development of general relativity and led Albert Einstein in 1913 erroneously to give up general covariance before recognizing his error and presenting his final correct field equations that are of course covariant. This story is instructive, circling around the famous 'hole problem', and is told in detail in Rovelli's book. Its solution is that points on a bare manifold do not make sense in physics; everything, including the gravitational field, is dragged around by a diffeomorphism - there is just no background available, only the fields exist. In loop quantum gravity, physical space (called 'quantum geometry') itself is formed by loop-like quantum states: a suitable orthonormal basis is provided by spin-network states (a spin-network is a graph with edges and nodes, where spins are assigned to the edges), and the quantum geometry is a superposition of such states. Time and space in the usual sense have disappeared. In the second half of his book, Rovelli discusses at length the major successes of this approach. First of all, the formalism yields a unique kinematical Hilbert space for the quantum states obeying the Gauss and diffeomorphism constraints. The situation with the Hamiltonian constraint is more subtle. The need for a Hilbert-space structure in quantum gravity is, however, not discussed. After all, the Hilbert-space structure in quantum mechanics is tied to the presence of an external time and the conservation of probability with respect to this external time. But in quantum gravity there is no background structure, in particular no external time. Secondly, there exist two important operators that are connected, respectively, with area and volume in the classical limit. These operators have a discrete spectrum and thus provide elementary 'quanta' of area and volume. This gives a vague hint of a discrete structure at the Planck scale, about which there were speculations for many decades. In spite of these promising results, loop quantum gravity is still far away from a physical theory. This is also reflected in this volume where the technical treatment prevails and where physical applications are relegated to about 20 pages. These applications deal with quantum cosmology and black holes. The part on loop quantum cosmology summarizes briefly recent results about a possible singularity avoidance and a new mechanism for inflation. These results are not derived from loop quantum gravity but from imposing the discrete structure of the full theory directly on the quantum cosmological models. The part on black holes discusses the derivation of the Bekenstein-Hawking entropy from counting the number of relevant spin-network states. Since the theory contains a free parameter (the 'Barbero-Immirzi parameter'), the best one can do is to determine this parameter by demanding that the result be the Bekenstein-Hawking entropy. The book does not yet contain the results of recent papers, published in 2004, that correct the earlier entropy calculations presented here. From the new value of the Barbero-Immirzi parameter, the appealing connection with quasi-normal modes, as discussed in the book, may be lost. The book concludes with a brief discussion of the major open issues. Among these are the following: a well-defined and physically sensible semiclassical limit, the precise form of the Hamiltonian, the role of unification (most of the work in loop quantum gravity deals only with pure gravity) and, last but not least, the issue of quantitative and testable predictions. Whether loop quantum gravity will become a physical theory is not clear. Nor is this clear for string theory or any other approach. However, loop quantum gravity provides a fascinating line of research and has much conceptual appeal. The present volume gives both an introduction and a review of this approach, making it suitable for advanced students as well as experts. It is certainly of interest for the readers of Classical and Quantum Gravity.

Generic isolated horizons in loop quantum gravity

NASA Astrophysics Data System (ADS)

Beetle, Christopher; Engle, Jonathan

2010-12-01

Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the literature and has since been extended to axisymmetry. This paper extends the quantum theory to horizons of arbitrary shape. Surprisingly, the Hilbert space obtained by quantizing the full phase space of all generic horizons with a fixed area is identical to that originally found in spherical symmetry. The entropy of a large horizon remains one-quarter its area, with the Barbero-Immirzi parameter retaining its value from symmetric analyses. These results suggest a reinterpretation of the intrinsic quantum geometry of the horizon surface.

Light-quark, heavy-quark systems: An update

NASA Astrophysics Data System (ADS)

Grinstein, B.

1993-06-01

We review many of the recently developed applications of Heavy Quark Effective Theory techniques. After a brief update on Luke's theorem, we describe striking relations between heavy baryon form factors, and how to use them to estimate the accuracy of the extraction of (vert bar)V(sub cb)(vert bar). We discuss factorization and compare with experiment. An elementary presentation, with sample applications, of reparametrization invariance comes next. The final and most extensive chapter in this review deals with phenomenological lagrangians that incorporate heavy-quark spin-flavor as well as light quark chiral symmetries. We compile many interesting results and discuss the validity of the calculations.

Random SU(2) invariant tensors

NASA Astrophysics Data System (ADS)

Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei

2018-04-01

SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n  =  4. In this paper, we show that for n  >  4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.

Generalized ensemble method applied to study systems with strong first order transitions

DOE PAGES

Malolepsza, E.; Kim, J.; Keyes, T.

2015-09-28

At strong first-order phase transitions, the entropy versus energy or, at constant pressure, enthalpy, exhibits convex behavior, and the statistical temperature curve correspondingly exhibits an S-loop or back-bending. In the canonical and isothermal-isobaric ensembles, with temperature as the control variable, the probability density functions become bimodal with peaks localized outside of the S-loop region. Inside, states are unstable, and as a result simulation of equilibrium phase coexistence becomes impossible. To overcome this problem, a method was proposed by Kim, Keyes and Straub, where optimally designed generalized ensemble sampling was combined with replica exchange, and denoted generalized replica exchange method (gREM).more » This new technique uses parametrized effective sampling weights that lead to a unimodal energy distribution, transforming unstable states into stable ones. In the present study, the gREM, originally developed as a Monte Carlo algorithm, was implemented to work with molecular dynamics in an isobaric ensemble and coded into LAMMPS, a highly optimized open source molecular simulation package. Lastly, the method is illustrated in a study of the very strong solid/liquid transition in water.« less

A system architecture for online data interpretation and reduction in fluorescence microscopy

NASA Astrophysics Data System (ADS)

Röder, Thorsten; Geisbauer, Matthias; Chen, Yang; Knoll, Alois; Uhl, Rainer

2010-01-01

In this paper we present a high-throughput sample screening system that enables real-time data analysis and reduction for live cell analysis using fluorescence microscopy. We propose a novel system architecture capable of analyzing a large amount of samples during the experiment and thus greatly minimizing the post-analysis phase that is the common practice today. By utilizing data reduction algorithms, relevant information of the target cells is extracted from the online collected data stream, and then used to adjust the experiment parameters in real-time, allowing the system to dynamically react on changing sample properties and to control the microscope setup accordingly. The proposed system consists of an integrated DSP-FPGA hybrid solution to ensure the required real-time constraints, to execute efficiently the underlying computer vision algorithms and to close the perception-action loop. We demonstrate our approach by addressing the selective imaging of cells with a particular combination of markers. With this novel closed-loop system the amount of superfluous collected data is minimized, while at the same time the information entropy increases.

Generalized ensemble method applied to study systems with strong first order transitions

NASA Astrophysics Data System (ADS)

Małolepsza, E.; Kim, J.; Keyes, T.

2015-09-01

At strong first-order phase transitions, the entropy versus energy or, at constant pressure, enthalpy, exhibits convex behavior, and the statistical temperature curve correspondingly exhibits an S-loop or back-bending. In the canonical and isothermal-isobaric ensembles, with temperature as the control variable, the probability density functions become bimodal with peaks localized outside of the S-loop region. Inside, states are unstable, and as a result simulation of equilibrium phase coexistence becomes impossible. To overcome this problem, a method was proposed by Kim, Keyes and Straub [1], where optimally designed generalized ensemble sampling was combined with replica exchange, and denoted generalized replica exchange method (gREM). This new technique uses parametrized effective sampling weights that lead to a unimodal energy distribution, transforming unstable states into stable ones. In the present study, the gREM, originally developed as a Monte Carlo algorithm, was implemented to work with molecular dynamics in an isobaric ensemble and coded into LAMMPS, a highly optimized open source molecular simulation package. The method is illustrated in a study of the very strong solid/liquid transition in water.

Entropy gives rise to topologically associating domains

PubMed Central

Vasquez, Paula A.; Hult, Caitlin; Adalsteinsson, David; Lawrimore, Josh; Forest, Mark G.; Bloom, Kerry

2016-01-01

We investigate chromosome organization within the nucleus using polymer models whose formulation is closely guided by experiments in live yeast cells. We employ bead-spring chromosome models together with loop formation within the chains and the presence of nuclear bodies to quantify the extent to which these mechanisms shape the topological landscape in the interphase nucleus. By investigating the genome as a dynamical system, we show that domains of high chromosomal interactions can arise solely from the polymeric nature of the chromosome arms due to entropic interactions and nuclear confinement. In this view, the role of bio-chemical related processes is to modulate and extend the duration of the interacting domains. PMID:27257057

The entropic boundary law in BF theory

NASA Astrophysics Data System (ADS)

Livine, Etera R.; Terno, Daniel R.

2009-01-01

We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More precisely, we consider a fixed graph embedded in space and study the flat connection spin network state without and with particle-like topological defects. We regularize and compute exactly the entanglement for a bipartite splitting of the graph and show it scales at leading order with the number of vertices on the boundary (or equivalently with the number of loops crossing the boundary). More generally these results apply to BF theory with any compact gauge group in any space-time dimension.

Functional roles of H98 and W99 and β2α2 loop dynamics in the α-l-arabinofuranosidase from Thermobacillus xylanilyticus.

PubMed

Arab-Jaziri, Faten; Bissaro, Bastien; Barbe, Sophie; Saurel, Olivier; Débat, Hélène; Dumon, Claire; Gervais, Virginie; Milon, Alain; André, Isabelle; Fauré, Régis; O'Donohue, Michael J

2012-10-01

This study is focused on the elucidation of the functional role of the mobile β2α2 loop in the α-L-arabinofuranosidase from Thermobacillus xylanilyticus, and particularly on the roles of loop residues H98 and W99. Using site-directed mutagenesis, coupled to characterization methods including isothermal titration calorimetry (ITC) and saturation transfer difference nuclear magnetic resonance (STD-NMR) spectroscopy, and molecular dynamics simulations, it has been possible to provide a molecular level view of interactions and the consequences of mutations. Binding of para-nitrophenyl α-L-arabinofuranoside (pNP-α-l-Araf) to the wild-type arabinofuranosidase was characterized by K(d) values (0.32 and 0.16 mm, from ITC and STD-NMR respectively) that highly resembled that of the arabinoxylo-oligosaccharide XA(3)XX (0.21 mm), and determination of the thermodynamic parameters of enzyme : pNP-α-L-Araf binding revealed that this process is driven by favourable entropy, which is linked to the movement of the β2α2 loop. Loop closure relocates the solvent-exposed W99 into a buried location, allowing its involvement in substrate binding and in the formation of a functional active site. Similarly, the data underline the role of H98 in the ‘dynamic’ formation and definition of a catalytically operational active site, which may be a specific feature of a subset of GH51 arabinofuranosidases. Substitution of H98 and W99 by alanine or phenylalanine revealed that mutations affected K(M) and/or k(cat). Molecular dynamics performed on W99A implied that this mutation causes the loss of a hydrogen bond and leads to an alternative binding mode that is detrimental for catalysis. STD-NMR experiments revealed altered binding of the aglycon motif in the active site, combined with reduced STD intensities of the α-L-arabinofuranosyl moiety for W99 substitutions. © 2012 The Authors Journal compilation © 2012 FEBS.

Disordered quivers and cold horizons

DOE PAGES

Anninos, Dionysios; Anous, Tarek; Denef, Frederik

2016-12-15

We analyze the low temperature structure of a supersymmetric quiver quantum mechanics with randomized superpotential coefficients, treating them as quenched disorder. These theories describe features of the low energy dynamics of wrapped branes, which in large number backreact into extremal black holes. We show that the low temperature theory, in the limit of a large number of bifundamentals, exhibits a time reparametrization symmetry as well as a specific heat linear in the temperature. Both these features resemble the behavior of black hole horizons in the zero temperature limit. We demonstrate similarities between the low temperature physics of the random quivermore » model and a theory of large N free fermions with random masses.« less

NMR structure and dynamics of the engineered fluorescein-binding lipocalin FluA reveal rigidification of beta-barrel and variable loops upon enthalpy-driven ligand binding.

PubMed

Mills, Jeffrey L; Liu, Gaohua; Skerra, Arne; Szyperski, Thomas

2009-08-11

The NMR structure of the 21 kDa lipocalin FluA, which was previously obtained by combinatorial design, elucidates a reshaped binding site specific for the dye fluorescein resulting from 21 side chain replacements with respect to the parental lipocalin, the naturally occurring bilin-binding protein (BBP). As expected, FluA exhibits the lipocalin fold of BBP, comprising eight antiparallel beta-strands forming a beta-barrel with an alpha-helix attached to its side. Comparison of the NMR structure of free FluA with the X-ray structures of BBP.biliverdin IX(gamma) and FluA.fluorescein complexes revealed significant conformational changes in the binding pocket, which is formed by four loops at the open end of the beta-barrel as well as adjoining beta-strand segments. An "induced fit" became apparent for the side chain conformations of Arg 88 and Phe 99, which contact the bound fluorescein in the complex and undergo concerted rearrangement upon ligand binding. Moreover, slower internal motional modes of the polypeptide backbone were identified by measuring transverse (15)N backbone spin relaxation times in the rotating frame for free FluA and also for the FluA.fluorescein complex. A reduction in the level of such motions was detected upon complex formation, indicating rigidification of the protein structure and loss of conformational entropy. This hypothesis was confirmed by isothermal titration calorimetry, showing that ligand binding is enthalpy-driven, thus overcompensating for the negative entropy associated with both ligand binding per se and rigidification of the protein. Our investigation of the solution structure and dynamics as well as thermodynamics of lipocalin-ligand interaction not only provides insight into the general mechanism of small molecule accommodation in the deep and narrow cavity of this abundant class of proteins but also supports the future design of corresponding binding proteins with novel specificities, so-called "anticalins".

Overall heat transfer coefficient and pressure drop in a typical tubular exchanger employing alumina nano-fluid as the tube side hot fluid

NASA Astrophysics Data System (ADS)

Kabeel, A. E.; Abdelgaied, Mohamed

2016-08-01

Nano-fluids are used to improve the heat transfer rates in heat exchangers, especially; the shell-and-tube heat exchanger that is considered one of the most important types of heat exchangers. In the present study, an experimental loop is constructed to study the thermal characteristics of the shell-and-tube heat exchanger; at different concentrations of Al2O3 nonmetallic particles (0.0, 2, 4, and 6 %). This material concentrations is by volume concentrations in pure water as a base fluid. The effects of nano-fluid concentrations on the performance of shell and tube heat exchanger have been conducted based on the overall heat transfer coefficient, the friction factor, the pressure drop in tube side, and the entropy generation rate. The experimental results show that; the highest heat transfer coefficient is obtained at a nano-fluid concentration of 4 % of the shell side. In shell side the maximum percentage increase in the overall heat transfer coefficient has reached 29.8 % for a nano-fluid concentration of 4 %, relative to the case of the base fluid (water) at the same tube side Reynolds number. However; in the tube side the maximum relative increase in pressure drop has recorded the values of 12, 28 and 48 % for a nano-material concentration of 2, 4 and 6 %, respectively, relative to the case without nano-fluid, at an approximate value of 56,000 for Reynolds number. The entropy generation reduces with increasing the nonmetallic particle volume fraction of the same flow rates. For increase the nonmetallic particle volume fraction from 0.0 to 6 % the rate of entropy generation decrease by 10 %.

MaxEnt analysis of a water distribution network in Canberra, ACT, Australia

NASA Astrophysics Data System (ADS)

Waldrip, Steven H.; Niven, Robert K.; Abel, Markus; Schlegel, Michael; Noack, Bernd R.

2015-01-01

A maximum entropy (MaxEnt) method is developed to infer the state of a pipe flow network, for situations in which there is insufficient information to form a closed equation set. This approach substantially extends existing deterministic methods for the analysis of engineered flow networks (e.g. Newton's method or the Hardy Cross scheme). The network is represented as an undirected graph structure, in which the uncertainty is represented by a continuous relative entropy on the space of internal and external flow rates. The head losses (potential differences) on the network are treated as dependent variables, using specified pipe-flow resistance functions. The entropy is maximised subject to "observable" constraints on the mean values of certain flow rates and/or potential differences, and also "physical" constraints arising from the frictional properties of each pipe and from Kirchhoff's nodal and loop laws. A numerical method is developed in Matlab for solution of the integral equation system, based on multidimensional quadrature. Several nonlinear resistance functions (e.g. power-law and Colebrook) are investigated, necessitating numerical solution of the implicit Lagrangian by a double iteration scheme. The method is applied to a 1123-node, 1140-pipe water distribution network for the suburb of Torrens in the Australian Capital Territory, Australia, using network data supplied by water authority ACTEW Corporation Limited. A number of different assumptions are explored, including various network geometric representations, prior probabilities and constraint settings, yielding useful predictions of network demand and performance. We also propose this methodology be used in conjunction with in-flow monitoring systems, to obtain better inferences of user consumption without large investments in monitoring equipment and maintenance.

Geodesic active fields--a geometric framework for image registration.

PubMed

Zosso, Dominique; Bresson, Xavier; Thiran, Jean-Philippe

2011-05-01

In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including nonflat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Second, this method is, to the best of our knowledge, the first reparametrization invariant registration method introduced in the literature. Thirdly, the multiplicative coupling between the registration term, i.e. local image discrepancy, and the regularization term naturally results in a data-dependent tuning of the regularization strength. Finally, by choosing the metric on the deformation field one can freely interpolate between classic Gaussian and more interesting anisotropic, TV-like regularization.

Simulations of flow induced structural transition of the β-switch region of glycoprotein Ibα.

PubMed

Han, Mengzhi; Xu, Ji; Ren, Ying; Li, Jinghai

2016-02-01

Binding of glycoprotein Ibα to von Willebrand factor induces platelet adhesion to injured vessel walls and initiates a multistep hemostatic process. It has been hypothesized that the flow condition could induce a loop to β-sheet conformational change in the β-switch region of glycoprotein Ibα, which regulates it binding to the von Willebrand factor and facilitates the blood clot formation and wound healing. In this work, direct molecular dynamics (MD), flow MD and metadynamics, were employed to investigate the mechanisms of this flow induced conformational transition process. Specifically, the free energy landscape of the whole transition process was drawn by metadynamics with the path collective variable approach. The results reveal that without flow, the free energy landscape has two main basins, including a random loop basin stabilized by large conformational entropy and a partially folded β-sheet basin. The free energy barrier separating these two basins is relatively high and the β-switch could not fold from loop to β-sheet state spontaneously. The fully β-sheet conformations located in high free energy regions, which are also unstable and gradually unfold into partially folded β-sheet state with flow. Relatively weak flow could trigger some folding of the β-switch but could not fold it into fully β-sheet state. Under strong flow conditions, the β-switch could readily overcome the high free energy barrier and fold into fully β-sheet state. Copyright © 2015 Elsevier B.V. All rights reserved.

Action at a Distance in the Cell's Nucleus

NASA Astrophysics Data System (ADS)

Kondev, Jane

Various functions performed by chromosomes involve long-range communication between DNA sequences that are tens of thousands of bases apart along the genome, and microns apart in the nucleus. In this talk I will discuss experiments and theory relating to two distinct modes of long-range communication in the nucleus, chromosome looping and protein hopping along the chromosome, both in the context of DNA-break repair in yeast. Yeast is an excellent model system for studies that link chromosome conformations to their function as there is ample experimental evidence that yeast chromosome conformations are well described by a simple, random-walk polymer model. Using a combination of polymer physics theory and experiments on yeast cells, I will demonstrate that loss of polymer entropy due to chromosome looping is the driving force for homology search during repair of broken DNA by homologous recombination. I will also discuss the spread of histone modifications along the chromosome and away from the DNA break point in the context of simple physics models based on chromosome looping and kinase hopping, and show how combining physics theory and cell-biology experiment can be used to dissect the molecular mechanism of the spreading process. These examples demonstrate how combined theoretical and experimental studies can reveal physical principles of long-range communication in the nucleus, which play important roles in regulation of gene expression, DNA recombination, and chromatin modification. This work was supported by the NSF DMR-1206146.

Dynamical Heterogeneity in Granular Fluids and Structural Glasses

NASA Astrophysics Data System (ADS)

Avila, Karina E.

Our current understanding of the dynamics of supercooled liquids and other similar slowly evolving (glassy) systems is rather limited. One aspect that is particularly poorly understood is the origin and behavior of the strong non trivial fluctuations that appear in the relaxation process toward equilibrium. Glassy systems and granular systems both present regions of particles moving cooperatively and at different rates from other regions. This phenomenon is known as spatially heterogeneous dynamics. A detailed explanation of this phenomenon may lead to a better understanding of the slow relaxation process, and perhaps it could even help to explain the presence of the glass transition. This dissertation concentrates on studying dynamical heterogeneity by analyzing simulation data for models of granular materials and structural glasses. For dissipative granular fluids, the growing behavior of dynamical heterogeneities is studied for different densities and different degrees of inelasticity in the particle collisions. The correlated regions are found to grow rapidly as the system approaches dynamical arrest. Their geometry is conserved even when probing at different cutoff length in the correlation function or when the energy dissipation in the system is increased. For structural glasses, I test a theoretical framework that models dynamical heterogeneity as originated in the presence of Goldstone modes, which emerge from a broken continuous time reparametrization symmetry. This analysis is based on quantifying the size and the spatial correlations of fluctuations in the time variable and of other kinds of fluctuations. The results obtained here agree with the predictions of the hypothesis. In particular, the fluctuations associated to the time reparametrization invariance become stronger for low temperatures, long timescales, and large coarse graining lengths. Overall, this research points to dynamical heterogeneity to be described for granular systems similarly than for other glassy systems and it provides evidence in favor of a particular theory for the origin of dynamical heterogeneity.

Fate of the Hoop Conjecture in Quantum Gravity.

PubMed

Anzà, Fabio; Chirco, Goffredo

2017-12-08

We consider a closed region R of 3D quantum space described via SU(2) spin networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary ∂R and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interpret such phenomenon as a pregeometric analogue of Thorne's "hoop conjecture," at the core of the formation of a horizon in general relativity.

Order by disorder and gaugelike degeneracy in a quantum pyrochlore antiferromagnet.

PubMed

Henley, Christopher L

2006-02-03

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length S is a highly frustrated model with a macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic-order) spin-wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating effective Hamiltonian, acting within the subspace of Ising spin configurations representing the collinear ground states. It consists of products of Ising spins around loops, i.e., has the form of a Z2 lattice gauge theory. The remaining ground-state entropy is still infinite but not extensive, being O(L) for system size O(L3). All these ground states have unit cells bigger than those considered previously.

Effects of sensory augmentation on postural control and gait symmetry of transfemoral amputees: a case description.

PubMed

Pagel, Anna; Arieta, Alejandro Hernandez; Riener, Robert; Vallery, Heike

2016-10-01

Despite recent advances in leg prosthetics, transfemoral amputees still experience limitations in postural control and gait symmetry. It has been hypothesized that artificial sensory information might improve the integration of the prosthesis into the human sensory-motor control loops and, thus, reduce these limitations. In three transfemoral amputees, we investigated the effect of Electrotactile Moving Sensation for Sensory Augmentation (EMSSA) without training and present preliminary findings. Experimental conditions included standing with open/closed eyes on stable/unstable ground as well as treadmill walking. For standing conditions, spatiotemporal posturographic measures and sample entropy were derived from the center of pressure. For walking conditions, step length and stance duration were calculated. Conditions without feedback showed effects congruent with findings in the literature, e.g., asymmetric weight bearing and step length, and validated the collected data. During standing, with EMSSA a tendency to influence postural control in a negative way was found: Postural control was less effective and less efficient and the prosthetic leg was less involved. Sample entropy tended to decrease, suggesting that EMSSA demanded increased attention. During walking, with EMSSA no persistent positive effect was found. This contrasts the positive subjective assessment and the positive effect on one subject's step length.

Towards a next generation open-source video codec

NASA Astrophysics Data System (ADS)

Bankoski, Jim; Bultje, Ronald S.; Grange, Adrian; Gu, Qunshan; Han, Jingning; Koleszar, John; Mukherjee, Debargha; Wilkins, Paul; Xu, Yaowu

2013-02-01

Google has recently been developing a next generation opensource video codec called VP9, as part of the experimental branch of the libvpx repository included in the WebM project (http://www.webmproject.org/). Starting from the VP8 video codec released by Google in 2010 as the baseline, a number of enhancements and new tools have been added to improve the coding efficiency. This paper provides a technical overview of the current status of this project along with comparisons and other stateoftheart video codecs H. 264/AVC and HEVC. The new tools that have been added so far include: larger prediction block sizes up to 64x64, various forms of compound INTER prediction, more modes for INTRA prediction, ⅛pel motion vectors and 8tap switchable subpel interpolation filters, improved motion reference generation and motion vector coding, improved entropy coding and framelevel entropy adaptation for various symbols, improved loop filtering, incorporation of Asymmetric Discrete Sine Transforms and larger 16x16 and 32x32 DCTs, frame level segmentation to group similar areas together, etc. Other tools and various bitstream features are being actively worked on as well. The VP9 bitstream is expected to be finalized by earlyto mid2013. Results show VP9 to be quite competitive in performance with mainstream stateoftheart codecs.

Thermal and magnetic hysteresis associated with martensitic and magnetic phase transformations in Ni52Mn25In16Co7 Heusler alloy

NASA Astrophysics Data System (ADS)

Madiligama, A. S. B.; Ari-Gur, P.; Ren, Y.; Koledov, V. V.; Dilmieva, E. T.; Kamantsev, A. P.; Mashirov, A. V.; Shavrov, V. G.; Gonzalez-Legarreta, L.; Grande, B. H.

2017-11-01

Ni-Mn-In-Co Heusler alloys demonstrate promising magnetocaloric performance for use as refrigerants in magnetic cooling systems with the goal of replacing the lower efficiency, eco-adverse fluid-compression technology. The largest change in entropy occurs when the applied magnetic field causes a merged structural and magnetic transformation and the associated entropy changes of the two transformations works constructively. In this study, magnetic and crystalline phase transformations were each treated separately and the effects of the application of magnetic field on thermal hystereses associated with both structural and magnetic transformations of the Ni52Mn25In16Co7 were studied. From the analysis of synchrotron diffraction data and thermomagnetic measurements, it was revealed that the alloy undergoes both structural (from cubic austenite to a mixture of 7M &5M modulated martensite) and magnetic (ferromagnetic to a low-magnetization phase) phase transformations. Thermal hysteresis is associated with both transformations, and the variation of the thermal hystereses of the magnetic and structural transformations with applied magnetic field is significantly different. Because of the differences between the hystereses loops of the two transformations, they merge only upon heating under a certain magnetic field.

Conformational Entropy from NMR Relaxation in Proteins: The SRLS Perspective.

PubMed

Tchaicheeyan, Oren; Meirovitch, Eva

2017-02-02

Conformational entropy changes associated with bond-vector motions in proteins contribute to the free energy of ligand-binding. To derive such contributions, we apply the slowly relaxing local structure (SRLS) approach to NMR relaxation from 15 N-H bonds or C-CDH 2 moieties of several proteins in free and ligand-bound form. The spatial restraints on probe motion, which determine the extent of local order, are expressed in SRLS by a well-defined potential, u(θ). The latter yields the orientational probability density, P eq  = exp(-u(θ)), and hence the related conformational entropy, Ŝ = -∫P eq (θ) ln[P eq (θ)] sin θ dθ (Ŝ is "entropy" in units of k B T, and θ represents the bond-vector orientation in the protein). SRLS is applied to 4-oxalocrotonate tautomerase (4-OT), the acyl-coenzyme A binding protein (ACBP), the C-terminal SH2 domain of phospholipase C γ 1 (PLC γ 1C SH2), the construct dihydrofolate reductase-E:folate (DHFR-E:folate), and their complexes with appropriate ligands, to determine ΔŜ. Eglin C and its V18A and V34A mutants are also studied. Finally, SRLS is applied to the structurally homologous proteins TNfn3 and FNfn10 to characterize within its scope the unusual "dynamics" of the TNfn3 core. Upon ligand-binding, the backbones of 4-OT, ACBP, and PLC γ 1C SH2 show limited, increased, and decreased order, respectively; the cores of DHFR-E:folate and PLC γ 1C SH2 become more ordered. The V18A (V34A) mutation increases (decreases) the order within the eglin C core. The core of TNfn3 is less ordered structurally and more mobile kinetically. Secondary structure versus loops, surface-binding versus core insertion, and ligand size emerged as being important in rationalizing ΔŜ. The consistent and general tool developed herein is expected to provide further insights in future work.

Nonequilibrium evolution of scalar fields in FRW cosmologies

NASA Astrophysics Data System (ADS)

Boyanovsky, D.; de Vega, H. J.; Holman, R.

1994-03-01

We derive the effective equations for the out of equilibrium time evolution of the order parameter and the fluctuations of a scalar field theory in spatially flat FRW cosmologies. The calculation is performed both to one loop and in a nonperturbative, self-consistent Hartree approximation. The method consists of evolving an initial functional thermal density matrix in time and is suitable for studying phase transitions out of equilibrium. The renormalization aspects are studied in detail and we find that the counterterms depend on the initial state. We investigate the high temperature expansion and show that it breaks down at long times. We also obtain the time evolution of the initial Boltzmann distribution functions, and argue that to one-loop order or in the Hartree approximation the time evolved state is a ``squeezed'' state. We illustrate the departure from thermal equilibrium by numerically studying the case of a free massive scalar field in de Sitter and radiation-dominated cosmologies. It is found that a suitably defined nonequilibrium entropy per mode increases linearly with comoving time in a de Sitter cosmology, whereas it is not a monotonically increasing function in the radiation-dominated case.

Prediction-guided quantization for video tone mapping

NASA Astrophysics Data System (ADS)

Le Dauphin, Agnès.; Boitard, Ronan; Thoreau, Dominique; Olivier, Yannick; Francois, Edouard; LeLéannec, Fabrice

2014-09-01

Tone Mapping Operators (TMOs) compress High Dynamic Range (HDR) content to address Low Dynamic Range (LDR) displays. However, before reaching the end-user, this tone mapped content is usually compressed for broadcasting or storage purposes. Any TMO includes a quantization step to convert floating point values to integer ones. In this work, we propose to adapt this quantization, in the loop of an encoder, to reduce the entropy of the tone mapped video content. Our technique provides an appropriate quantization for each mode of both the Intra and Inter-prediction that is performed in the loop of a block-based encoder. The mode that minimizes a rate-distortion criterion uses its associated quantization to provide integer values for the rest of the encoding process. The method has been implemented in HEVC and was tested over two different scenarios: the compression of tone mapped LDR video content (using the HM10.0) and the compression of perceptually encoded HDR content (HM14.0). Results show an average bit-rate reduction under the same PSNR for all the sequences and TMO considered of 20.3% and 27.3% for tone mapped content and 2.4% and 2.7% for HDR content.

Predictive Computational Modeling of Chromatin Folding

NASA Astrophysics Data System (ADS)

di Pierro, Miichele; Zhang, Bin; Wolynes, Peter J.; Onuchic, Jose N.

In vivo, the human genome folds into well-determined and conserved three-dimensional structures. The mechanism driving the folding process remains unknown. We report a theoretical model (MiChroM) for chromatin derived by using the maximum entropy principle. The proposed model allows Molecular Dynamics simulations of the genome using as input the classification of loci into chromatin types and the presence of binding sites of loop forming protein CTCF. The model was trained to reproduce the Hi-C map of chromosome 10 of human lymphoblastoid cells. With no additional tuning the model was able to predict accurately the Hi-C maps of chromosomes 1-22 for the same cell line. Simulations show unknotted chromosomes, phase separation of chromatin types and a preference of chromatin of type A to sit at the periphery of the chromosomes.

Loop Quantum Gravity.

PubMed

Rovelli, Carlo

2008-01-01

The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime , is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler's "spacetime foam" intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n -point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

Fusion basis for lattice gauge theory and loop quantum gravity

NASA Astrophysics Data System (ADS)

Delcamp, Clement; Dittrich, Bianca; Riello, Aldo

2017-02-01

We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2 + 1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel'd double of the gauge group, and can be readily "fused" together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi-local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse-graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin-network basis, in which it is much more complicated to account for electric excitations, i.e. for Gauß constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi-scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2 + 1) gravity coupled to point particles. In a follow-up work, we have exploited this notion to provide a new definition of entanglement entropy for these theories.

Characterizing Peptide β-HAIRPIN Loops via Cold Ion Spectroscopy of Model Compounds

NASA Astrophysics Data System (ADS)

Lawler, John T.; DeBlase, Andrew F.; Harrilal, Christopher P.; Fischer, Joshua L.; McLuckey, Scott A.; Zwier, Timothy S.

2017-06-01

The introduction of non-native D-amino acids into peptides is known to reduce conformational entropy in peptides. D-proline has been shown to promote the formation of β-hairpin loops when paired with Gly, providing a framework for building these loops with different lengths of anti-parallel beta-sheet. This study seeks to characterize and compare the conformational preferences of a model protonated pentapeptide containing DPG, [YAP^{D}GA+H]^{+}, with its L-Pro counterpart via conformation specific cold ion spectroscopy as a foundation for future consideration of larger beta-hairpin models. The UV spectrum of YAP^{D}GA of the Tyr chromophore is beautifully sharp, but contains a complicated set of transitions that could arise from the presence of more than one conformer. To assess this possibility, we recorded non-conformation specific IR "gain" spectra in the hydride stretch region. The IR spectrum so obtained displays a set of five strong IR transitions that bear a close resemblance to those found in one of the conformers of its close analog, [YAP^{D}AA+H]^{+}, signaling that a single conformer dominates the population. Two transitions at 3392 and 3464 cm-1 are slightly shifted versions of the C10 and C14 hydrogen bonds found in one of the conformers of [YAP^{D}AA+H]^{+}, and are characteristic of formation of a β-hairpin loop. Notably, in [YAP^{D}GA+H]^{+}, there is at most a minor second conformer with a free carboxylic acid OH, appearing weakly in the IR "gain" spectrum. As expected, the UV spectrum of YAP^{L}GA is more congested, which suggests the presence of multiple conformers. Further investigation into this peptide will reveal the conformational preferences of the L-pro containing molecule. Preliminary data affirms that D-proline containing peptides show reduced conformational states when compared to their natural counterparts.

Effects of ligand binding on the dynamics of rice nonspecific lipid transfer protein 1: a model from molecular simulations.

PubMed

Lai, Yen-Ting; Cheng, Chao-Sheng; Liu, Yu-Nan; Liu, Yaw-Jen; Lyu, Ping-Chiang

2008-09-01

Plant nonspecific lipid transfer proteins (nsLTPs) are small, basic proteins constituted mainly of alpha-helices and stabilized by four conserved disulfide bridges. They are characterized by the presence of a tunnel-like hydrophobic cavity, capable of transferring various lipid molecules between lipid bilayers in vitro. In this study, molecular dynamics (MD) simulations were performed at room temperature to investigate the effects of lipid binding on the dynamic properties of rice nsLTP1. Rice nsLTP1, either in the free form or complexed with one or two lipids was subjected to MD simulations. The C-terminal loop was very flexible both before and after lipid binding, as revealed by calculating the root-mean-square fluctuation. After lipid binding, the flexibility of some residues that were not in direct contact with lipid molecules increased significantly, indicating an increase of entropy in the region distal from the binding site. Essential dynamics analysis revealed clear differences in motion between unliganded and liganded rice nsLTP1s. In the free form of rice nsLTP1, loop1 exhibited the largest directional motion. This specific essential motion mode diminished after binding one or two lipid molecules. To verify the origin of the essential motion observed in the free form of rice nsLTP1, we performed multiple sequence alignments to probe the intrinsic motion encoded in the primary sequence. We found that the amino acid sequence of loop1 is highly conserved among plant nsLTP1s, thus revealing its functional importance during evolution. Furthermore, the sequence of loop1 is composed mainly of amino acids with short side chains. In this study, we show that MD simulations, together with essential dynamics analysis, can be used to determine structural and dynamic differences of rice nsLTP1 upon lipid binding. 2008 Wiley-Liss, Inc.

Entropic and Electrostatic Effects on the Folding Free Energy of a Surface-Attached Biomolecule: An Experimental and Theoretical Study

PubMed Central

Watkins, Herschel M.; Vallée-Bélisle, Alexis; Ricci, Francesco; Makarov, Dmitrii E.; Plaxco, Kevin W.

2012-01-01

Surface-tethered biomolecules play key roles in many biological processes and biotechnologies. However, while the physical consequences of such surface attachment have seen significant theoretical study, to date this issue has seen relatively little experimental investigation. In response we present here a quantitative experimental and theoretical study of the extent to which attachment to a charged –but otherwise apparently inert– surface alters the folding free energy of a simple biomolecule. Specifically, we have measured the folding free energy of a DNA stem loop both in solution and when site-specifically attached to a negatively charged, hydroxyl-alkane-coated gold surface. We find that, whereas surface attachment is destabilizing at low ionic strength it becomes stabilizing at ionic strengths above ~130 mM. This behavior presumably reflects two competing mechanisms: excluded volume effects, which stabilize the folded conformation by reducing the entropy of the unfolded state, and electrostatics, which, at lower ionic strengths, destabilizes the more compact folded state via repulsion from the negatively charged surface. To test this hypothesis we have employed existing theories of the electrostatics of surface-bound polyelectrolytes and the entropy of surface-bound polymers to model both effects. Despite lacking any fitted parameters, these theoretical models quantitatively fit our experimental results, suggesting that, for this system, current knowledge of both surface electrostatics and excluded volume effects is reasonably complete and accurate. PMID:22239220

Whole-Lesion Apparent Diffusion Coefficient-Based Entropy-Related Parameters for Characterizing Cervical Cancers: Initial Findings.

PubMed

Guan, Yue; Li, Weifeng; Jiang, Zhuoran; Chen, Ying; Liu, Song; He, Jian; Zhou, Zhengyang; Ge, Yun

2016-12-01

This study aimed to develop whole-lesion apparent diffusion coefficient (ADC)-based entropy-related parameters of cervical cancer to preliminarily assess intratumoral heterogeneity of this lesion in comparison to adjacent normal cervical tissues. A total of 51 women (mean age, 49 years) with cervical cancers confirmed by biopsy underwent 3-T pelvic diffusion-weighted magnetic resonance imaging with b values of 0 and 800 s/mm 2 prospectively. ADC-based entropy-related parameters including first-order entropy and second-order entropies were derived from the whole tumor volume as well as adjacent normal cervical tissues. Intraclass correlation coefficient, Wilcoxon test with Bonferroni correction, Kruskal-Wallis test, and receiver operating characteristic curve were used for statistical analysis. All the parameters showed excellent interobserver agreement (all intraclass correlation coefficients  > 0.900). Entropy, entropy(H) 0 , entropy(H) 45 , entropy(H) 90 , entropy(H) 135 , and entropy(H) mean were significantly higher, whereas entropy(H) range and entropy(H) std were significantly lower in cervical cancers compared to adjacent normal cervical tissues (all P <.0001). Kruskal-Wallis test showed that there were no significant differences among the values of various second-order entropies including entropy(H) 0, entropy(H) 45 , entropy(H) 90 , entropy(H) 135 , and entropy(H) mean. All second-order entropies had larger area under the receiver operating characteristic curve than first-order entropy in differentiating cervical cancers from adjacent normal cervical tissues. Further, entropy(H) 45 , entropy(H) 90 , entropy(H) 135 , and entropy(H) mean had the same largest area under the receiver operating characteristic curve of 0.867. Whole-lesion ADC-based entropy-related parameters of cervical cancers were developed successfully, which showed initial potential in characterizing intratumoral heterogeneity in comparison to adjacent normal cervical tissues. Copyright © 2016 The Association of University Radiologists. Published by Elsevier Inc. All rights reserved.

Global stability and exact solution of an arbitrary-solute nonlinear cellular mass transport system.

PubMed

Benson, James D

2014-12-01

The prediction of the cellular state as a function of extracellular concentrations and temperatures has been of interest to physiologists for nearly a century. One of the most widely used models in the field is one where mass flux is linearly proportional to the concentration difference across the membrane. These fluxes define a nonlinear differential equation system for the intracellular state, which when coupled with appropriate initial conditions, define the intracellular state as a function of the extracellular concentrations of both permeating and nonpermeating solutes. Here we take advantage of a reparametrization scheme to extend existing stability results to a more general setting and to a develop analytical solutions to this model for an arbitrary number of extracellular solutes. Copyright © 2014 Elsevier Inc. All rights reserved.

Discreteness of time in the evolution of the universe

NASA Astrophysics Data System (ADS)

Faizal, Mir; Ali, Ahmed Farag; Das, Saurya

2017-04-01

In this paper, we will first derive the Wheeler-DeWitt equation for the generalized geometry which occurs in M-theory. Then we will observe that M2-branes act as probes for this generalized geometry, and as M2-branes have an extended structure, their extended structure will limits the resolution to which this generalized geometry can be defined. We will demonstrate that this will deform the Wheeler-DeWitt equation for the generalized geometry. We analyze such a deformed Wheeler-DeWitt equation in the minisuperspace approximation, and observe that this deformation can be used as a solution to the problem of time. This is because this deformation gives rise to time crystals in our universe due to the spontaneous breaking of time reparametrization invariance.

On a `time' reparametrization in relativistic electrodynamics with travelling waves

NASA Astrophysics Data System (ADS)

Fiore, Gaetano

2018-01-01

We briefly report on our method [23] of simplifying the equations of motion of charged particles in an electromagnetic (EM) field that is the sum of a plane travelling wave and a static part; it is based on changes of the dependent variables and the independent one (light-like coordinate ξ instead of time t). We sketch its application to a few cases of extreme laser-induced accelerations, both in vacuum and in plane problems at the vacuum-plasma interface, where we are able to reduce the system of the (Lorentz-Maxwell and continuity) partial differential equations into a family of decoupled systems of Hamilton equations in 1 dimension. Since Fourier analysis plays no role, the method can be applied to all kind of travelling waves, ranging from almost monochromatic to socalled "impulses".

Solving the Hamilton-Jacobi equation for general relativity

NASA Astrophysics Data System (ADS)

Parry, J.; Salopek, D. S.; Stewart, J. M.

1994-03-01

We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparametrizations of the spatial coordinates (``gauge invariant''). At each order we solve the Hamiltonian constraint using a conformal transformation of the three-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the three-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.

On quantum Rényi entropies: A new generalization and some properties

NASA Astrophysics Data System (ADS)

Müller-Lennert, Martin; Dupuis, Frédéric; Szehr, Oleg; Fehr, Serge; Tomamichel, Marco

2013-12-01

The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation.

Molecular View of CO2 Capture by Polyethylenimine: Role of Structural and Dynamical Heterogeneity.

PubMed

Sharma, Pragati; Chakrabarty, Suman; Roy, Sudip; Kumar, Rajnish

2018-05-01

The molecular thermodynamics and kinetics of CO 2 sorption in Polyethylenimine (PEI) melt have been investigated systematically using GCMC and MD simulations. We elucidate presence of significant structural and dynamic heterogeneity associated with the overall absorption process. CO 2 adsorption in a PEI membrane shows a distinct two-stage process of a rapid CO 2 adsorption at the interfaces (hundreds of picoseconds) followed by a significantly slower diffusion limited release toward the interior bulk regions of PEI melt (hundreds of nanoseconds to microseconds). The spatial heterogeneity of local structural features of the PEI chains lead to significantly heterogeneous absorption characterized by clustering and trapping of CO 2 molecules that then lead to subdiffusive motion of CO 2 . In the complex interplay of interaction and entropy, the latter emerges out to be the major determining factor with significantly higher solubility of CO 2 near the interfaces despite having lower density of binding amine groups. Regions having higher free-volume (entropically favorable) viz. interfaces, pores and loops demonstrate higher CO 2 capture ability. Various local structural features of PEI conformations, for example, inter- and intrachain loops, pores of different radii, and di- or tricoordinated pores are explored for their effects on the varying CO 2 adsorption abilities.

Combined collapse by bridging and self-adhesion in a prototypical polymer model inspired by the bacterial nucleoid

NASA Astrophysics Data System (ADS)

Scolari, Vittore F.; Cosentino Lagomarsino, Marco

Recent experimental results suggest that the E. coli chromosome feels a self-attracting interaction of osmotic origin, and is condensed in foci by bridging interactions. Motivated by these findings, we explore a generic modeling framework combining solely these two ingredients, in order to characterize their joint effects. Specifically, we study a simple polymer physics computational model with weak ubiquitous short-ranged self attraction and stronger sparse bridging interactions. Combining theoretical arguments and simulations, we study the general phenomenology of polymer collapse induced by these dual contributions, in the case of regularly-spaced bridging. Our results distinguish a regime of classical Flory-like coil-globule collapse dictated by the interplay of excluded volume and attractive energy and a switch-like collapse where bridging interaction compete with entropy loss terms from the looped arms of a star-like rosette. Additionally, we show that bridging can induce stable compartmentalized domains. In these configurations, different "cores" of bridging proteins are kept separated by star-like polymer loops in an entropically favorable multi-domain configuration, with a mechanism that parallels micellar polysoaps. Such compartmentalized domains are stable, and do not need any intra-specific interactions driving their segregation. Domains can be stable also in presence of uniform attraction, as long as the uniform collapse is above its theta point.

Upper entropy axioms and lower entropy axioms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Jin-Li, E-mail: phd5816@163.com; Suo, Qi

2015-04-15

The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak upper entropy axioms and weak lower entropy axioms. Their conditions are weaker than those of Shannon–Khinchin axioms and Tsallis axioms, while these conditions are stronger than those of the axiomatics based on the first three Shannon–Khinchin axioms. The subadditivity and strong subadditivity of entropy are obtained in the new axiomatics. Tsallis statistics is a special case of satisfying our axioms. Moreover,more » different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics.« less

EEG entropy measures in anesthesia

PubMed Central

Liang, Zhenhu; Wang, Yinghua; Sun, Xue; Li, Duan; Voss, Logan J.; Sleigh, Jamie W.; Hagihira, Satoshi; Li, Xiaoli

2015-01-01

Highlights: ► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in assessing anesthesia drugs' effect is lacking. In this study, we compare the capability of 12 entropy indices for monitoring depth of anesthesia (DoA) and detecting the burst suppression pattern (BSP), in anesthesia induced by GABAergic agents. Methods: Twelve indices were investigated, namely Response Entropy (RE) and State entropy (SE), three wavelet entropy (WE) measures [Shannon WE (SWE), Tsallis WE (TWE), and Renyi WE (RWE)], Hilbert-Huang spectral entropy (HHSE), approximate entropy (ApEn), sample entropy (SampEn), Fuzzy entropy, and three permutation entropy (PE) measures [Shannon PE (SPE), Tsallis PE (TPE) and Renyi PE (RPE)]. Two EEG data sets from sevoflurane-induced and isoflurane-induced anesthesia respectively were selected to assess the capability of each entropy index in DoA monitoring and BSP detection. To validate the effectiveness of these entropy algorithms, pharmacokinetic/pharmacodynamic (PK/PD) modeling and prediction probability (Pk) analysis were applied. The multifractal detrended fluctuation analysis (MDFA) as a non-entropy measure was compared. Results: All the entropy and MDFA indices could track the changes in EEG pattern during different anesthesia states. Three PE measures outperformed the other entropy indices, with less baseline variability, higher coefficient of determination (R2) and prediction probability, and RPE performed best; ApEn and SampEn discriminated BSP best. Additionally, these entropy measures showed an advantage in computation efficiency compared with MDFA. Conclusion: Each entropy index has its advantages and disadvantages in estimating DoA. Overall, it is suggested that the RPE index was a superior measure. Investigating the advantages and disadvantages of these entropy indices could help improve current clinical indices for monitoring DoA. PMID:25741277

An Improved Otsu Threshold Segmentation Method for Underwater Simultaneous Localization and Mapping-Based Navigation

PubMed Central

Yuan, Xin; Martínez, José-Fernán; Eckert, Martina; López-Santidrián, Lourdes

2016-01-01

The main focus of this paper is on extracting features with SOund Navigation And Ranging (SONAR) sensing for further underwater landmark-based Simultaneous Localization and Mapping (SLAM). According to the characteristics of sonar images, in this paper, an improved Otsu threshold segmentation method (TSM) has been developed for feature detection. In combination with a contour detection algorithm, the foreground objects, although presenting different feature shapes, are separated much faster and more precisely than by other segmentation methods. Tests have been made with side-scan sonar (SSS) and forward-looking sonar (FLS) images in comparison with other four TSMs, namely the traditional Otsu method, the local TSM, the iterative TSM and the maximum entropy TSM. For all the sonar images presented in this work, the computational time of the improved Otsu TSM is much lower than that of the maximum entropy TSM, which achieves the highest segmentation precision among the four above mentioned TSMs. As a result of the segmentations, the centroids of the main extracted regions have been computed to represent point landmarks which can be used for navigation, e.g., with the help of an Augmented Extended Kalman Filter (AEKF)-based SLAM algorithm. The AEKF-SLAM approach is a recursive and iterative estimation-update process, which besides a prediction and an update stage (as in classical Extended Kalman Filter (EKF)), includes an augmentation stage. During navigation, the robot localizes the centroids of different segments of features in sonar images, which are detected by our improved Otsu TSM, as point landmarks. Using them with the AEKF achieves more accurate and robust estimations of the robot pose and the landmark positions, than with those detected by the maximum entropy TSM. Together with the landmarks identified by the proposed segmentation algorithm, the AEKF-SLAM has achieved reliable detection of cycles in the map and consistent map update on loop closure, which is shown in simulated experiments. PMID:27455279

An Improved Otsu Threshold Segmentation Method for Underwater Simultaneous Localization and Mapping-Based Navigation.

PubMed

Yuan, Xin; Martínez, José-Fernán; Eckert, Martina; López-Santidrián, Lourdes

2016-07-22

The main focus of this paper is on extracting features with SOund Navigation And Ranging (SONAR) sensing for further underwater landmark-based Simultaneous Localization and Mapping (SLAM). According to the characteristics of sonar images, in this paper, an improved Otsu threshold segmentation method (TSM) has been developed for feature detection. In combination with a contour detection algorithm, the foreground objects, although presenting different feature shapes, are separated much faster and more precisely than by other segmentation methods. Tests have been made with side-scan sonar (SSS) and forward-looking sonar (FLS) images in comparison with other four TSMs, namely the traditional Otsu method, the local TSM, the iterative TSM and the maximum entropy TSM. For all the sonar images presented in this work, the computational time of the improved Otsu TSM is much lower than that of the maximum entropy TSM, which achieves the highest segmentation precision among the four above mentioned TSMs. As a result of the segmentations, the centroids of the main extracted regions have been computed to represent point landmarks which can be used for navigation, e.g., with the help of an Augmented Extended Kalman Filter (AEKF)-based SLAM algorithm. The AEKF-SLAM approach is a recursive and iterative estimation-update process, which besides a prediction and an update stage (as in classical Extended Kalman Filter (EKF)), includes an augmentation stage. During navigation, the robot localizes the centroids of different segments of features in sonar images, which are detected by our improved Otsu TSM, as point landmarks. Using them with the AEKF achieves more accurate and robust estimations of the robot pose and the landmark positions, than with those detected by the maximum entropy TSM. Together with the landmarks identified by the proposed segmentation algorithm, the AEKF-SLAM has achieved reliable detection of cycles in the map and consistent map update on loop closure, which is shown in simulated experiments.

Refined two-index entropy and multiscale analysis for complex system

NASA Astrophysics Data System (ADS)

Bian, Songhan; Shang, Pengjian

2016-10-01

As a fundamental concept in describing complex system, entropy measure has been proposed to various forms, like Boltzmann-Gibbs (BG) entropy, one-index entropy, two-index entropy, sample entropy, permutation entropy etc. This paper proposes a new two-index entropy Sq,δ and we find the new two-index entropy is applicable to measure the complexity of wide range of systems in the terms of randomness and fluctuation range. For more complex system, the value of two-index entropy is smaller and the correlation between parameter δ and entropy Sq,δ is weaker. By combining the refined two-index entropy Sq,δ with scaling exponent h(δ), this paper analyzes the complexities of simulation series and classifies several financial markets in various regions of the world effectively.

Anomalous physical properties of Heusler-type Co2Cr (Ga,Si) alloys and thermodynamic study on reentrant martensitic transformation

NASA Astrophysics Data System (ADS)

Xu, Xiao; Nagasako, Makoto; Kataoka, Mitsuo; Umetsu, Rie Y.; Omori, Toshihiro; Kanomata, Takeshi; Kainuma, Ryosuke

2015-03-01

Electronic, magnetic, and thermodynamic properties of Co2Cr(Ga,Si) -based shape-memory alloys, which exhibit reentrant martensitic transformation (RMT) behavior, were studied experimentally. For electric resistivity (ER), an inverse (semiconductor-like) temperature dependence in the parent phase was found, along with anomalous behavior below its Curie temperature. A pseudobinary phase diagram was determined, which gives a "martensite loop" clearly showing the reentrant behavior. Differential scanning calorimetry and specific-heat measurements were used to derive the entropy change Δ S between martensite and parent phases. The temperature dependence of the derived Δ S was analyzed thermodynamically to confirm the appearances of both the RMT and normal martensitic transformation. Detailed studies on the specific heat in martensite and parent phases at low temperatures were also conducted.

Phase transitions between lower and higher level management learning in times of crisis: an experimental study based on synergetics.

PubMed

Liening, Andreas; Strunk, Guido; Mittelstadt, Ewald

2013-10-01

Much has been written about the differences between single- and double-loop learning, or more general between lower level and higher level learning. Especially in times of a fundamental crisis, a transition between lower and higher level learning would be an appropriate reaction to a challenge coming entirely out of the dark. However, so far there is no quantitative method to monitor such a transition. Therefore we introduce theory and methods of synergetics and present results from an experimental study based on the simulation of a crisis within a business simulation game. Hypothesized critical fluctuations - as a marker for so-called phase transitions - have been assessed with permutation entropy. Results show evidence for a phase transition during the crisis, which can be interpreted as a transition between lower and higher level learning.

Reparametrization of Protein Force Field Nonbonded Interactions Guided by Osmotic Coefficient Measurements from Molecular Dynamics Simulations.

PubMed

Miller, Mark S; Lay, Wesley K; Li, Shuxiang; Hacker, William C; An, Jiadi; Ren, Jianlan; Elcock, Adrian H

2017-04-11

There is a small, but growing, body of literature describing the use of osmotic coefficient measurements to validate and reparametrize simulation force fields. Here we have investigated the ability of five very commonly used force field and water model combinations to reproduce the osmotic coefficients of seven neutral amino acids and five small molecules. The force fields tested include AMBER ff99SB-ILDN, CHARMM36, GROMOS54a7, and OPLS-AA, with the first of these tested in conjunction with the TIP3P and TIP4P-Ew water models. In general, for both the amino acids and the small molecules, the tested force fields produce computed osmotic coefficients that are lower than experiment; this is indicative of excessively favorable solute-solute interactions. The sole exception to this general trend is provided by GROMOS54a7 when applied to amino acids: in this case, the computed osmotic coefficients are consistently too high. Importantly, we show that all of the force fields tested can be made to accurately reproduce the experimental osmotic coefficients of the amino acids when minor modifications-some previously reported by others and some that are new to this study-are made to the van der Waals interactions of the charged terminal groups. Special care is required, however, when simulating Proline with a number of the force fields, and a hydroxyl-group specific modification is required in order to correct Serine and Threonine when simulated with AMBER ff99SB-ILDN. Interestingly, an alternative parametrization of the van der Waals interactions in the latter force field, proposed by the Nerenberg and Head-Gordon groups, is shown to immediately produce osmotic coefficients that are in excellent agreement with experiment. Overall, this study reinforces the idea that osmotic coefficient measurements can be used to identify general shortcomings in commonly used force fields' descriptions of solute-solute interactions and further demonstrates that modifications to van der Waals parameters provide a simple route to optimizing agreement with experiment.

Cosmological perturbations in inflation and in de Sitter space

NASA Astrophysics Data System (ADS)

Pimentel, Guilherme Leite

This thesis focuses on various aspects of inflationary fluctuations. First, we study gravitational wave fluctuations in de Sitter space. The isometries of the spacetime constrain to a few parameters the Wheeler-DeWitt wavefunctional of the universe, to cubic order in fluctuations. At cubic order, there are three independent terms in the wavefunctional. From the point of view of the bulk action, one term corresponds to Einstein gravity, and a new term comes from a cubic term in the curvature tensor. The third term is a pure phase and does not give rise to a new shape for expectation values of graviton fluctuations. These results can be seen as the leading order non-gaussian contributions in a slow-roll expansion for inflationary observables. We also use the wavefunctional approach to explain a universal consistency condition of n-point expectation values in single field inflation. This consistency condition relates a soft limit of an n-point expectation value to ( n-1)-point expectation values. We show how these conditions can be easily derived from the wavefunctional point of view. Namely, they follow from the momentum constraint of general relativity, which is equivalent to the constraint of spatial diffeomorphism invariance. We also study expectation values beyond tree level. We show that subhorizon fluctuations in loop diagrams do not generate a mass term for superhorizon fluctuations. Such a mass term could spoil the predictivity of inflation, which is based on the existence of properly defined field variables that become constant once their wavelength is bigger than the size of the horizon. Such a mass term would be seen in the two point expectation value as a contribution that grows linearly with time at late times. The absence of this mass term is closely related to the soft limits studied in previous chapters. It is analogous to the absence of a mass term for the photon in quantum electrodynamics, due to gauge symmetry. Finally, we use the tools of holography and entanglement entropy to study superhorizon correlations in quantum field theories in de Sitter space. The entropy has interesting terms that have no equivalent in flat space field theories. These new terms are due to particle creation in an expanding universe. The entropy is calculated directly for free massive scalar theories. For theories with holographic duals, it is determined by the area of some extremal surface in the bulk geometry. We calculate the entropy for different classes of holographic duals. For one of these classes, the holographic dual geometry is an asymptotically Anti-de Sitter space that decays into a crunching cosmology, an open Friedmann-Robertson-Walker universe. The extremal surface used in the calculation of the entropy lies almost entirely on the slice of maximal scale factor of the crunching cosmology.

Microcanonical entropy for classical systems

NASA Astrophysics Data System (ADS)

Franzosi, Roberto

2018-03-01

The entropy definition in the microcanonical ensemble is revisited. We propose a novel definition for the microcanonical entropy that resolve the debate on the correct definition of the microcanonical entropy. In particular we show that this entropy definition fixes the problem inherent the exact extensivity of the caloric equation. Furthermore, this entropy reproduces results which are in agreement with the ones predicted with standard Boltzmann entropy when applied to macroscopic systems. On the contrary, the predictions obtained with the standard Boltzmann entropy and with the entropy we propose, are different for small system sizes. Thus, we conclude that the Boltzmann entropy provides a correct description for macroscopic systems whereas extremely small systems should be better described with the entropy that we propose here.

On S-mixing entropy of quantum channels

NASA Astrophysics Data System (ADS)

Mukhamedov, Farrukh; Watanabe, Noboru

2018-06-01

In this paper, an S-mixing entropy of quantum channels is introduced as a generalization of Ohya's S-mixing entropy. We investigate several properties of the introduced entropy. Moreover, certain relations between the S-mixing entropy and the existing map and output entropies of quantum channels are investigated as well. These relations allowed us to find certain connections between separable states and the introduced entropy. Hence, there is a sufficient condition to detect entangled states. Moreover, several properties of the introduced entropy are investigated. Besides, entropies of qubit and phase-damping channels are calculated.

Entropy and equilibrium via games of complexity

NASA Astrophysics Data System (ADS)

Topsøe, Flemming

2004-09-01

It is suggested that thermodynamical equilibrium equals game theoretical equilibrium. Aspects of this thesis are discussed. The philosophy is consistent with maximum entropy thinking of Jaynes, but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical principle. The games introduced are based on measures of complexity. Entropy is viewed as minimal complexity. It is demonstrated that Tsallis entropy ( q-entropy) and Kaniadakis entropy ( κ-entropy) can be obtained in this way, based on suitable complexity measures. A certain unifying effect is obtained by embedding these measures in a two-parameter family of entropy functions.

Quantile based Tsallis entropy in residual lifetime

NASA Astrophysics Data System (ADS)

Khammar, A. H.; Jahanshahi, S. M. A.

2018-02-01

Tsallis entropy is a generalization of type α of the Shannon entropy, that is a nonadditive entropy unlike the Shannon entropy. Shannon entropy may be negative for some distributions, but Tsallis entropy can always be made nonnegative by choosing appropriate value of α. In this paper, we derive the quantile form of this nonadditive's entropy function in the residual lifetime, namely the residual quantile Tsallis entropy (RQTE) and get the bounds for it, depending on the Renyi's residual quantile entropy. Also, we obtain relationship between RQTE and concept of proportional hazards model in the quantile setup. Based on the new measure, we propose a stochastic order and aging classes, and study its properties. Finally, we prove characterizations theorems for some well known lifetime distributions. It is shown that RQTE uniquely determines the parent distribution unlike the residual Tsallis entropy.

Unitarity of spin-2 theories with linearized Weyl symmetry in D=2+1 dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dalmazi, D.

2009-10-15

Here we prove unitarity of the recently found fourth-order (in derivatives) self-dual model of spin-2 by investigating the analytic structure of its propagator. The model describes massive particles of helicity +2 (or -2) in D=2+1 dimensions and corresponds to the quadratic truncation of a higher derivative topologically massive gravity about a flat background. It is an intriguing example of a theory where a term in the propagator of the form 1/[{open_square}{sup 2}({open_square}-m{sup 2})] does not lead to ghosts. The crucial role of the linearized Weyl symmetry in getting rid of the ghosts is pointed out. We use a peculiar pairmore » of gauge conditions which fix the linearized reparametrizations and linearized Weyl symmetries separately.« less

Fine Grained Chaos in AdS2 Gravity

NASA Astrophysics Data System (ADS)

Haehl, Felix M.; Rozali, Moshe

2018-03-01

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u^*. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS2 ) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2 k -point functions, characterized as being both "maximally braided" and "k -out of time order," which exhibit exponential growth until progressively longer time scales u^*(k)˜(k -1 )u^*. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Fine Grained Chaos in AdS_{2} Gravity.

PubMed

Haehl, Felix M; Rozali, Moshe

2018-03-23

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u[over ^]_{*}. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS_{2}) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2k-point functions, characterized as being both "maximally braided" and "k-out of time order," which exhibit exponential growth until progressively longer time scales u[over ^]_{*}^{(k)}∼(k-1)u[over ^]_{*}. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Hamiltonian dynamics of extended objects

NASA Astrophysics Data System (ADS)

Capovilla, R.; Guven, J.; Rojas, E.

2004-12-01

We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler Lagrange equations.

Time-dependent entropy evolution in microscopic and macroscopic electromagnetic relaxation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker-Jarvis, James

This paper is a study of entropy and its evolution in the time and frequency domains upon application of electromagnetic fields to materials. An understanding of entropy and its evolution in electromagnetic interactions bridges the boundaries between electromagnetism and thermodynamics. The approach used here is a Liouville-based statistical-mechanical theory. I show that the microscopic entropy is reversible and the macroscopic entropy satisfies an H theorem. The spectral entropy development can be very useful for studying the frequency response of materials. Using a projection-operator based nonequilibrium entropy, different equations are derived for the entropy and entropy production and are applied tomore » the polarization, magnetization, and macroscopic fields. I begin by proving an exact H theorem for the entropy, progress to application of time-dependent entropy in electromagnetics, and then apply the theory to relevant applications in electromagnetics. The paper concludes with a discussion of the relationship of the frequency-domain form of the entropy to the permittivity, permeability, and impedance.« less

Entropy flow and entropy production in the human body in basal conditions.

PubMed

Aoki, I

1989-11-08

Entropy inflow and outflow for the naked human body in basal conditions in the respiration calorimeter due to infrared radiation, convection, evaporation of water and mass-flow are calculated by use of the energetic data obtained by Hardy & Du Bois. Also, the change of entropy content in the body is estimated. The entropy production in the human body is obtained as the change of entropy content minus the net entropy flow into the body. The entropy production thus calculated becomes positive. The magnitude of entropy production per effective radiating surface area does not show any significant variation with subjects. The entropy production is nearly constant at the calorimeter temperatures of 26-32 degrees C; the average in this temperature range is 0.172 J m-2 sec-1 K-1. The forced air currents around the human body and also clothing have almost no effect in changing the entropy production. Thus, the entropy production of the naked human body in basal conditions does not depend on its environmental factors.

Three faces of entropy for complex systems: Information, thermodynamics, and the maximum entropy principle

NASA Astrophysics Data System (ADS)

Thurner, Stefan; Corominas-Murtra, Bernat; Hanel, Rudolf

2017-09-01

There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, H (p ) =-∑ipilogpi . For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as SEXT for extensive entropy, SIT for the source information rate in information theory, and SMEP for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.

Multiwavelet packet entropy and its application in transmission line fault recognition and classification.

PubMed

Liu, Zhigang; Han, Zhiwei; Zhang, Yang; Zhang, Qiaoge

2014-11-01

Multiwavelets possess better properties than traditional wavelets. Multiwavelet packet transformation has more high-frequency information. Spectral entropy can be applied as an analysis index to the complexity or uncertainty of a signal. This paper tries to define four multiwavelet packet entropies to extract the features of different transmission line faults, and uses a radial basis function (RBF) neural network to recognize and classify 10 fault types of power transmission lines. First, the preprocessing and postprocessing problems of multiwavelets are presented. Shannon entropy and Tsallis entropy are introduced, and their difference is discussed. Second, multiwavelet packet energy entropy, time entropy, Shannon singular entropy, and Tsallis singular entropy are defined as the feature extraction methods of transmission line fault signals. Third, the plan of transmission line fault recognition using multiwavelet packet entropies and an RBF neural network is proposed. Finally, the experimental results show that the plan with the four multiwavelet packet energy entropies defined in this paper achieves better performance in fault recognition. The performance with SA4 (symmetric antisymmetric) multiwavelet packet Tsallis singular entropy is the best among the combinations of different multiwavelet packets and the four multiwavelet packet entropies.

Uniqueness and characterization theorems for generalized entropies

NASA Astrophysics Data System (ADS)

Enciso, Alberto; Tempesta, Piergiulio

2017-12-01

The requirement that an entropy function be composable is key: it means that the entropy of a compound system can be calculated in terms of the entropy of its independent components. We prove that, under mild regularity assumptions, the only composable generalized entropy in trace form is the Tsallis one-parameter family (which contains Boltzmann-Gibbs as a particular case). This result leads to the use of generalized entropies that are not of trace form, such as Rényi’s entropy, in the study of complex systems. In this direction, we also present a characterization theorem for a large class of composable non-trace-form entropy functions with features akin to those of Rényi’s entropy.

Experimental heat capacities, excess entropies, and magnetic properties of bulk and nano Fe3O4-Co3O4 and Fe3O4-Mn3O4 spinel solid solutions

NASA Astrophysics Data System (ADS)

Schliesser, Jacob M.; Huang, Baiyu; Sahu, Sulata K.; Asplund, Megan; Navrotsky, Alexandra; Woodfield, Brian F.

2018-03-01

We have measured the heat capacities of several well-characterized bulk and nanophase Fe3O4-Co3O4 and Fe3O4-Mn3O4 spinel solid solution samples from which magnetic properties of transitions and third-law entropies have been determined. The magnetic transitions show several features common to effects of particle and magnetic domain sizes. From the standard molar entropies, excess entropies of mixing have been generated for these solid solutions and compared with configurational entropies determined previously by assuming appropriate cation and valence distributions. The vibrational and magnetic excess entropies for bulk materials are comparable in magnitude to the respective configurational entropies indicating that excess entropies of mixing must be included when analyzing entropies of mixing. The excess entropies for nanophase materials are even larger than the configurational entropies. Changes in valence, cation distribution, bonding and microstructure between the mixing ions are the likely sources of the positive excess entropies of mixing.

Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: a basis for q-exponential distributions.

PubMed

Abe, Sumiyoshi

2002-10-01

The q-exponential distributions, which are generalizations of the Zipf-Mandelbrot power-law distribution, are frequently encountered in complex systems at their stationary states. From the viewpoint of the principle of maximum entropy, they can apparently be derived from three different generalized entropies: the Rényi entropy, the Tsallis entropy, and the normalized Tsallis entropy. Accordingly, mere fittings of observed data by the q-exponential distributions do not lead to identification of the correct physical entropy. Here, stabilities of these entropies, i.e., their behaviors under arbitrary small deformation of a distribution, are examined. It is shown that, among the three, the Tsallis entropy is stable and can provide an entropic basis for the q-exponential distributions, whereas the others are unstable and cannot represent any experimentally observable quantities.

On the entropy variation in the scenario of entropic gravity

NASA Astrophysics Data System (ADS)

Xiao, Yong; Bai, Shi-Yang

2018-05-01

In the scenario of entropic gravity, entropy varies as a function of the location of the matter, while the tendency to increase entropy appears as gravity. We concentrate on studying the entropy variation of a typical gravitational system with different relative positions between the mass and the gravitational source. The result is that the entropy of the system doesn't increase when the mass is displaced closer to the gravitational source. In this way it disproves the proposal of entropic gravity from thermodynamic entropy. It doesn't exclude the possibility that gravity originates from non-thermodynamic entropy like entanglement entropy.

Entropy and climate. I - ERBE observations of the entropy production of the earth

NASA Technical Reports Server (NTRS)

Stephens, G. L.; O'Brien, D. M.

1993-01-01

An approximate method for estimating the global distributions of the entropy fluxes flowing through the upper boundary of the climate system is introduced, and an estimate of the entropy exchange between the earth and space and the entropy production of the planet is provided. Entropy fluxes calculated from the Earth Radiation Budget Experiment measurements show how the long-wave entropy flux densities dominate the total entropy fluxes at all latitudes compared with the entropy flux densities associated with reflected sunlight, although the short-wave flux densities are important in the context of clear sky-cloudy sky net entropy flux differences. It is suggested that the entropy production of the planet is both constant for the 36 months of data considered and very near its maximum possible value. The mean value of this production is 0.68 x 10 exp 15 W/K, and the amplitude of the annual cycle is approximately 1 to 2 percent of this value.

Logarithmic black hole entropy corrections and holographic Rényi entropy

NASA Astrophysics Data System (ADS)

Mahapatra, Subhash

2018-01-01

The entanglement and Rényi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Rényi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order GD^0. The entropic c-function and the inequalities of the Rényi entropy are also satisfied even with the correction terms.

Maximum Relative Entropy of Coherence: An Operational Coherence Measure.

PubMed

Bu, Kaifeng; Singh, Uttam; Fei, Shao-Ming; Pati, Arun Kumar; Wu, Junde

2017-10-13

The operational characterization of quantum coherence is the cornerstone in the development of the resource theory of coherence. We introduce a new coherence quantifier based on maximum relative entropy. We prove that the maximum relative entropy of coherence is directly related to the maximum overlap with maximally coherent states under a particular class of operations, which provides an operational interpretation of the maximum relative entropy of coherence. Moreover, we show that, for any coherent state, there are examples of subchannel discrimination problems such that this coherent state allows for a higher probability of successfully discriminating subchannels than that of all incoherent states. This advantage of coherent states in subchannel discrimination can be exactly characterized by the maximum relative entropy of coherence. By introducing a suitable smooth maximum relative entropy of coherence, we prove that the smooth maximum relative entropy of coherence provides a lower bound of one-shot coherence cost, and the maximum relative entropy of coherence is equivalent to the relative entropy of coherence in the asymptotic limit. Similar to the maximum relative entropy of coherence, the minimum relative entropy of coherence has also been investigated. We show that the minimum relative entropy of coherence provides an upper bound of one-shot coherence distillation, and in the asymptotic limit the minimum relative entropy of coherence is equivalent to the relative entropy of coherence.

The Dynameomics Entropy Dictionary: A Large-Scale Assessment of Conformational Entropy across Protein Fold Space.

PubMed

Towse, Clare-Louise; Akke, Mikael; Daggett, Valerie

2017-04-27

Molecular dynamics (MD) simulations contain considerable information with regard to the motions and fluctuations of a protein, the magnitude of which can be used to estimate conformational entropy. Here we survey conformational entropy across protein fold space using the Dynameomics database, which represents the largest existing data set of protein MD simulations for representatives of essentially all known protein folds. We provide an overview of MD-derived entropies accounting for all possible degrees of dihedral freedom on an unprecedented scale. Although different side chains might be expected to impose varying restrictions on the conformational space that the backbone can sample, we found that the backbone entropy and side chain size are not strictly coupled. An outcome of these analyses is the Dynameomics Entropy Dictionary, the contents of which have been compared with entropies derived by other theoretical approaches and experiment. As might be expected, the conformational entropies scale linearly with the number of residues, demonstrating that conformational entropy is an extensive property of proteins. The calculated conformational entropies of folding agree well with previous estimates. Detailed analysis of specific cases identifies deviations in conformational entropy from the average values that highlight how conformational entropy varies with sequence, secondary structure, and tertiary fold. Notably, α-helices have lower entropy on average than do β-sheets, and both are lower than coil regions.

Implementing Nonlinear Feedback Controllers Using DNA Strand Displacement Reactions.

PubMed

Sawlekar, Rucha; Montefusco, Francesco; Kulkarni, Vishwesh V; Bates, Declan G

2016-07-01

We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions and implemented via DNA strand displacement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, enthalpy/entropy driven DNA reactions using a toehold mediated strand displacement mechanism via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs.

Maxwell's demon in biochemical signal transduction with feedback loop

PubMed Central

Ito, Sosuke; Sagawa, Takahiro

2015-01-01

Signal transduction in living cells is vital to maintain life itself, where information transfer in noisy environment plays a significant role. In a rather different context, the recent intensive research on ‘Maxwell's demon'—a feedback controller that utilizes information of individual molecules—have led to a unified theory of information and thermodynamics. Here we combine these two streams of research, and show that the second law of thermodynamics with information reveals the fundamental limit of the robustness of signal transduction against environmental fluctuations. Especially, we find that the degree of robustness is quantitatively characterized by an informational quantity called transfer entropy. Our information-thermodynamic approach is applicable to biological communication inside cells, in which there is no explicit channel coding in contrast to artificial communication. Our result could open up a novel biophysical approach to understand information processing in living systems on the basis of the fundamental information–thermodynamics link. PMID:26099556

Fluctuation relations and Maxwell's demon in a circuit QED setup

NASA Astrophysics Data System (ADS)

Nakamura, Yasunobu

The recent progress in information thermodynamics has resolved the paradox of Maxwell's demon and clarified the relationship between the information and the entropy. Its extension to quantum mechanical systems has also attracted much interest, and experimental demonstrations are awaited. Circuit QED systems offer the following tools suitable for investigating the properties of a quantum system coupled with a controlled environment: (i) a well-controlled qubit with a long coherence time, (ii) dispersive readout allowing high-fidelity quantum nondemolition measurement, and (iii) fast feedback control. We first apply the so-called two-measurement protocol (TMP) to a superconducting transmon qubit in a microwave cavity and study how the decoherence affects the nonequilibrium thermodynamic relations. Next, we implement Maxwell's demon in the circuit QED system by introducing a feedback loop and confirm the fluctuation relation including the effect of the information obtained in the feedback process. These results constitute a first step towards quantum thermodynamics in circuit QED systems.

Hawking radiation due to photon and gravitino tunneling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Majhi, Bibhas Ranjan, E-mail: bibhas@bose.res.i; Samanta, Saurav, E-mail: srvsmnt@gmail.co

2010-11-15

Applying the Hamilton-Jacobi method we investigate the tunneling of photon across the event horizon of a static spherically symmetric black hole. The necessity of the gauge condition on the photon field, to derive the semiclassical Hawking temperature, is explicitly shown. Also, the tunneling of photon and gravitino beyond this semiclassical approximation are presented separately. Quantum corrections of the action for both cases are found to be proportional to the semiclassical contribution. Modifications to the Hawking temperature and Bekenstein-Hawking area law are thereby obtained. Using this corrected temperature and Hawking's periodicity argument, the modified metric for the Schwarzschild black hole ismore » given. This corrected version of the metric, up to h order is equivalent to the metric obtained by including one loop back reaction effect. Finally, the coefficient of the leading order correction of entropy is shown to be related to the trace anomaly.« less

Small black holes and near-extremal CFTs

DOE PAGES

Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; ...

2016-08-02

Pure theories of AdS 3 quantum gravity are conjectured to be dual to CFTs with sparse spectra of light primary operators. The sparsest possible spectrum consistent with modular invariance includes only black hole states above the vacuum. Witten conjectured the existence of a family of extremal CFTs, which realize this spectrum for all admissible values of the central charge. We consider the quantum corrections to the classical spectrum, and propose a specific modification of Witten’s conjecture which takes into account the existence of “small” black hole states. These have zero classical horizon area, with a calculable entropy attributed solely tomore » loop effects. Lastly, our conjecture passes various consistency checks, especially when generalized to include theories with supersymmetry. In theories with N = 2 supersymmetry, this “near-extremal CFT” proposal precisely evades the no-go results of Gaberdiel et al.« less

Double symbolic joint entropy in nonlinear dynamic complexity analysis

NASA Astrophysics Data System (ADS)

Yao, Wenpo; Wang, Jun

2017-07-01

Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.

Effect of entropy on anomalous transport in ITG-modes of magneto-plasma

NASA Astrophysics Data System (ADS)

Yaqub Khan, M.; Qaiser Manzoor, M.; Haq, A. ul; Iqbal, J.

2017-04-01

The ideal gas equation and S={{c}v}log ≤ft(P/ρ \\right) (where S is entropy, P is pressure and ρ is the mass density) define the interconnection of entropy with the temperature and density of plasma. Therefore, different phenomena relating to plasma and entropy need to be investigated. By employing the Braginskii transport equations for a nonuniform electron-ion magnetoplasma, two new parameters—the entropy distribution function and the entropy gradient drift—are defined, a new dispersion relation is obtained, and the dependence of anomalous transport on entropy is also proved. Some results, like monotonicity, the entropy principle and the second law of thermodynamics, are proved with a new definition of entropy. This work will open new horizons in fusion processes, not only by controlling entropy in tokamak plasmas—particularly in the pedestal regions of the H-mode and space plasmas—but also in engineering sciences.

Quantifying and minimizing entropy generation in AMTEC cells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hendricks, T.J.; Huang, C.

1997-12-31

Entropy generation in an AMTEC cell represents inherent power loss to the AMTEC cell. Minimizing cell entropy generation directly maximizes cell power generation and efficiency. An internal project is on-going at AMPS to identify, quantify and minimize entropy generation mechanisms within an AMTEC cell, with the goal of determining cost-effective design approaches for maximizing AMTEC cell power generation. Various entropy generation mechanisms have been identified and quantified. The project has investigated several cell design techniques in a solar-driven AMTEC system to minimize cell entropy generation and produce maximum power cell designs. In many cases, various sources of entropy generation aremore » interrelated such that minimizing entropy generation requires cell and system design optimization. Some of the tradeoffs between various entropy generation mechanisms are quantified and explained and their implications on cell design are discussed. The relationship between AMTEC cell power and efficiency and entropy generation is presented and discussed.« less

Thermodynamic and Differential Entropy under a Change of Variables

PubMed Central

Hnizdo, Vladimir; Gilson, Michael K.

2013-01-01

The differential Shannon entropy of information theory can change under a change of variables (coordinates), but the thermodynamic entropy of a physical system must be invariant under such a change. This difference is puzzling, because the Shannon and Gibbs entropies have the same functional form. We show that a canonical change of variables can, indeed, alter the spatial component of the thermodynamic entropy just as it alters the differential Shannon entropy. However, there is also a momentum part of the entropy, which turns out to undergo an equal and opposite change when the coordinates are transformed, so that the total thermodynamic entropy remains invariant. We furthermore show how one may correctly write the change in total entropy for an isothermal physical process in any set of spatial coordinates. PMID:24436633

Entropy for Mechanically Vibrating Systems

NASA Astrophysics Data System (ADS)

Tufano, Dante

The research contained within this thesis deals with the subject of entropy as defined for and applied to mechanically vibrating systems. This work begins with an overview of entropy as it is understood in the fields of classical thermodynamics, information theory, statistical mechanics, and statistical vibroacoustics. Khinchin's definition of entropy, which is the primary definition used for the work contained in this thesis, is introduced in the context of vibroacoustic systems. The main goal of this research is to to establish a mathematical framework for the application of Khinchin's entropy in the field of statistical vibroacoustics by examining the entropy context of mechanically vibrating systems. The introduction of this thesis provides an overview of statistical energy analysis (SEA), a modeling approach to vibroacoustics that motivates this work on entropy. The objective of this thesis is given, and followed by a discussion of the intellectual merit of this work as well as a literature review of relevant material. Following the introduction, an entropy analysis of systems of coupled oscillators is performed utilizing Khinchin's definition of entropy. This analysis develops upon the mathematical theory relating to mixing entropy, which is generated by the coupling of vibroacoustic systems. The mixing entropy is shown to provide insight into the qualitative behavior of such systems. Additionally, it is shown that the entropy inequality property of Khinchin's entropy can be reduced to an equality using the mixing entropy concept. This equality can be interpreted as a facet of the second law of thermodynamics for vibroacoustic systems. Following this analysis, an investigation of continuous systems is performed using Khinchin's entropy. It is shown that entropy analyses using Khinchin's entropy are valid for continuous systems that can be decomposed into a finite number of modes. The results are shown to be analogous to those obtained for simple oscillators, which demonstrates the applicability of entropy-based approaches to real-world systems. Three systems are considered to demonstrate these findings: 1) a rod end-coupled to a simple oscillator, 2) two end-coupled rods, and 3) two end-coupled beams. The aforementioned work utilizes the weak coupling assumption to determine the entropy of composite systems. Following this discussion, a direct method of finding entropy is developed which does not rely on this limiting assumption. The resulting entropy provides a useful benchmark for evaluating the accuracy of the weak coupling approach, and is validated using systems of coupled oscillators. The later chapters of this work discuss Khinchin's entropy as applied to nonlinear and nonconservative systems, respectively. The discussion of entropy for nonlinear systems is motivated by the desire to expand the applicability of SEA techniques beyond the linear regime. The discussion of nonconservative systems is also crucial, since real-world systems interact with their environment, and it is necessary to confirm the validity of an entropy approach for systems that are relevant in the context of SEA. Having developed a mathematical framework for determining entropy under a number of previously unexplored cases, the relationship between thermodynamics and statistical vibroacoustics can be better understood. Specifically, vibroacoustic temperatures can be obtained for systems that are not necessarily linear or weakly coupled. In this way, entropy provides insight into how the power flow proportionality of statistical energy analysis (SEA) can be applied to a broader class of vibroacoustic systems. As such, entropy is a useful tool for both justifying and expanding the foundational results of SEA.

Entropy is more resistant to artifacts than bispectral index in brain-dead organ donors.

PubMed

Wennervirta, Johanna; Salmi, Tapani; Hynynen, Markku; Yli-Hankala, Arvi; Koivusalo, Anna-Maria; Van Gils, Mark; Pöyhiä, Reino; Vakkuri, Anne

2007-01-01

To evaluate the usefulness of entropy and the bispectral index (BIS) in brain-dead subjects. A prospective, open, nonselective, observational study in the university hospital. 16 brain-dead organ donors. Time-domain electroencephalography (EEG), spectral entropy of the EEG, and BIS were recorded during solid organ harvest. State entropy differed significantly from 0 (isoelectric EEG) 28%, response entropy 29%, and BIS 68% of the total recorded time. The median values during the operation were state entropy 0.0, response entropy 0.0, and BIS 3.0. In four of 16 organ donors studied the EEG was not isoelectric, and nonreactive rhythmic activity was noted in time-domain EEG. After excluding the results from subjects with persistent residual EEG activity state entropy, response entropy, and BIS values differed from zero 17%, 18%, and 62% of the recorded time, respectively. Median values were 0.0, 0.0, and 2.0 for state entropy, response entropy, and BIS, respectively. The highest index values in entropy and BIS monitoring were recorded without neuromuscular blockade. The main sources of artifacts were electrocauterization, 50-Hz artifact, handling of the donor, ballistocardiography, electromyography, and electrocardiography. Both entropy and BIS showed nonzero values due to artifacts after brain death diagnosis. BIS was more liable to artifacts than entropy. Neither of these indices are diagnostic tools, and care should be taken when interpreting EEG and EEG-derived indices in the evaluation of brain death.

Mathematical investigations of branch length similarity entropy profiles of shapes for various resolutions

NASA Astrophysics Data System (ADS)

Jeon, Wonju; Lee, Sang-Hee

2012-12-01

In our previous study, we defined the branch length similarity (BLS) entropy for a simple network consisting of a single node and numerous branches. As the first application of this entropy to characterize shapes, the BLS entropy profiles of 20 battle tank shapes were calculated from simple networks created by connecting pixels in the boundary of the shape. The profiles successfully characterized the tank shapes through a comparison of their BLS entropy profiles. Following the application, this entropy was used to characterize human's emotional faces, such as happiness and sad, and to measure the degree of complexity for termite tunnel networks. These applications indirectly indicate that the BLS entropy profile can be a useful tool to characterize networks and shapes. However, the ability of the BLS entropy in the characterization depends on the image resolution because the entropy is determined by the number of nodes for the boundary of a shape. Higher resolution means more nodes. If the entropy is to be widely used in the scientific community, the effect of the resolution on the entropy profile should be understood. In the present study, we mathematically investigated the BLS entropy profile of a shape with infinite resolution and numerically investigated the variation in the pattern of the entropy profile caused by changes in the resolution change in the case of finite resolution.

A diameter-sensitive flow entropy method for reliability consideration in water distribution system design

NASA Astrophysics Data System (ADS)

Liu, Haixing; Savić, Dragan; Kapelan, Zoran; Zhao, Ming; Yuan, Yixing; Zhao, Hongbin

2014-07-01

Flow entropy is a measure of uniformity of pipe flows in water distribution systems. By maximizing flow entropy one can identify reliable layouts or connectivity in networks. In order to overcome the disadvantage of the common definition of flow entropy that does not consider the impact of pipe diameter on reliability, an extended definition of flow entropy, termed as diameter-sensitive flow entropy, is proposed. This new methodology is then assessed by using other reliability methods, including Monte Carlo Simulation, a pipe failure probability model, and a surrogate measure (resilience index) integrated with water demand and pipe failure uncertainty. The reliability assessment is based on a sample of WDS designs derived from an optimization process for each of the two benchmark networks. Correlation analysis is used to evaluate quantitatively the relationship between entropy and reliability. To ensure reliability, a comparative analysis between the flow entropy and the new method is conducted. The results demonstrate that the diameter-sensitive flow entropy shows consistently much stronger correlation with the three reliability measures than simple flow entropy. Therefore, the new flow entropy method can be taken as a better surrogate measure for reliability and could be potentially integrated into the optimal design problem of WDSs. Sensitivity analysis results show that the velocity parameters used in the new flow entropy has no significant impact on the relationship between diameter-sensitive flow entropy and reliability.

Entropy generation of nanofluid flow in a microchannel heat sink

NASA Astrophysics Data System (ADS)

Manay, Eyuphan; Akyürek, Eda Feyza; Sahin, Bayram

2018-06-01

Present study aims to investigate the effects of the presence of nano sized TiO2 particles in the base fluid on entropy generation rate in a microchannel heat sink. Pure water was chosen as base fluid, and TiO2 particles were suspended into the pure water in five different particle volume fractions of 0.25%, 0.5%, 1.0%, 1.5% and 2.0%. Under laminar, steady state flow and constant heat flux boundary conditions, thermal, frictional, total entropy generation rates and entropy generation number ratios of nanofluids were experimentally analyzed in microchannel flow for different channel heights of 200 μm, 300 μm, 400 μm and 500 μm. It was observed that frictional and total entropy generation rates increased as thermal entropy generation rate were decreasing with an increase in particle volume fraction. In microchannel flows, thermal entropy generation could be neglected due to its too low rate smaller than 1.10e-07 in total entropy generation. Higher channel heights caused higher thermal entropy generation rates, and increasing channel height yielded an increase from 30% to 52% in thermal entropy generation. When channel height decreased, an increase of 66%-98% in frictional entropy generation was obtained. Adding TiO2 nanoparticles into the base fluid caused thermal entropy generation to decrease about 1.8%-32.4%, frictional entropy generation to increase about 3.3%-21.6%.

Entropy and entropy production in Fokker–Plank equation under the generalized fluctuation–dissipation relation

NASA Astrophysics Data System (ADS)

Guo, Ran

2018-04-01

In this paper, we investigate the definition of the entropy in the Fokker–Planck equation under the generalized fluctuation–dissipation relation (FDR), which describes a Brownian particle moving in a complex medium with friction and multiplicative noise. The friction and the noise are related by the generalized FDR. The entropy for such a system is defined first. According to the definition of the entropy, we calculate the entropy production and the entropy flux. Lastly, we make a numerical calculation to display the results in figures.

Single water entropy: hydrophobic crossover and application to drug binding.

PubMed

Sasikala, Wilbee D; Mukherjee, Arnab

2014-09-11

Entropy of water plays an important role in both chemical and biological processes e.g. hydrophobic effect, molecular recognition etc. Here we use a new approach to calculate translational and rotational entropy of the individual water molecules around different hydrophobic and charged solutes. We show that for small hydrophobic solutes, the translational and rotational entropies of each water molecule increase as a function of its distance from the solute reaching finally to a constant bulk value. As the size of the solute increases (0.746 nm), the behavior of the translational entropy is opposite; water molecules closest to the solute have higher entropy that reduces with distance from the solute. This indicates that there is a crossover in translational entropy of water molecules around hydrophobic solutes from negative to positive values as the size of the solute is increased. Rotational entropy of water molecules around hydrophobic solutes for all sizes increases with distance from the solute, indicating the absence of crossover in rotational entropy. This makes the crossover in total entropy (translation + rotation) of water molecule happen at much larger size (>1.5 nm) for hydrophobic solutes. Translational entropy of single water molecule scales logarithmically (Str(QH) = C + kB ln V), with the volume V obtained from the ellipsoid of inertia. We further discuss the origin of higher entropy of water around water and show the possibility of recovering the entropy loss of some hypothetical solutes. The results obtained are helpful to understand water entropy behavior around various hydrophobic and charged environments within biomolecules. Finally, we show how our approach can be used to calculate the entropy of the individual water molecules in a protein cavity that may be replaced during ligand binding.

RNA Thermodynamic Structural Entropy

PubMed Central

Garcia-Martin, Juan Antonio; Clote, Peter

2015-01-01

Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner’99 and Turner’04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http://bioinformatics.bc.edu/clotelab/RNAentropy, including source code and ancillary programs. PMID:26555444

RNA Thermodynamic Structural Entropy.

PubMed

Garcia-Martin, Juan Antonio; Clote, Peter

2015-01-01

Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner'99 and Turner'04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http://bioinformatics.bc.edu/clotelab/RNAentropy, including source code and ancillary programs.

Relating different quantum generalizations of the conditional Rényi entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tomamichel, Marco; School of Physics, The University of Sydney, Sydney 2006; Berta, Mario

2014-08-15

Recently a new quantum generalization of the Rényi divergence and the corresponding conditional Rényi entropies was proposed. Here, we report on a surprising relation between conditional Rényi entropies based on this new generalization and conditional Rényi entropies based on the quantum relative Rényi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Rényi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Rényi entropies and derive a new entropicmore » uncertainty relation.« less

Exact analytical thermodynamic expressions for a Brownian heat engine

NASA Astrophysics Data System (ADS)

Taye, Mesfin Asfaw

2015-09-01

The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time t . Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we find exact closed form expressions for the free energy, the rate of entropy production, and the rate of entropy flow from the system to the outside. We show that when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In the long time limit, the rate of entropy production balances the rate of entropy extraction, and at equilibrium both entropy production and extraction rates become zero. Furthermore, via the present model, many thermodynamic theories can be checked.

Exact analytical thermodynamic expressions for a Brownian heat engine.

PubMed

Taye, Mesfin Asfaw

2015-09-01

The nonequilibrium thermodynamics feature of a Brownian motor operating between two different heat baths is explored as a function of time t. Using the Gibbs entropy and Schnakenberg microscopic stochastic approach, we find exact closed form expressions for the free energy, the rate of entropy production, and the rate of entropy flow from the system to the outside. We show that when the system is out of equilibrium, it constantly produces entropy and at the same time extracts entropy out of the system. Its entropy production and extraction rates decrease in time and saturate to a constant value. In the long time limit, the rate of entropy production balances the rate of entropy extraction, and at equilibrium both entropy production and extraction rates become zero. Furthermore, via the present model, many thermodynamic theories can be checked.

Modeling the Overalternating Bias with an Asymmetric Entropy Measure

PubMed Central

Gronchi, Giorgio; Raglianti, Marco; Noventa, Stefano; Lazzeri, Alessandro; Guazzini, Andrea

2016-01-01

Psychological research has found that human perception of randomness is biased. In particular, people consistently show the overalternating bias: they rate binary sequences of symbols (such as Heads and Tails in coin flipping) with an excess of alternation as more random than prescribed by the normative criteria of Shannon's entropy. Within data mining for medical applications, Marcellin proposed an asymmetric measure of entropy that can be ideal to account for such bias and to quantify subjective randomness. We fitted Marcellin's entropy and Renyi's entropy (a generalized form of uncertainty measure comprising many different kinds of entropies) to experimental data found in the literature with the Differential Evolution algorithm. We observed a better fit for Marcellin's entropy compared to Renyi's entropy. The fitted asymmetric entropy measure also showed good predictive properties when applied to different datasets of randomness-related tasks. We concluded that Marcellin's entropy can be a parsimonious and effective measure of subjective randomness that can be useful in psychological research about randomness perception. PMID:27458418

Entropy for the Complexity of Physiological Signal Dynamics.

PubMed

Zhang, Xiaohua Douglas

2017-01-01

Recently, the rapid development of large data storage technologies, mobile network technology, and portable medical devices makes it possible to measure, record, store, and track analysis of biological dynamics. Portable noninvasive medical devices are crucial to capture individual characteristics of biological dynamics. The wearable noninvasive medical devices and the analysis/management of related digital medical data will revolutionize the management and treatment of diseases, subsequently resulting in the establishment of a new healthcare system. One of the key features that can be extracted from the data obtained by wearable noninvasive medical device is the complexity of physiological signals, which can be represented by entropy of biological dynamics contained in the physiological signals measured by these continuous monitoring medical devices. Thus, in this chapter I present the major concepts of entropy that are commonly used to measure the complexity of biological dynamics. The concepts include Shannon entropy, Kolmogorov entropy, Renyi entropy, approximate entropy, sample entropy, and multiscale entropy. I also demonstrate an example of using entropy for the complexity of glucose dynamics.

Information Entropy Analysis of the H1N1 Genetic Code

NASA Astrophysics Data System (ADS)

Martwick, Andy

2010-03-01

During the current H1N1 pandemic, viral samples are being obtained from large numbers of infected people world-wide and are being sequenced on the NCBI Influenza Virus Resource Database. The information entropy of the sequences was computed from the probability of occurrence of each nucleotide base at every position of each set of sequences using Shannon's definition of information entropy, [ H=∑bpb,2( 1pb ) ] where H is the observed information entropy at each nucleotide position and pb is the probability of the base pair of the nucleotides A, C, G, U. Information entropy of the current H1N1 pandemic is compared to reference human and swine H1N1 entropy. As expected, the current H1N1 entropy is in a low entropy state and has a very large mutation potential. Using the entropy method in mature genes we can identify low entropy regions of nucleotides that generally correlate to critical protein function.

Generalized Entanglement Entropy and Holography

NASA Astrophysics Data System (ADS)

Obregón, O.

2018-04-01

A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ 2) distribution that depends on β and also on pl . The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2dCFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV (for c = 1) ones and also than those due to the area dependent AdS 3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu-Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS 3 area dependent entropy.

Quench action and Rényi entropies in integrable systems

NASA Astrophysics Data System (ADS)

Alba, Vincenzo; Calabrese, Pasquale

2017-09-01

Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the nonequilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary thermodynamic entropy is the von Neumann entanglement entropy of a large subsystem embedded in an infinite system. Also motivated by cold-atom experiments, here we consider the generalization to Rényi entropies. We develop a new technique to calculate the diagonal Rényi entropy in the quench action formalism. In the spirit of the replica treatment for the entanglement entropy, the diagonal Rényi entropies are generalized free energies evaluated over a thermodynamic macrostate which depends on the Rényi index and, in particular, is not the same state describing von Neumann entropy. The technical reason for this perhaps surprising result is that the evaluation of the moments of the diagonal density matrix shifts the saddle point of the quench action. An interesting consequence is that different Rényi entropies encode information about different regions of the spectrum of the postquench Hamiltonian. Our approach provides a very simple proof of the long-standing issue that, for integrable systems, the diagonal entropy is half of the thermodynamic one and it allows us to generalize this result to the case of arbitrary Rényi entropy.

Radiative entropy generation in a gray absorbing, emitting, and scattering planar medium at radiative equilibrium

NASA Astrophysics Data System (ADS)

Sadeghi, Pegah; Safavinejad, Ali

2017-11-01

Radiative entropy generation through a gray absorbing, emitting, and scattering planar medium at radiative equilibrium with diffuse-gray walls is investigated. The radiative transfer equation and radiative entropy generation equations are solved using discrete ordinates method. Components of the radiative entropy generation are considered for two different boundary conditions: two walls are at a prescribed temperature and mixed boundary conditions, which one wall is at a prescribed temperature and the other is at a prescribed heat flux. The effect of wall emissivities, optical thickness, single scattering albedo, and anisotropic-scattering factor on the entropy generation is attentively investigated. The results reveal that entropy generation in the system mainly arises from irreversible radiative transfer at wall with lower temperature. Total entropy generation rate for the system with prescribed temperature at walls remarkably increases as wall emissivity increases; conversely, for system with mixed boundary conditions, total entropy generation rate slightly decreases. Furthermore, as the optical thickness increases, total entropy generation rate remarkably decreases for the system with prescribed temperature at walls; nevertheless, for the system with mixed boundary conditions, total entropy generation rate increases. The variation of single scattering albedo does not considerably affect total entropy generation rate. This parametric analysis demonstrates that the optical thickness and wall emissivities have a significant effect on the entropy generation in the system at radiative equilibrium. Considering the parameters affecting radiative entropy generation significantly, provides an opportunity to optimally design or increase overall performance and efficiency by applying entropy minimization techniques for the systems at radiative equilibrium.

Efficient Verification of Holograms Using Mobile Augmented Reality.

PubMed

Hartl, Andreas Daniel; Arth, Clemens; Grubert, Jens; Schmalstieg, Dieter

2016-07-01

Paper documents such as passports, visas and banknotes are frequently checked by inspection of security elements. In particular, optically variable devices such as holograms are important, but difficult to inspect. Augmented Reality can provide all relevant information on standard mobile devices. However, hologram verification on mobiles still takes long and provides lower accuracy than inspection by human individuals using appropriate reference information. We aim to address these drawbacks by automatic matching combined with a special parametrization of an efficient goal-oriented user interface which supports constrained navigation. We first evaluate a series of similarity measures for matching hologram patches to provide a sound basis for automatic decisions. Then a re-parametrized user interface is proposed based on observations of typical user behavior during document capture. These measures help to reduce capture time to approximately 15 s with better decisions regarding the evaluated samples than what can be achieved by untrained users.

Elementary Particles and the Universe

NASA Astrophysics Data System (ADS)

Schwarz, John H.

2005-07-01

1. Excess baggage J. Hartle; 2. Through the clouds E. Witten; 3. Covariant foundations of the superparticle L. Brink; 4. Chiral symmetry and confinement T. Goldman; 5. The original fifth interaction Y. Neeman; 6. The mass hierarchy of leptons and quarks H. Fritzsch; 7. Spacetime duality in string theory J. H. Schwarz; 8. Symmetry and quasi-symmetry Y. Nambu; 9. On an exceptional non-associative superspace M. Gunaydin; 10. Algebra of reparametrization-invariant and normal ordered operators in open string field theory P. Ramond; 11. Superconductivity of an ideal charged boson system T. D. Lee; 12. Some remarks on the symmetry approach to nuclear rotational motion L. C. Biedebharn and P. Truini; 13. Uncomputability, intractability and the efficiency of heat engines S. Lloyd; 14. The new mathematical physics I. Singer; 15. For the birds V. Telegdi; 16. Gell-Mann's approach to physics A. Salam; 17. Remarks M. Goldberger.

Aging dynamics of quantum spin glasses of rotors

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio; Ye, Jinwu

2001-12-01

We study the long time dynamics of quantum spin glasses of rotors using the nonequilibrium Schwinger-Keldysh formalism. These models are known to have a quantum phase transition from a paramagnetic to a spin-glass phase, which we approach by looking at the divergence of the spin-relaxation rate at the transition point. In the aging regime, we determine the dynamical equations governing the time evolution of the spin response and correlation functions, and show that all terms in the equations that arise solely from quantum effects are irrelevant at long times under time reparametrization group (RPG) transformations. At long times, quantum effects enter only through the renormalization of the parameters in the dynamical equations for the classical counterpart of the rotor model. Consequently, quantum effects only modify the out-of-equilibrium fluctuation-dissipation relation (OEFDR), i.e. the ratio X between the temperature and the effective temperature, but not the form of the classical OEFDR.

Riemannian geometric approach to human arm dynamics, movement optimization, and invariance

NASA Astrophysics Data System (ADS)

Biess, Armin; Flash, Tamar; Liebermann, Dario G.

2011-03-01

We present a generally covariant formulation of human arm dynamics and optimization principles in Riemannian configuration space. We extend the one-parameter family of mean-squared-derivative (MSD) cost functionals from Euclidean to Riemannian space, and we show that they are mathematically identical to the corresponding dynamic costs when formulated in a Riemannian space equipped with the kinetic energy metric. In particular, we derive the equivalence of the minimum-jerk and minimum-torque change models in this metric space. Solutions of the one-parameter family of MSD variational problems in Riemannian space are given by (reparametrized) geodesic paths, which correspond to movements with least muscular effort. Finally, movement invariants are derived from symmetries of the Riemannian manifold. We argue that the geometrical structure imposed on the arm’s configuration space may provide insights into the emerging properties of the movements generated by the motor system.

Massless spinning particle and null-string on AdS d : projective-space approach

NASA Astrophysics Data System (ADS)

Uvarov, D. V.

2018-07-01

The massless spinning particle and the tensionless string models on an AdS d background in the projective-space realization are proposed as constrained Hamiltonian systems. Various forms of particle and string Lagrangians are derived and classical mechanics is studied including the Lax-type representation of the equations of motion. After that, the transition to the quantum theory is discussed. The analysis of potential anomalies in the tensionless string model necessitates the introduction of ghosts and BRST charge. It is shown that a quantum BRST charge is nilpotent for any d if coordinate-momentum ordering for the phase-space bosonic variables, Weyl ordering for the fermions and cb () ordering for the ghosts is chosen, while conformal reparametrizations and space-time dilatations turn out to be anomalous for ordering in terms of positive and negative Fourier modes of the phase-space variables and ghosts.

New Gogny interaction suitable for astrophysical applications

NASA Astrophysics Data System (ADS)

Gonzalez-Boquera, C.; Centelles, M.; Viñas, X.; Robledo, L. M.

2018-04-01

The D1 family of parametrizations of the Gogny interaction commonly suffers from a rather soft neutron matter equation of state that leads to maximal masses of neutron stars well below the observational value of two solar masses. We propose a reparametrization scheme that preserves the good properties of the Gogny force but allows one to tune the density dependence of the symmetry energy, which, in turn, modifies the predictions for the maximum stellar mass. The scheme works well for D1M, and leads to a new parameter set, dubbed D1M*. In the neutron-star domain, D1M* predicts a maximal mass of two solar masses and global properties of the star in harmony with those obtained with the SLy4 Skyrme interaction. By means of a set of selected calculations in finite nuclei, we check that D1M* performs comparably well to D1M in several aspects of nuclear structure in nuclei.

A generalized non-Gaussian consistency relation for single field inflation

NASA Astrophysics Data System (ADS)

Bravo, Rafael; Mooij, Sander; Palma, Gonzalo A.; Pradenas, Bastián

2018-05-01

We show that a perturbed inflationary spacetime, driven by a canonical single scalar field, is invariant under a special class of coordinate transformations together with a field reparametrization of the curvature perturbation in co-moving gauge. This transformation may be used to derive the squeezed limit of the 3-point correlation function of the co-moving curvature perturbations valid in the case that these do not freeze after horizon crossing. This leads to a generalized version of Maldacena's non-Gaussian consistency relation in the sense that the bispectrum squeezed limit is completely determined by spacetime diffeomorphisms. Just as in the case of the standard consistency relation, this result may be understood as the consequence of how long-wavelength modes modulate those of shorter wavelengths. This relation allows one to derive the well known violation to the consistency relation encountered in ultra slow-roll, where curvature perturbations grow exponentially after horizon crossing.

Ensemble formulation of surface fluxes and improvement in evapotranspiration and cloud parameterizations in a GCM. [General Circulation Model

NASA Technical Reports Server (NTRS)

Sud, Y. C.; Smith, W. E.

1984-01-01

The influence of some modifications to the parameters of the current general circulation model (GCM) is investigated. The aim of the modifications was to eliminate strong occasional bursts of oscillations in planetary boundary layer (PBL) fluxes. Smoothly varying bulk aerodynamic friction and heat transport coefficients were found by ensemble averaging of the PBL fluxes in the current GCM. A comparison was performed of the simulations of the modified model and the unmodified model. The comparison showed that the surface fluxes and cloudiness in the modified model simulations were much more accurate. The planetary albedo in the model was also realistic. Weaknesses persisted in the models positioning of the Inter-tropical convergence zone (ICTZ) and in the temperature estimates for polar regions. A second simulation of the model following reparametrization of the cloud data showed improved results and these are described in detail.

Improved Force Fields for Peptide Nucleic Acids with Optimized Backbone Torsion Parameters.

PubMed

Jasiński, Maciej; Feig, Michael; Trylska, Joanna

2018-06-06

Peptide nucleic acids are promising nucleic acid analogs for antisense therapies as they can form stable duplex and triplex structures with DNA and RNA. Computational studies of PNA-containing duplexes and triplexes are an important component for guiding their design, yet existing force fields have not been well validated and parametrized with modern computational capabilities. We present updated CHARMM and Amber force fields for PNA that greatly improve the stability of simulated PNA-containing duplexes and triplexes in comparison with experimental structures and allow such systems to be studied on microsecond time scales. The force field modifications focus on reparametrized PNA backbone torsion angles to match high-level quantum mechanics reference energies for a model compound. The microsecond simulations of PNA-PNA, PNA-DNA, PNA-RNA, and PNA-DNA-PNA complexes also allowed a comprehensive analysis of hydration and ion interactions with such systems.

High Order Entropy-Constrained Residual VQ for Lossless Compression of Images

NASA Technical Reports Server (NTRS)

Kossentini, Faouzi; Smith, Mark J. T.; Scales, Allen

1995-01-01

High order entropy coding is a powerful technique for exploiting high order statistical dependencies. However, the exponentially high complexity associated with such a method often discourages its use. In this paper, an entropy-constrained residual vector quantization method is proposed for lossless compression of images. The method consists of first quantizing the input image using a high order entropy-constrained residual vector quantizer and then coding the residual image using a first order entropy coder. The distortion measure used in the entropy-constrained optimization is essentially the first order entropy of the residual image. Experimental results show very competitive performance.

Using entropy measures to characterize human locomotion.

PubMed

Leverick, Graham; Szturm, Tony; Wu, Christine Q

2014-12-01

Entropy measures have been widely used to quantify the complexity of theoretical and experimental dynamical systems. In this paper, the value of using entropy measures to characterize human locomotion is demonstrated based on their construct validity, predictive validity in a simple model of human walking and convergent validity in an experimental study. Results show that four of the five considered entropy measures increase meaningfully with the increased probability of falling in a simple passive bipedal walker model. The same four entropy measures also experienced statistically significant increases in response to increasing age and gait impairment caused by cognitive interference in an experimental study. Of the considered entropy measures, the proposed quantized dynamical entropy (QDE) and quantization-based approximation of sample entropy (QASE) offered the best combination of sensitivity to changes in gait dynamics and computational efficiency. Based on these results, entropy appears to be a viable candidate for assessing the stability of human locomotion.

The Conditional Entropy Power Inequality for Bosonic Quantum Systems

NASA Astrophysics Data System (ADS)

De Palma, Giacomo; Trevisan, Dario

2018-06-01

We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally independent given the memory and have given quantum conditional entropies. We also prove that, for any couple of values of the quantum conditional entropies of the two inputs, the minimum of the quantum conditional entropy of the output given by the conditional Entropy Power Inequality is asymptotically achieved by a suitable sequence of quantum Gaussian input states. Our proof of the conditional Entropy Power Inequality is based on a new Stam inequality for the quantum conditional Fisher information and on the determination of the universal asymptotic behaviour of the quantum conditional entropy under the heat semigroup evolution. The beam-splitter and the squeezing are the central elements of quantum optics, and can model the attenuation, the amplification and the noise of electromagnetic signals. This conditional Entropy Power Inequality will have a strong impact in quantum information and quantum cryptography. Among its many possible applications there is the proof of a new uncertainty relation for the conditional Wehrl entropy.

Giant onsite electronic entropy enhances the performance of ceria for water splitting.

PubMed

Naghavi, S Shahab; Emery, Antoine A; Hansen, Heine A; Zhou, Fei; Ozolins, Vidvuds; Wolverton, Chris

2017-08-18

Previous studies have shown that a large solid-state entropy of reduction increases the thermodynamic efficiency of metal oxides, such as ceria, for two-step thermochemical water splitting cycles. In this context, the configurational entropy arising from oxygen off-stoichiometry in the oxide, has been the focus of most previous work. Here we report a different source of entropy, the onsite electronic configurational entropy, arising from coupling between orbital and spin angular momenta in lanthanide f orbitals. We find that onsite electronic configurational entropy is sizable in all lanthanides, and reaches a maximum value of ≈4.7 k B per oxygen vacancy for Ce 4+ /Ce 3+ reduction. This unique and large positive entropy source in ceria explains its excellent performance for high-temperature catalytic redox reactions such as water splitting. Our calculations also show that terbium dioxide has a high electronic entropy and thus could also be a potential candidate for solar thermochemical reactions.Solid-state entropy of reduction increases the thermodynamic efficiency of ceria for two-step thermochemical water splitting. Here, the authors report a large and different source of entropy, the onsite electronic configurational entropy arising from coupling between orbital and spin angular momenta in f orbitals.

Crowd macro state detection using entropy model

NASA Astrophysics Data System (ADS)

Zhao, Ying; Yuan, Mengqi; Su, Guofeng; Chen, Tao

2015-08-01

In the crowd security research area a primary concern is to identify the macro state of crowd behaviors to prevent disasters and to supervise the crowd behaviors. The entropy is used to describe the macro state of a self-organization system in physics. The entropy change indicates the system macro state change. This paper provides a method to construct crowd behavior microstates and the corresponded probability distribution using the individuals' velocity information (magnitude and direction). Then an entropy model was built up to describe the crowd behavior macro state. Simulation experiments and video detection experiments were conducted. It was verified that in the disordered state, the crowd behavior entropy is close to the theoretical maximum entropy; while in ordered state, the entropy is much lower than half of the theoretical maximum entropy. The crowd behavior macro state sudden change leads to the entropy change. The proposed entropy model is more applicable than the order parameter model in crowd behavior detection. By recognizing the entropy mutation, it is possible to detect the crowd behavior macro state automatically by utilizing cameras. Results will provide data support on crowd emergency prevention and on emergency manual intervention.

The Conditional Entropy Power Inequality for Bosonic Quantum Systems

NASA Astrophysics Data System (ADS)

De Palma, Giacomo; Trevisan, Dario

2018-01-01

We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally independent given the memory and have given quantum conditional entropies. We also prove that, for any couple of values of the quantum conditional entropies of the two inputs, the minimum of the quantum conditional entropy of the output given by the conditional Entropy Power Inequality is asymptotically achieved by a suitable sequence of quantum Gaussian input states. Our proof of the conditional Entropy Power Inequality is based on a new Stam inequality for the quantum conditional Fisher information and on the determination of the universal asymptotic behaviour of the quantum conditional entropy under the heat semigroup evolution. The beam-splitter and the squeezing are the central elements of quantum optics, and can model the attenuation, the amplification and the noise of electromagnetic signals. This conditional Entropy Power Inequality will have a strong impact in quantum information and quantum cryptography. Among its many possible applications there is the proof of a new uncertainty relation for the conditional Wehrl entropy.

How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems.

PubMed

Hanel, Rudolf; Thurner, Stefan; Gell-Mann, Murray

2014-05-13

The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and Markovian systems in statistical mechanics, information theory, and statistics. For several decades there has been an ongoing controversy over whether the notion of the maximum entropy principle can be extended in a meaningful way to nonextensive, nonergodic, and complex statistical systems and processes. In this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related to multiplicities of independent random processes. We then show how the relaxation of independence naturally leads to the most general entropies that are compatible with the first three Shannon-Khinchin axioms, the (c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept for nonergodic and complex statistical systems if their relative entropy can be factored into a generalized multiplicity and a constraint term. The problem of finding such a factorization reduces to finding an appropriate representation of relative entropy in a linear basis. In a particular example we show that path-dependent random processes with memory naturally require specific generalized entropies. The example is to our knowledge the first exact derivation of a generalized entropy from the microscopic properties of a path-dependent random process.

Use of mutual information to decrease entropy: Implications for the second law of thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lloyd, S.

1989-05-15

Several theorems on the mechanics of gathering information are proved, and the possibility of violating the second law of thermodynamics by obtaining information is discussed in light of these theorems. Maxwell's demon can lower the entropy of his surroundings by an amount equal to the difference between the maximum entropy of his recording device and its initial entropy, without generating a compensating entropy increase. A demon with human-scale recording devices can reduce the entropy of a gas by a negligible amount only, but the proof of the demon's impracticability leaves open the possibility that systems highly correlated with their environmentmore » can reduce the environment's entropy by a substantial amount without increasing entropy elsewhere. In the event that a boundary condition for the universe requires it to be in a state of low entropy when small, the correlations induced between different particle modes during the expansion phase allow the modes to behave like Maxwell's demons during the contracting phase, reducing the entropy of the universe to a low value.« less

Renyi entropy measures of heart rate Gaussianity.

PubMed

Lake, Douglas E

2006-01-01

Sample entropy and approximate entropy are measures that have been successfully utilized to study the deterministic dynamics of heart rate (HR). A complementary stochastic point of view and a heuristic argument using the Central Limit Theorem suggests that the Gaussianity of HR is a complementary measure of the physiological complexity of the underlying signal transduction processes. Renyi entropy (or q-entropy) is a widely used measure of Gaussianity in many applications. Particularly important members of this family are differential (or Shannon) entropy (q = 1) and quadratic entropy (q = 2). We introduce the concepts of differential and conditional Renyi entropy rate and, in conjunction with Burg's theorem, develop a measure of the Gaussianity of a linear random process. Robust algorithms for estimating these quantities are presented along with estimates of their standard errors.

Valence bond and von Neumann entanglement entropy in Heisenberg ladders.

PubMed

Kallin, Ann B; González, Iván; Hastings, Matthew B; Melko, Roger G

2009-09-11

We present a direct comparison of the recently proposed valence bond entanglement entropy and the von Neumann entanglement entropy on spin-1/2 Heisenberg systems using quantum Monte Carlo and density-matrix renormalization group simulations. For one-dimensional chains we show that the valence bond entropy can be either less or greater than the von Neumann entropy; hence, it cannot provide a bound on the latter. On ladder geometries, simulations with up to seven legs are sufficient to indicate that the von Neumann entropy in two dimensions obeys an area law, even though the valence bond entanglement entropy has a multiplicative logarithmic correction.

Entropy in molecular recognition by proteins

PubMed Central

Caro, José A.; Harpole, Kyle W.; Kasinath, Vignesh; Lim, Jackwee; Granja, Jeffrey; Valentine, Kathleen G.; Sharp, Kim A.

2017-01-01

Molecular recognition by proteins is fundamental to molecular biology. Dissection of the thermodynamic energy terms governing protein–ligand interactions has proven difficult, with determination of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quantitatively obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein–ligand complexes are used to show a quantitative relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodynamic variable to modulate protein–ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biologically meaningless. The dynamical proxy for conformational entropy or “entropy meter” also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water–protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity molecular recognition by proteins. PMID:28584100

Statistical mechanical theory of liquid entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wallace, D.C.

The multiparticle correlation expansion for the entropy of a classical monatomic liquid is presented. This entropy expresses the physical picture in which there is no free particle motion, but rather, each atom moves within a cage formed by its neighbors. The liquid expansion, including only pair correlations, gives an excellent account of the experimental entropy of most liquid metals, of liquid argon, and the hard sphere liquid. The pair correlation entropy is well approximated by a universal function of temperature. Higher order correlation entropy, due to n-particle irreducible correlations for n{ge}3, is significant in only a few liquid metals, andmore » its occurrence suggests the presence of n-body forces. When the liquid theory is applied to the study of melting, the author discovers the important classification of normal and anomalous melting, according to whether there is not or is a significant change in the electronic structure upon melting, and he discovers the universal disordering entropy for melting of a monatomic crystal. Interesting directions for future research are: extension to include orientational correlations of molecules, theoretical calculation of the entropy of water, application to the entropy of the amorphous state, and correlational entropy of compressed argon. The author clarifies the relation among different entropy expansions in the recent literature.« less

Characterization of time series via Rényi complexity-entropy curves

NASA Astrophysics Data System (ADS)

Jauregui, M.; Zunino, L.; Lenzi, E. K.; Mendes, R. S.; Ribeiro, H. V.

2018-05-01

One of the most useful tools for distinguishing between chaotic and stochastic time series is the so-called complexity-entropy causality plane. This diagram involves two complexity measures: the Shannon entropy and the statistical complexity. Recently, this idea has been generalized by considering the Tsallis monoparametric generalization of the Shannon entropy, yielding complexity-entropy curves. These curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature. Here we further explore these complexity-entropy curves in the context of the Rényi entropy, which is another monoparametric generalization of the Shannon entropy. By combining the Rényi entropy with the proper generalization of the statistical complexity, we associate a parametric curve (the Rényi complexity-entropy curve) with a given time series. We explore this approach in a series of numerical and experimental applications, demonstrating the usefulness of this new technique for time series analysis. We show that the Rényi complexity-entropy curves enable the differentiation among time series of chaotic, stochastic, and periodic nature. In particular, time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points, whereas curves related to chaotic phenomena have a negative curvature; finally, periodic time series are represented by vertical straight lines.

Beyond the Shannon–Khinchin formulation: The composability axiom and the universal-group entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tempesta, Piergiulio, E-mail: p.tempesta@fis.ucm.es

2016-02-15

The notion of entropy is ubiquitous both in natural and social sciences. In the last two decades, a considerable effort has been devoted to the study of new entropic forms, which generalize the standard Boltzmann–Gibbs (BG) entropy and could be applicable in thermodynamics, quantum mechanics and information theory. In Khinchin (1957), by extending previous ideas of Shannon (1948) and Shannon and Weaver (1949), Khinchin proposed a characterization of the BG entropy, based on four requirements, nowadays known as the Shannon–Khinchin (SK) axioms. The purpose of this paper is twofold. First, we show that there exists an intrinsic group-theoretical structure behindmore » the notion of entropy. It comes from the requirement of composability of an entropy with respect to the union of two statistically independent systems, that we propose in an axiomatic formulation. Second, we show that there exists a simple universal family of trace-form entropies. This class contains many well known examples of entropies and infinitely many new ones, a priori multi-parametric. Due to its specific relation with Lazard’s universal formal group of algebraic topology, the new general entropy introduced in this work will be called the universal-group entropy. A new example of multi-parametric entropy is explicitly constructed.« less

Formal groups and Z-entropies

PubMed Central

2016-01-01

We shall prove that the celebrated Rényi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies. Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Rényi. A crucial aspect is that every Z-entropy is composable (Tempesta 2016 Ann. Phys. 365, 180–197. (doi:10.1016/j.aop.2015.08.013)). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only. Further properties are also required to describe the composition process in terms of a group law. The composability axiom, introduced as a generalization of the fourth Shannon–Khinchin axiom (postulating additivity), is a highly non-trivial requirement. Indeed, in the trace-form class, the Boltzmann entropy and Tsallis entropy are the only known composable cases. However, in the non-trace form class, the Z-entropies arise as new entropic functions possessing the mathematical properties necessary for information-theoretical applications, in both classical and quantum contexts. From a mathematical point of view, composability is intimately related to formal group theory of algebraic topology. The underlying group-theoretical structure determines crucially the statistical properties of the corresponding entropies. PMID:27956871

Entropy in molecular recognition by proteins.

PubMed

Caro, José A; Harpole, Kyle W; Kasinath, Vignesh; Lim, Jackwee; Granja, Jeffrey; Valentine, Kathleen G; Sharp, Kim A; Wand, A Joshua

2017-06-20

Molecular recognition by proteins is fundamental to molecular biology. Dissection of the thermodynamic energy terms governing protein-ligand interactions has proven difficult, with determination of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quantitatively obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein-ligand complexes are used to show a quantitative relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodynamic variable to modulate protein-ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biologically meaningless. The dynamical proxy for conformational entropy or "entropy meter" also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water-protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity molecular recognition by proteins.

New classes of Lorenz curves by maximizing Tsallis entropy under mean and Gini equality and inequality constraints

NASA Astrophysics Data System (ADS)

Preda, Vasile; Dedu, Silvia; Gheorghe, Carmen

2015-10-01

In this paper, by using the entropy maximization principle with Tsallis entropy, new distribution families for modeling the income distribution are derived. Also, new classes of Lorenz curves are obtained by applying the entropy maximization principle with Tsallis entropy, under mean and Gini index equality and inequality constraints.

Entropy change of biological dynamics in COPD.

PubMed

Jin, Yu; Chen, Chang; Cao, Zhixin; Sun, Baoqing; Lo, Iek Long; Liu, Tzu-Ming; Zheng, Jun; Sun, Shixue; Shi, Yan; Zhang, Xiaohua Douglas

2017-01-01

In this century, the rapid development of large data storage technologies, mobile network technology, and portable medical devices makes it possible to measure, record, store, and track analysis of large amount of data in human physiological signals. Entropy is a key metric for quantifying the irregularity contained in physiological signals. In this review, we focus on how entropy changes in various physiological signals in COPD. Our review concludes that the entropy change relies on the types of physiological signals under investigation. For major physiological signals related to respiratory diseases, such as airflow, heart rate variability, and gait variability, the entropy of a patient with COPD is lower than that of a healthy person. However, in case of hormone secretion and respiratory sound, the entropy of a patient is higher than that of a healthy person. For mechanomyogram signal, the entropy increases with the increased severity of COPD. This result should give valuable guidance for the use of entropy for physiological signals measured by wearable medical device as well as for further research on entropy in COPD.

Visualizing Entropy

NASA Astrophysics Data System (ADS)

Lechner, Joseph H.

1999-10-01

This report describes two classroom activities that help students visualize the abstract concept of entropy and apply the second law of thermodynamics to real situations. (i) A sealed "rainbow tube" contains six smaller vessels, each filled with a different brightly colored solution (low entropy). When the tube is inverted, the solutions mix together and react to form an amorphous precipitate (high entropy). The change from low entropy to high entropy is irreversible as long as the tube remains sealed. (ii) When U.S. currency is withdrawn from circulation, intact bills (low entropy) are shredded into small fragments (high entropy). Shredding is quick and easy; the reverse process is clearly nonspontaneous. It is theoretically possible, but it is time-consuming and energy-intensive, to reassemble one bill from a pile that contains fragments of hundreds of bills. We calculate the probability P of drawing pieces of only one specific bill from a mixture containing one pound of bills, each shredded into n fragments. This result can be related to Boltzmann's entropy formula S?=klnW.

Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

PubMed Central

Ito, Sosuke

2016-01-01

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics. PMID:27833120

Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

NASA Astrophysics Data System (ADS)

Ito, Sosuke

2016-11-01

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics.

Thermodynamics of T cell receptor – peptide/MHC interactions: progress and opportunities

PubMed Central

Armstrong, Kathryn M.; Insaidoo, Francis K.; Baker, Brian M.

2013-01-01

αβ T cell receptors (TCR) recognize peptide antigens presented by class I or class II major histocompatibility complex molecules (pMHC). Here we review the use of thermodynamic measurements in the study of TCR-pMHC interactions, with attention to the diversity in binding thermodynamics and how this is related to the variation in TCR-pMHC interfaces. We show that there is no enthalpic or entropic signature for TCR binding; rather, enthalpy and entropy changes vary in a compensatory manner that reflects a narrow free energy window for the interactions that have been characterized. Binding enthalpy and entropy changes do not correlate with structural features such as buried surface area or the number of hydrogen bonds within TCR-pMHC interfaces, possibly reflecting the myriad of contributors to binding thermodynamics, but likely also reflecting a reliance on van’t Hoff over calorimetric measurements and the unaccounted influence of equilibria linked to binding. TCR-pMHC binding heat capacity changes likewise vary considerably. In some cases the heat capacity changes are consistent with conformational differences between bound and free receptors, but there is little data indicating these conformational differences represent the need to organize commonly disordered CDR loops. In this regard, we discuss how thermodynamics may provide additional insight into conformational changes occurring upon TCR binding. Finally, we highlight opportunities for the further use of thermodynamic measurements in the study of TCR-pMHC interactions, not only for understanding TCR binding in general, but for understanding specifics of individual interactions and the engineering of T cell receptors with desired molecular recognition properties. PMID:18496839

Measuring Information-Transfer Delays

PubMed Central

Wibral, Michael; Pampu, Nicolae; Priesemann, Viola; Siebenhühner, Felix; Seiwert, Hannes; Lindner, Michael; Lizier, Joseph T.; Vicente, Raul

2013-01-01

In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics. PMID:23468850

Wavelet entropy characterization of elevated intracranial pressure.

PubMed

Xu, Peng; Scalzo, Fabien; Bergsneider, Marvin; Vespa, Paul; Chad, Miller; Hu, Xiao

2008-01-01

Intracranial Hypertension (ICH) often occurs for those patients with traumatic brain injury (TBI), stroke, tumor, etc. Pathology of ICH is still controversial. In this work, we used wavelet entropy and relative wavelet entropy to study the difference existed between normal and hypertension states of ICP for the first time. The wavelet entropy revealed the similar findings as the approximation entropy that entropy during ICH state is smaller than that in normal state. Moreover, with wavelet entropy, we can see that ICH state has the more focused energy in the low wavelet frequency band (0-3.1 Hz) than the normal state. The relative wavelet entropy shows that the energy distribution in the wavelet bands between these two states is actually different. Based on these results, we suggest that ICH may be formed by the re-allocation of oscillation energy within brain.

The second law of thermodynamics under unitary evolution and external operations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ikeda, Tatsuhiko N., E-mail: ikeda@cat.phys.s.u-tokyo.ac.jp; Physics Department, Boston University, Boston, MA 02215; Sakumichi, Naoyuki

The von Neumann entropy cannot represent the thermodynamic entropy of equilibrium pure states in isolated quantum systems. The diagonal entropy, which is the Shannon entropy in the energy eigenbasis at each instant of time, is a natural generalization of the von Neumann entropy and applicable to equilibrium pure states. We show that the diagonal entropy is consistent with the second law of thermodynamics upon arbitrary external unitary operations. In terms of the diagonal entropy, thermodynamic irreversibility follows from the facts that quantum trajectories under unitary evolution are restricted by the Hamiltonian dynamics and that the external operation is performed withoutmore » reference to the microscopic state of the system.« less

Nonadditive entropies yield probability distributions with biases not warranted by the data.

PubMed

Pressé, Steve; Ghosh, Kingshuk; Lee, Julian; Dill, Ken A

2013-11-01

Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann-Gibbs form of the entropy ensures that probability distributions inferred satisfy the multiplication rule of probability for independent events in the absence of data coupling such events. Other types of entropies that violate the Shore and Johnson axioms, including nonadditive entropies such as the Tsallis entropy, violate this basic consistency requirement. Here we use the axiomatic framework of Shore and Johnson to show how such nonadditive entropy functions generate biases in probability distributions that are not warranted by the underlying data.

On determining absolute entropy without quantum theory or the third law of thermodynamics

NASA Astrophysics Data System (ADS)

Steane, Andrew M.

2016-04-01

We employ classical thermodynamics to gain information about absolute entropy, without recourse to statistical methods, quantum mechanics or the third law of thermodynamics. The Gibbs-Duhem equation yields various simple methods to determine the absolute entropy of a fluid. We also study the entropy of an ideal gas and the ionization of a plasma in thermal equilibrium. A single measurement of the degree of ionization can be used to determine an unknown constant in the entropy equation, and thus determine the absolute entropy of a gas. It follows from all these examples that the value of entropy at absolute zero temperature does not need to be assigned by postulate, but can be deduced empirically.

Maximum Tsallis entropy with generalized Gini and Gini mean difference indices constraints

NASA Astrophysics Data System (ADS)

Khosravi Tanak, A.; Mohtashami Borzadaran, G. R.; Ahmadi, J.

2017-04-01

Using the maximum entropy principle with Tsallis entropy, some distribution families for modeling income distribution are obtained. By considering income inequality measures, maximum Tsallis entropy distributions under the constraint on generalized Gini and Gini mean difference indices are derived. It is shown that the Tsallis entropy maximizers with the considered constraints belong to generalized Pareto family.

Diffusive mixing and Tsallis entropy

DOE PAGES

O'Malley, Daniel; Vesselinov, Velimir V.; Cushman, John H.

2015-04-29

Brownian motion, the classical diffusive process, maximizes the Boltzmann-Gibbs entropy. The Tsallis q-entropy, which is non-additive, was developed as an alternative to the classical entropy for systems which are non-ergodic. A generalization of Brownian motion is provided that maximizes the Tsallis entropy rather than the Boltzmann-Gibbs entropy. This process is driven by a Brownian measure with a random diffusion coefficient. In addition, the distribution of this coefficient is derived as a function of q for 1 < q < 3. Applications to transport in porous media are considered.

Holographic charged Rényi entropies

NASA Astrophysics Data System (ADS)

Belin, Alexandre; Hung, Ling-Yan; Maloney, Alexander; Matsuura, Shunji; Myers, Robert C.; Sierens, Todd

2013-12-01

We construct a new class of entanglement measures by extending the usual definition of Rényi entropy to include a chemical potential. These charged Rényi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFT's with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Rényi entropies in free field theories.

Wavelet entropy of BOLD time series: An application to Rolandic epilepsy.

PubMed

Gupta, Lalit; Jansen, Jacobus F A; Hofman, Paul A M; Besseling, René M H; de Louw, Anton J A; Aldenkamp, Albert P; Backes, Walter H

2017-12-01

To assess the wavelet entropy for the characterization of intrinsic aberrant temporal irregularities in the time series of resting-state blood-oxygen-level-dependent (BOLD) signal fluctuations. Further, to evaluate the temporal irregularities (disorder/order) on a voxel-by-voxel basis in the brains of children with Rolandic epilepsy. The BOLD time series was decomposed using the discrete wavelet transform and the wavelet entropy was calculated. Using a model time series consisting of multiple harmonics and nonstationary components, the wavelet entropy was compared with Shannon and spectral (Fourier-based) entropy. As an application, the wavelet entropy in 22 children with Rolandic epilepsy was compared to 22 age-matched healthy controls. The images were obtained by performing resting-state functional magnetic resonance imaging (fMRI) using a 3T system, an 8-element receive-only head coil, and an echo planar imaging pulse sequence ( T2*-weighted). The wavelet entropy was also compared to spectral entropy, regional homogeneity, and Shannon entropy. Wavelet entropy was found to identify the nonstationary components of the model time series. In Rolandic epilepsy patients, a significantly elevated wavelet entropy was observed relative to controls for the whole cerebrum (P = 0.03). Spectral entropy (P = 0.41), regional homogeneity (P = 0.52), and Shannon entropy (P = 0.32) did not reveal significant differences. The wavelet entropy measure appeared more sensitive to detect abnormalities in cerebral fluctuations represented by nonstationary effects in the BOLD time series than more conventional measures. This effect was observed in the model time series as well as in Rolandic epilepsy. These observations suggest that the brains of children with Rolandic epilepsy exhibit stronger nonstationary temporal signal fluctuations than controls. 2 Technical Efficacy: Stage 3 J. Magn. Reson. Imaging 2017;46:1728-1737. © 2017 International Society for Magnetic Resonance in Medicine.

Characterization of complexity in the electroencephalograph activity of Alzheimer's disease based on fuzzy entropy.

PubMed

Cao, Yuzhen; Cai, Lihui; Wang, Jiang; Wang, Ruofan; Yu, Haitao; Cao, Yibin; Liu, Jing

2015-08-01

In this paper, experimental neurophysiologic recording and statistical analysis are combined to investigate the nonlinear characteristic and the cognitive function of the brain. Fuzzy approximate entropy and fuzzy sample entropy are applied to characterize the model-based simulated series and electroencephalograph (EEG) series of Alzheimer's disease (AD). The effectiveness and advantages of these two kinds of fuzzy entropy are first verified through the simulated EEG series generated by the alpha rhythm model, including stronger relative consistency and robustness. Furthermore, in order to detect the abnormality of irregularity and chaotic behavior in the AD brain, the complexity features based on these two fuzzy entropies are extracted in the delta, theta, alpha, and beta bands. It is demonstrated that, due to the introduction of fuzzy set theory, the fuzzy entropies could better distinguish EEG signals of AD from that of the normal than the approximate entropy and sample entropy. Moreover, the entropy values of AD are significantly decreased in the alpha band, particularly in the temporal brain region, such as electrode T3 and T4. In addition, fuzzy sample entropy could achieve higher group differences in different brain regions and higher average classification accuracy of 88.1% by support vector machine classifier. The obtained results prove that fuzzy sample entropy may be a powerful tool to characterize the complexity abnormalities of AD, which could be helpful in further understanding of the disease.

Characterization of complexity in the electroencephalograph activity of Alzheimer's disease based on fuzzy entropy

NASA Astrophysics Data System (ADS)

Cao, Yuzhen; Cai, Lihui; Wang, Jiang; Wang, Ruofan; Yu, Haitao; Cao, Yibin; Liu, Jing

2015-08-01

In this paper, experimental neurophysiologic recording and statistical analysis are combined to investigate the nonlinear characteristic and the cognitive function of the brain. Fuzzy approximate entropy and fuzzy sample entropy are applied to characterize the model-based simulated series and electroencephalograph (EEG) series of Alzheimer's disease (AD). The effectiveness and advantages of these two kinds of fuzzy entropy are first verified through the simulated EEG series generated by the alpha rhythm model, including stronger relative consistency and robustness. Furthermore, in order to detect the abnormality of irregularity and chaotic behavior in the AD brain, the complexity features based on these two fuzzy entropies are extracted in the delta, theta, alpha, and beta bands. It is demonstrated that, due to the introduction of fuzzy set theory, the fuzzy entropies could better distinguish EEG signals of AD from that of the normal than the approximate entropy and sample entropy. Moreover, the entropy values of AD are significantly decreased in the alpha band, particularly in the temporal brain region, such as electrode T3 and T4. In addition, fuzzy sample entropy could achieve higher group differences in different brain regions and higher average classification accuracy of 88.1% by support vector machine classifier. The obtained results prove that fuzzy sample entropy may be a powerful tool to characterize the complexity abnormalities of AD, which could be helpful in further understanding of the disease.

Entropy Filtered Density Function for Large Eddy Simulation of Turbulent Reacting Flows

NASA Astrophysics Data System (ADS)

Safari, Mehdi

Analysis of local entropy generation is an effective means to optimize the performance of energy and combustion systems by minimizing the irreversibilities in transport processes. Large eddy simulation (LES) is employed to describe entropy transport and generation in turbulent reacting flows. The entropy transport equation in LES contains several unclosed terms. These are the subgrid scale (SGS) entropy flux and entropy generation caused by irreversible processes: heat conduction, mass diffusion, chemical reaction and viscous dissipation. The SGS effects are taken into account using a novel methodology based on the filtered density function (FDF). This methodology, entitled entropy FDF (En-FDF), is developed and utilized in the form of joint entropy-velocity-scalar-turbulent frequency FDF and the marginal scalar-entropy FDF, both of which contain the chemical reaction effects in a closed form. The former constitutes the most comprehensive form of the En-FDF and provides closure for all the unclosed filtered moments. This methodology is applied for LES of a turbulent shear layer involving transport of passive scalars. Predictions show favor- able agreements with the data generated by direct numerical simulation (DNS) of the same layer. The marginal En-FDF accounts for entropy generation effects as well as scalar and entropy statistics. This methodology is applied to a turbulent nonpremixed jet flame (Sandia Flame D) and predictions are validated against experimental data. In both flows, sources of irreversibility are predicted and analyzed.

Use of information entropy measures of sitting postural sway to quantify developmental delay in infants

PubMed Central

Deffeyes, Joan E; Harbourne, Regina T; DeJong, Stacey L; Kyvelidou, Anastasia; Stuberg, Wayne A; Stergiou, Nicholas

2009-01-01

Background By quantifying the information entropy of postural sway data, the complexity of the postural movement of different populations can be assessed, giving insight into pathologic motor control functioning. Methods In this study, developmental delay of motor control function in infants was assessed by analysis of sitting postural sway data acquired from force plate center of pressure measurements. Two types of entropy measures were used: symbolic entropy, including a new asymmetric symbolic entropy measure, and approximate entropy, a more widely used entropy measure. For each method of analysis, parameters were adjusted to optimize the separation of the results from the infants with delayed development from infants with typical development. Results The method that gave the widest separation between the populations was the asymmetric symbolic entropy method, which we developed by modification of the symbolic entropy algorithm. The approximate entropy algorithm also performed well, using parameters optimized for the infant sitting data. The infants with delayed development were found to have less complex patterns of postural sway in the medial-lateral direction, and were found to have different left-right symmetry in their postural sway, as compared to typically developing infants. Conclusion The results of this study indicate that optimization of the entropy algorithm for infant sitting postural sway data can greatly improve the ability to separate the infants with developmental delay from typically developing infants. PMID:19671183

The gravity dual of Rényi entropy.

PubMed

Dong, Xi

2016-08-12

A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Rényi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Rényi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Rényi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.

The gravity dual of Rényi entropy

PubMed Central

Dong, Xi

2016-01-01

A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Rényi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Rényi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Rényi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity. PMID:27515122

Entropy-based financial asset pricing.

PubMed

Ormos, Mihály; Zibriczky, Dávid

2014-01-01

We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.

Entropy-Based Financial Asset Pricing

PubMed Central

Ormos, Mihály; Zibriczky, Dávid

2014-01-01

We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return – entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy. PMID:25545668

Entropy coders for image compression based on binary forward classification

NASA Astrophysics Data System (ADS)

Yoo, Hoon; Jeong, Jechang

2000-12-01

Entropy coders as a noiseless compression method are widely used as final step compression for images, and there have been many contributions to increase of entropy coder performance and to reduction of entropy coder complexity. In this paper, we propose some entropy coders based on the binary forward classification (BFC). The BFC requires overhead of classification but there is no change between the amount of input information and the total amount of classified output information, which we prove this property in this paper. And using the proved property, we propose entropy coders that are the BFC followed by Golomb-Rice coders (BFC+GR) and the BFC followed by arithmetic coders (BFC+A). The proposed entropy coders introduce negligible additional complexity due to the BFC. Simulation results also show better performance than other entropy coders that have similar complexity to the proposed coders.

Entropy Generation Across Earth's Bow Shock

NASA Technical Reports Server (NTRS)

Parks, George K.; McCarthy, Michael; Fu, Suiyan; Lee E. s; Cao, Jinbin; Goldstein, Melvyn L.; Canu, Patrick; Dandouras, Iannis S.; Reme, Henri; Fazakerley, Andrew;

Nonparametric entropy estimation using kernel densities.

PubMed

Lake, Douglas E

2009-01-01

The entropy of experimental data from the biological and medical sciences provides additional information over summary statistics. Calculating entropy involves estimates of probability density functions, which can be effectively accomplished using kernel density methods. Kernel density estimation has been widely studied and a univariate implementation is readily available in MATLAB. The traditional definition of Shannon entropy is part of a larger family of statistics, called Renyi entropy, which are useful in applications that require a measure of the Gaussianity of data. Of particular note is the quadratic entropy which is related to the Friedman-Tukey (FT) index, a widely used measure in the statistical community. One application where quadratic entropy is very useful is the detection of abnormal cardiac rhythms, such as atrial fibrillation (AF). Asymptotic and exact small-sample results for optimal bandwidth and kernel selection to estimate the FT index are presented and lead to improved methods for entropy estimation.

Entropy of Stationary Nonequilibrium Measures of Boundary Driven Symmetric Simple Exclusion Processes

NASA Astrophysics Data System (ADS)

Bernardin, Cédric; Landim, Claudio

2010-12-01

We examine the entropy of stationary nonequilibrium measures of boundary driven symmetric simple exclusion processes. In contrast with the Gibbs-Shannon entropy (Bahadoran in J. Stat. Phys. 126(4-5):1069-1082, 2007; Derrida et al. in J. Stat. Phys. 126(4-5):1083-1108, 2007), the entropy of nonequilibrium stationary states differs from the entropy of local equilibrium states.

Information entropy to measure the spatial and temporal complexity of solute transport in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Li, Weiyao; Huang, Guanhua; Xiong, Yunwu

2016-04-01

The complexity of the spatial structure of porous media, randomness of groundwater recharge and discharge (rainfall, runoff, etc.) has led to groundwater movement complexity, physical and chemical interaction between groundwater and porous media cause solute transport in the medium more complicated. An appropriate method to describe the complexity of features is essential when study on solute transport and conversion in porous media. Information entropy could measure uncertainty and disorder, therefore we attempted to investigate complexity, explore the contact between the information entropy and complexity of solute transport in heterogeneous porous media using information entropy theory. Based on Markov theory, two-dimensional stochastic field of hydraulic conductivity (K) was generated by transition probability. Flow and solute transport model were established under four conditions (instantaneous point source, continuous point source, instantaneous line source and continuous line source). The spatial and temporal complexity of solute transport process was characterized and evaluated using spatial moment and information entropy. Results indicated that the entropy increased as the increase of complexity of solute transport process. For the point source, the one-dimensional entropy of solute concentration increased at first and then decreased along X and Y directions. As time increased, entropy peak value basically unchanged, peak position migrated along the flow direction (X direction) and approximately coincided with the centroid position. With the increase of time, spatial variability and complexity of solute concentration increase, which result in the increases of the second-order spatial moment and the two-dimensional entropy. Information entropy of line source was higher than point source. Solute entropy obtained from continuous input was higher than instantaneous input. Due to the increase of average length of lithoface, media continuity increased, flow and solute transport complexity weakened, and the corresponding information entropy also decreased. Longitudinal macro dispersivity declined slightly at early time then rose. Solute spatial and temporal distribution had significant impacts on the information entropy. Information entropy could reflect the change of solute distribution. Information entropy appears a tool to characterize the spatial and temporal complexity of solute migration and provides a reference for future research.

Time dependence of Hawking radiation entropy

NASA Astrophysics Data System (ADS)

Page, Don N.

2013-09-01

If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its original Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4πM02, or about 7.509M02 ≈ 6.268 × 1076(M0/Msolar)2, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018M02 ≈ 1.254 × 1077(M0/Msolar)2, and then decreases back down to 4πM02 = 1.049 × 1077(M0/Msolar)2.

Time-series analysis of sleep wake stage of rat EEG using time-dependent pattern entropy

NASA Astrophysics Data System (ADS)

Ishizaki, Ryuji; Shinba, Toshikazu; Mugishima, Go; Haraguchi, Hikaru; Inoue, Masayoshi

2008-05-01

We performed electroencephalography (EEG) for six male Wistar rats to clarify temporal behaviors at different levels of consciousness. Levels were identified both by conventional sleep analysis methods and by our novel entropy method. In our method, time-dependent pattern entropy is introduced, by which EEG is reduced to binary symbolic dynamics and the pattern of symbols in a sliding temporal window is considered. A high correlation was obtained between level of consciousness as measured by the conventional method and mean entropy in our entropy method. Mean entropy was maximal while awake (stage W) and decreased as sleep deepened. These results suggest that time-dependent pattern entropy may offer a promising method for future sleep research.

Bayesian or Laplacien inference, entropy and information theory and information geometry in data and signal processing

NASA Astrophysics Data System (ADS)

Mohammad-Djafari, Ali

2015-01-01

The main object of this tutorial article is first to review the main inference tools using Bayesian approach, Entropy, Information theory and their corresponding geometries. This review is focused mainly on the ways these tools have been used in data, signal and image processing. After a short introduction of the different quantities related to the Bayes rule, the entropy and the Maximum Entropy Principle (MEP), relative entropy and the Kullback-Leibler divergence, Fisher information, we will study their use in different fields of data and signal processing such as: entropy in source separation, Fisher information in model order selection, different Maximum Entropy based methods in time series spectral estimation and finally, general linear inverse problems.

Entropy change of biological dynamics in COPD

PubMed Central

Cao, Zhixin; Sun, Baoqing; Lo, Iek Long; Liu, Tzu-Ming; Zheng, Jun; Sun, Shixue; Shi, Yan; Zhang, Xiaohua Douglas

2017-01-01

In this century, the rapid development of large data storage technologies, mobile network technology, and portable medical devices makes it possible to measure, record, store, and track analysis of large amount of data in human physiological signals. Entropy is a key metric for quantifying the irregularity contained in physiological signals. In this review, we focus on how entropy changes in various physiological signals in COPD. Our review concludes that the entropy change relies on the types of physiological signals under investigation. For major physiological signals related to respiratory diseases, such as airflow, heart rate variability, and gait variability, the entropy of a patient with COPD is lower than that of a healthy person. However, in case of hormone secretion and respiratory sound, the entropy of a patient is higher than that of a healthy person. For mechanomyogram signal, the entropy increases with the increased severity of COPD. This result should give valuable guidance for the use of entropy for physiological signals measured by wearable medical device as well as for further research on entropy in COPD. PMID:29066881

Informational basis of sensory adaptation: entropy and single-spike efficiency in rat barrel cortex.

PubMed

Adibi, Mehdi; Clifford, Colin W G; Arabzadeh, Ehsan

2013-09-11

We showed recently that exposure to whisker vibrations enhances coding efficiency in rat barrel cortex despite increasing correlations in variability (Adibi et al., 2013). Here, to understand how adaptation achieves this improvement in sensory representation, we decomposed the stimulus information carried in neuronal population activity into its fundamental components in the framework of information theory. In the context of sensory coding, these components are the entropy of the responses across the entire stimulus set (response entropy) and the entropy of the responses conditional on the stimulus (conditional response entropy). We found that adaptation decreased response entropy and conditional response entropy at both the level of single neurons and the pooled activity of neuronal populations. However, the net effect of adaptation was to increase the mutual information because the drop in the conditional entropy outweighed the drop in the response entropy. The information transmitted by a single spike also increased under adaptation. As population size increased, the information content of individual spikes declined but the relative improvement attributable to adaptation was maintained.

The Holographic Entropy Cone

DOE PAGES

Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; ...

2015-09-21

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phasemore » space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.« less

Thermality and excited state Rényi entropy in two-dimensional CFT

NASA Astrophysics Data System (ADS)

Lin, Feng-Li; Wang, Huajia; Zhang, Jia-ju

2016-11-01

We evaluate one-interval Rényi entropy and entanglement entropy for the excited states of two-dimensional conformal field theory (CFT) on a cylinder, and examine their differences from the ones for the thermal state. We assume the interval to be short so that we can use operator product expansion (OPE) of twist operators to calculate Rényi entropy in terms of sum of one-point functions of OPE blocks. We find that the entanglement entropy for highly excited state and thermal state behave the same way after appropriate identification of the conformal weight of the state with the temperature. However, there exists no such universal identification for the Rényi entropy in the short-interval expansion. Therefore, the highly excited state does not look thermal when comparing its Rényi entropy to the thermal state one. As the Rényi entropy captures the higher moments of the reduced density matrix but the entanglement entropy only the average, our results imply that the emergence of thermality depends on how refined we look into the entanglement structure of the underlying pure excited state.

Enhanced performance of ferroelectric materials under hydrostatic pressure

NASA Astrophysics Data System (ADS)

Chauhan, Aditya; Patel, Satyanarayan; Wang, Shuai; Novak, Nikola; Xu, Bai-Xiang; Lv, Peng; Vaish, Rahul; Lynch, Christopher S.

2017-12-01

Mechanical confinement or restricted degrees of freedom have been explored for its potential to enhance the performance of ferroelectric devices. It presents an easy and reversible method to tune the response for specific applications. However, such studies have been mainly limited to uni- or bi-axial stress. This study investigates the effect of hydrostatic pressure on the ferroelectric behavior of bulk polycrystalline Pb0.99Nb0.02(Zr0.95Ti0.05)0.98O3. Polarization versus electric field hysteresis plots were generated as a function of hydrostatic pressure for a range of operating temperatures (298-398 K). The application of hydrostatic pressure was observed to induce anti-ferroelectric like double hysteresis loops. This in turn enhances the piezoelectric, energy storage, energy harvesting, and electrocaloric effects. The hydrostatic piezoelectric coefficient (dh) was increased from 50 pCN-1 (0 MPa) to ˜900 pC N-1 (265 MPa) and ˜3200 pCN-1 (330 MPa) at 298 K. Energy storage density was observed to improve by more than 4 times under pressure, in the whole temperature range. The relative change in entropy was also observed to shift from ˜0 to 4.8 J kg-1 K-1 under an applied pressure of 325 MPa. This behavior can be attributed to the evolution of pinched hysteresis loops that have been explained using a phenomenological model. All values represent an improvement of several hundred percent compared to unbiased performance, indicating the potential benefits of the proposed methodology.

Step-wise addition of disulfide bridge in firefly luciferase controls color shift through a flexible loop: a thermodynamic perspective.

PubMed

Nazari, Mahboobeh; Hosseinkhani, Saman; Hassani, Leila

2013-02-01

Multi-color bioluminescence is developed using the introduction of single/double disulfide bridges in firefly luciferase. The bioluminescence reaction, which uses luciferin, Mg(2+)-ATP and molecular oxygen to yield an electronically excited oxyluciferin, is carried out by the luciferase and emits visible light. The bioluminescence color of firefly luciferases is determined by the luciferase sequence and assay conditions. It has been proposed that the stability of a protein may increase through the introduction of a disulfide bridge that decreases the configurational entropy of unfolding. Single and double disulfide bridges are introduced into Photinus pyralis firefly luciferase to make separate mutant enzymes with a single/double bridge (C(81)-A(105)C, L(306)C-L(309)C, P(451)C-V(469)C; C(81)-A(105)C/P(451)C-V(469)C, and A(296)C-A(326)C/P(451)C-V(469)C). By introduction of disulfide bridges using site-directed mutagenesis in Photinus pyralis luciferase the color of emitted light was changed to red or kept in different extents. The bioluminescence color shift occurred with displacement of a critical loop in the luciferase structure without any change in green emitter mutants. Thermodynamic analysis revealed that among mutants, L(306)C-L(309)C shows a remarkable stability against urea denaturation and also a considerable increase in kinetic stability and a clear shift in bioluminescence spectra towards red.

Introduction of a proline residue into position 31 of the loop of the dimeric 4-alpha-helical protein ROP causes a drastic destabilization.

PubMed

Peters, K; Hinz, H J; Cesareni, G

1997-10-01

The exchange of an alanine with a proline residue in position 31 of the loop region of the dimeric 4-alpha-helical-bundle protein ROP causes a reduction in the alpha-helix content of 7% and a reduction in stability of about 40% compared to the wild type parameters. The Gibbs energy of unfolding by denaturants extrapolated linearly to zero denaturant concentration, delta G0D (buffer, 25 degrees C), has been determined to be 43 kJ (mol dimer)-1. The corresponding ROPwt value is 72 kJ (mol dimer)-1 (Steif et al., 1993). The extrapolated delta G0D values obtained from urea and GdmHCI un- and refolding studies are identical within error limits. Deconvolution of the stability values into enthalpy and entropy terms resulted in the following parameters. At T1/2 = 43 degrees C (Cprotein = 0.05 mg.ml-1) the ROP A31P mutant is characterized by delta Hv.H.0 = 272 kJ (mol dimer)-1, delta Cp = 7.2 kJ (mol dimer)-1 K-1, delta S0 = 762 J (mol dimer)-1 K-1. These parameters are only approximately 50% as large as the corresponding values of ROPwt. We assume that the significant reduction in stability reflects the absence of at least one hydrogen bond as well as deformation of the protein structure. This interpretation is supported by the reduction in the change in heat capacity observed for the A31P mutant relative to ROPwt, by the increased aggregation tendency of the mutant and by the reduced specific CD absorption at 222 nm. All results support the view that in the case of ROP protein the loop region plays a significant role in the maintenance of native structure and conformational stability.

Controlling the Shannon Entropy of Quantum Systems

PubMed Central

Xing, Yifan; Wu, Jun

2013-01-01

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking. PMID:23818819

Controlling the shannon entropy of quantum systems.

PubMed

Xing, Yifan; Wu, Jun

2013-01-01

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

Comment on "Route from discreteness to the continuum for the Tsallis q -entropy"

NASA Astrophysics Data System (ADS)

Ou, Congjie; Abe, Sumiyoshi

2018-06-01

Several years ago, it had been discussed that nonlogarithmic entropies, such as the Tsallis q -entropy cannot be applied to systems with continuous variables. Now, in their recent paper [Phys. Rev. E 97, 012104 (2018), 10.1103/PhysRevE.97.012104], Oikonomou and Bagci have modified the form of the q -entropy for discrete variables in such a way that its continuum limit exists. Here, it is shown that this modification violates the expandability property of entropy, and their work is actually supporting evidence for the absence of the q -entropy for systems with continuous variables.

Entanglement Entropy of Black Holes.

PubMed

Solodukhin, Sergey N

2011-01-01

The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as 't Hooft's brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.

Entanglement Entropy of Black Holes

NASA Astrophysics Data System (ADS)

Solodukhin, Sergey N.

2011-10-01

The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as 't Hooft's brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.

Excess Entropy Production in Quantum System: Quantum Master Equation Approach

NASA Astrophysics Data System (ADS)

Nakajima, Satoshi; Tokura, Yasuhiro

2017-12-01

For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by ln \\breve{ρ }_0 and ρ _0 where ρ _0 is the instantaneous steady state of the QME and \\breve{ρ }_0 is that of the QME which is given by reversing the sign of the Lamb shift term. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. Additionally, we point out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and show that these are approximately equivalent only in the weakly nonequilibrium regime.

Coherence and entanglement measures based on Rényi relative entropies

NASA Astrophysics Data System (ADS)

Zhu, Huangjun; Hayashi, Masahito; Chen, Lin

2017-11-01

We study systematically resource measures of coherence and entanglement based on Rényi relative entropies, which include the logarithmic robustness of coherence, geometric coherence, and conventional relative entropy of coherence together with their entanglement analogues. First, we show that each Rényi relative entropy of coherence is equal to the corresponding Rényi relative entropy of entanglement for any maximally correlated state. By virtue of this observation, we establish a simple operational connection between entanglement measures and coherence measures based on Rényi relative entropies. We then prove that all these coherence measures, including the logarithmic robustness of coherence, are additive. Accordingly, all these entanglement measures are additive for maximally correlated states. In addition, we derive analytical formulas for Rényi relative entropies of entanglement of maximally correlated states and bipartite pure states, which reproduce a number of classic results on the relative entropy of entanglement and logarithmic robustness of entanglement in a unified framework. Several nontrivial bounds for Rényi relative entropies of coherence (entanglement) are further derived, which improve over results known previously. Moreover, we determine all states whose relative entropy of coherence is equal to the logarithmic robustness of coherence. As an application, we provide an upper bound for the exact coherence distillation rate, which is saturated for pure states.

An Equation for Moist Entropy in a Precipitating and Icy Atmosphere

NASA Technical Reports Server (NTRS)

Tao, Wei-Kuo; Simpson, Joanne; Zeng, Xiping

2003-01-01

Moist entropy is nearly conserved in adiabatic motion. It is redistributed rather than created by moist convection. Thus moist entropy and its equation, as a healthy direction, can be used to construct analytical and numerical models for the interaction between tropical convective clouds and large-scale circulations. Hence, an accurate equation of moist entropy is needed for the analysis and modeling of atmospheric convective clouds. On the basis of the consistency between the energy and the entropy equations, a complete equation of moist entropy is derived from the energy equation. The equation expresses explicitly the internal and external sources of moist entropy, including those in relation to the microphysics of clouds and precipitation. In addition, an accurate formula for the surface flux of moist entropy from the underlying surface into the air above is derived. Because moist entropy deals "easily" with the transition among three water phases, it will be used as a prognostic variable in the next generation of cloud-resolving models (e. g. a global cloud-resolving model) for low computational noise. Its equation that is derived in this paper is accurate and complete, providing a theoretical basis for using moist entropy as a prognostic variable in the long-term modeling of clouds and large-scale circulations.

Connectivity in the human brain dissociates entropy and complexity of auditory inputs☆

PubMed Central

Nastase, Samuel A.; Iacovella, Vittorio; Davis, Ben; Hasson, Uri

2015-01-01

Complex systems are described according to two central dimensions: (a) the randomness of their output, quantified via entropy; and (b) their complexity, which reflects the organization of a system's generators. Whereas some approaches hold that complexity can be reduced to uncertainty or entropy, an axiom of complexity science is that signals with very high or very low entropy are generated by relatively non-complex systems, while complex systems typically generate outputs with entropy peaking between these two extremes. In understanding their environment, individuals would benefit from coding for both input entropy and complexity; entropy indexes uncertainty and can inform probabilistic coding strategies, whereas complexity reflects a concise and abstract representation of the underlying environmental configuration, which can serve independent purposes, e.g., as a template for generalization and rapid comparisons between environments. Using functional neuroimaging, we demonstrate that, in response to passively processed auditory inputs, functional integration patterns in the human brain track both the entropy and complexity of the auditory signal. Connectivity between several brain regions scaled monotonically with input entropy, suggesting sensitivity to uncertainty, whereas connectivity between other regions tracked entropy in a convex manner consistent with sensitivity to input complexity. These findings suggest that the human brain simultaneously tracks the uncertainty of sensory data and effectively models their environmental generators. PMID:25536493

Global sensitivity analysis for fuzzy inputs based on the decomposition of fuzzy output entropy

NASA Astrophysics Data System (ADS)

Shi, Yan; Lu, Zhenzhou; Zhou, Yicheng

2018-06-01

To analyse the component of fuzzy output entropy, a decomposition method of fuzzy output entropy is first presented. After the decomposition of fuzzy output entropy, the total fuzzy output entropy can be expressed as the sum of the component fuzzy entropy contributed by fuzzy inputs. Based on the decomposition of fuzzy output entropy, a new global sensitivity analysis model is established for measuring the effects of uncertainties of fuzzy inputs on the output. The global sensitivity analysis model can not only tell the importance of fuzzy inputs but also simultaneously reflect the structural composition of the response function to a certain degree. Several examples illustrate the validity of the proposed global sensitivity analysis, which is a significant reference in engineering design and optimization of structural systems.

An Entropy-Based Measure for Assessing Fuzziness in Logistic Regression

PubMed Central

Weiss, Brandi A.; Dardick, William

2015-01-01

This article introduces an entropy-based measure of data–model fit that can be used to assess the quality of logistic regression models. Entropy has previously been used in mixture-modeling to quantify how well individuals are classified into latent classes. The current study proposes the use of entropy for logistic regression models to quantify the quality of classification and separation of group membership. Entropy complements preexisting measures of data–model fit and provides unique information not contained in other measures. Hypothetical data scenarios, an applied example, and Monte Carlo simulation results are used to demonstrate the application of entropy in logistic regression. Entropy should be used in conjunction with other measures of data–model fit to assess how well logistic regression models classify cases into observed categories. PMID:29795897

ECG contamination of EEG signals: effect on entropy.

PubMed

Chakrabarti, Dhritiman; Bansal, Sonia

2016-02-01

Entropy™ is a proprietary algorithm which uses spectral entropy analysis of electroencephalographic (EEG) signals to produce indices which are used as a measure of depth of hypnosis. We describe a report of electrocardiographic (ECG) contamination of EEG signals leading to fluctuating erroneous Entropy values. An explanation is provided for mechanism behind this observation by describing the spread of ECG signals in head and neck and its influence on EEG/Entropy by correlating the observation with the published Entropy algorithm. While the Entropy algorithm has been well conceived, there are still instances in which it can produce erroneous values. Such erroneous values and their cause may be identified by close scrutiny of the EEG waveform if Entropy values seem out of sync with that expected at given anaesthetic levels.

An Entropy-Based Measure for Assessing Fuzziness in Logistic Regression.

PubMed

Weiss, Brandi A; Dardick, William

2016-12-01

This article introduces an entropy-based measure of data-model fit that can be used to assess the quality of logistic regression models. Entropy has previously been used in mixture-modeling to quantify how well individuals are classified into latent classes. The current study proposes the use of entropy for logistic regression models to quantify the quality of classification and separation of group membership. Entropy complements preexisting measures of data-model fit and provides unique information not contained in other measures. Hypothetical data scenarios, an applied example, and Monte Carlo simulation results are used to demonstrate the application of entropy in logistic regression. Entropy should be used in conjunction with other measures of data-model fit to assess how well logistic regression models classify cases into observed categories.

Entropy of isolated quantum systems after a quench.

PubMed

Santos, Lea F; Polkovnikov, Anatoli; Rigol, Marcos

2011-07-22

A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability.

Clausius entropy for arbitrary bifurcate null surfaces

NASA Astrophysics Data System (ADS)

Baccetti, Valentina; Visser, Matt

2014-02-01

Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation {\\rm{d}}S = \\unicode{x111} Q/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations.

Noise and complexity in human postural control: interpreting the different estimations of entropy.

PubMed

Rhea, Christopher K; Silver, Tobin A; Hong, S Lee; Ryu, Joong Hyun; Studenka, Breanna E; Hughes, Charmayne M L; Haddad, Jeffrey M

2011-03-17

Over the last two decades, various measures of entropy have been used to examine the complexity of human postural control. In general, entropy measures provide information regarding the health, stability and adaptability of the postural system that is not captured when using more traditional analytical techniques. The purpose of this study was to examine how noise, sampling frequency and time series length influence various measures of entropy when applied to human center of pressure (CoP) data, as well as in synthetic signals with known properties. Such a comparison is necessary to interpret data between and within studies that use different entropy measures, equipment, sampling frequencies or data collection durations. The complexity of synthetic signals with known properties and standing CoP data was calculated using Approximate Entropy (ApEn), Sample Entropy (SampEn) and Recurrence Quantification Analysis Entropy (RQAEn). All signals were examined at varying sampling frequencies and with varying amounts of added noise. Additionally, an increment time series of the original CoP data was examined to remove long-range correlations. Of the three measures examined, ApEn was the least robust to sampling frequency and noise manipulations. Additionally, increased noise led to an increase in SampEn, but a decrease in RQAEn. Thus, noise can yield inconsistent results between the various entropy measures. Finally, the differences between the entropy measures were minimized in the increment CoP data, suggesting that long-range correlations should be removed from CoP data prior to calculating entropy. The various algorithms typically used to quantify the complexity (entropy) of CoP may yield very different results, particularly when sampling frequency and noise are different. The results of this study are discussed within the context of the neural noise and loss of complexity hypotheses.

Time dependence of Hawking radiation entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Page, Don N., E-mail: profdonpage@gmail.com

2013-09-01

If a black hole starts in a pure quantum state and evaporates completely by a unitary process, the von Neumann entropy of the Hawking radiation initially increases and then decreases back to zero when the black hole has disappeared. Here numerical results are given for an approximation to the time dependence of the radiation entropy under an assumption of fast scrambling, for large nonrotating black holes that emit essentially only photons and gravitons. The maximum of the von Neumann entropy then occurs after about 53.81% of the evaporation time, when the black hole has lost about 40.25% of its originalmore » Bekenstein-Hawking (BH) entropy (an upper bound for its von Neumann entropy) and then has a BH entropy that equals the entropy in the radiation, which is about 59.75% of the original BH entropy 4πM{sub 0}{sup 2}, or about 7.509M{sub 0}{sup 2} ≈ 6.268 × 10{sup 76}(M{sub 0}/M{sub s}un){sup 2}, using my 1976 calculations that the photon and graviton emission process into empty space gives about 1.4847 times the BH entropy loss of the black hole. Results are also given for black holes in initially impure states. If the black hole starts in a maximally mixed state, the von Neumann entropy of the Hawking radiation increases from zero up to a maximum of about 119.51% of the original BH entropy, or about 15.018M{sub 0}{sup 2} ≈ 1.254 × 10{sup 77}(M{sub 0}/M{sub s}un){sup 2}, and then decreases back down to 4πM{sub 0}{sup 2} = 1.049 × 10{sup 77}(M{sub 0}/M{sub s}un){sup 2}.« less

Quantifying selection and diversity in viruses by entropy methods, with application to the haemagglutinin of H3N2 influenza

PubMed Central

Pan, Keyao; Deem, Michael W.

2011-01-01

Many viruses evolve rapidly. For example, haemagglutinin (HA) of the H3N2 influenza A virus evolves to escape antibody binding. This evolution of the H3N2 virus means that people who have previously been exposed to an influenza strain may be infected by a newly emerged virus. In this paper, we use Shannon entropy and relative entropy to measure the diversity and selection pressure by an antibody in each amino acid site of H3 HA between the 1992–1993 season and the 2009–2010 season. Shannon entropy and relative entropy are two independent state variables that we use to characterize H3N2 evolution. The entropy method estimates future H3N2 evolution and migration using currently available H3 HA sequences. First, we show that the rate of evolution increases with the virus diversity in the current season. The Shannon entropy of the sequence in the current season predicts relative entropy between sequences in the current season and those in the next season. Second, a global migration pattern of H3N2 is assembled by comparing the relative entropy flows of sequences sampled in China, Japan, the USA and Europe. We verify this entropy method by describing two aspects of historical H3N2 evolution. First, we identify 54 amino acid sites in HA that have evolved in the past to evade the immune system. Second, the entropy method shows that epitopes A and B on the top of HA evolve most vigorously to escape antibody binding. Our work provides a novel entropy-based method to predict and quantify future H3N2 evolution and to describe the evolutionary history of H3N2. PMID:21543352

Using heteroclinic orbits to quantify topological entropy in fluid flows

NASA Astrophysics Data System (ADS)

Sattari, Sulimon; Chen, Qianting; Mitchell, Kevin A.

2016-03-01

Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or "ghost," rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding of ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.

Cosmological Entropy Bounds

NASA Astrophysics Data System (ADS)

Brustein, R.

I review some basic facts about entropy bounds in general and about cosmological entropy bounds. Then I review the causal entropy bound, the conditions for its validity and its application to the study of cosmological singularities. This article is based on joint work with Gabriele Veneziano and subsequent related research.

Time evolution of Rényi entropy under the Lindblad equation.

PubMed

Abe, Sumiyoshi

2016-08-01

In recent years, the Rényi entropy has repeatedly been discussed for characterization of quantum critical states and entanglement. Here, time evolution of the Rényi entropy is studied. A compact general formula is presented for the lower bound on the entropy rate.

Rogue waves and entropy consumption

NASA Astrophysics Data System (ADS)

Hadjihoseini, Ali; Lind, Pedro G.; Mori, Nobuhito; Hoffmann, Norbert P.; Peinke, Joachim

2017-11-01

Based on data from the Sea of Japan and the North Sea the occurrence of rogue waves is analyzed by a scale-dependent stochastic approach, which interlinks fluctuations of waves for different spacings. With this approach we are able to determine a stochastic cascade process, which provides information of the general multipoint statistics. Furthermore the evolution of single trajectories in scale, which characterize wave height fluctuations in the surroundings of a chosen location, can be determined. The explicit knowledge of the stochastic process enables to assign entropy values to all wave events. We show that for these entropies the integral fluctuation theorem, a basic law of non-equilibrium thermodynamics, is valid. This implies that positive and negative entropy events must occur. Extreme events like rogue waves are characterized as negative entropy events. The statistics of these entropy fluctuations changes with the wave state, thus for the Sea of Japan the statistics of the entropies has a more pronounced tail for negative entropy values, indicating a higher probability of rogue waves.

Fundamental limits on quantum dynamics based on entropy change

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Khatri, Sumeet; Siopsis, George; Wilde, Mark M.

2018-01-01

It is well known in the realm of quantum mechanics and information theory that the entropy is non-decreasing for the class of unital physical processes. However, in general, the entropy does not exhibit monotonic behavior. This has restricted the use of entropy change in characterizing evolution processes. Recently, a lower bound on the entropy change was provided in the work of Buscemi, Das, and Wilde [Phys. Rev. A 93(6), 062314 (2016)]. We explore the limit that this bound places on the physical evolution of a quantum system and discuss how these limits can be used as witnesses to characterize quantum dynamics. In particular, we derive a lower limit on the rate of entropy change for memoryless quantum dynamics, and we argue that it provides a witness of non-unitality. This limit on the rate of entropy change leads to definitions of several witnesses for testing memory effects in quantum dynamics. Furthermore, from the aforementioned lower bound on entropy change, we obtain a measure of non-unitarity for unital evolutions.

The maximum entropy production and maximum Shannon information entropy in enzyme kinetics

NASA Astrophysics Data System (ADS)

Dobovišek, Andrej; Markovič, Rene; Brumen, Milan; Fajmut, Aleš

2018-04-01

We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.

The gravity dual of Rényi entropy

DOE PAGES

Dong, Xi

2016-08-12

A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Re´nyi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometricmore » prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Re´nyi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Re´nyi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.« less

Giant onsite electronic entropy enhances the performance of ceria for water splitting

DOE PAGES

Naghavi, S. Shahab; Emery, Antoine A.; Hansen, Heine A.; ...

2017-08-18

Previous studies have shown that a large solid-state entropy of reduction increases the thermodynamic efficiency of metal oxides, such as ceria, for two-step thermochemical water splitting cycles. In this context, the configurational entropy arising from oxygen off-stoichiometry in the oxide, has been the focus of most previous work. Here we report a different source of entropy, the onsite electronic configurational entropy, arising from coupling between orbital and spin angular momenta in lanthanide f orbitals. We find that onsite electronic configurational entropy is sizable in all lanthanides, and reaches a maximum value of ≈4.7 k B per oxygen vacancy for Cemore » 4+/Ce 3+ reduction. This unique and large positive entropy source in ceria explains its excellent performance for high-temperature catalytic redox reactions such as water splitting. Our calculations also show that terbium dioxide has a high electronic entropy and thus could also be a potential candidate for solar thermochemical reactions.« less

On entropy, financial markets and minority games

NASA Astrophysics Data System (ADS)

Zapart, Christopher A.

2009-04-01

The paper builds upon an earlier statistical analysis of financial time series with Shannon information entropy, published in [L. Molgedey, W. Ebeling, Local order, entropy and predictability of financial time series, European Physical Journal B-Condensed Matter and Complex Systems 15/4 (2000) 733-737]. A novel generic procedure is proposed for making multistep-ahead predictions of time series by building a statistical model of entropy. The approach is first demonstrated on the chaotic Mackey-Glass time series and later applied to Japanese Yen/US dollar intraday currency data. The paper also reinterprets Minority Games [E. Moro, The minority game: An introductory guide, Advances in Condensed Matter and Statistical Physics (2004)] within the context of physical entropy, and uses models derived from minority game theory as a tool for measuring the entropy of a model in response to time series. This entropy conditional upon a model is subsequently used in place of information-theoretic entropy in the proposed multistep prediction algorithm.

Entropy is in Flux V3.4

NASA Astrophysics Data System (ADS)

Kadanoff, Leo P.

2017-05-01

The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium ones. Since thermodynamics does not define entropy out of equilibrium, pure thermodynamics cannot follow the details of how this increase occurs. However, starting with the work of Ludwig Boltzmann in 1872, and continuing to the present day, various models of non-equilibrium behavior have been put together with the specific aim of generalizing the concept of entropy to non-equilibrium situations. This kind of entropy has been termed kinetic entropy to distinguish it from the thermodynamic variety. Knowledge of kinetic entropy started from Boltzmann's insight about his equation for the time dependence of gaseous systems. In this paper, his result is stated as a definition of kinetic entropy in terms of a local equation for the entropy density. This definition is then applied to Landau's theory of the Fermi liquid thereby giving the kinetic entropy within that theory. The dynamics of many condensed matter systems including Fermi liquids, low temperature superfluids, and ordinary metals lend themselves to the definition of kinetic entropy. In fact, entropy has been defined and used for a wide variety of situations in which a condensed matter system has been allowed to relax for a sufficient period so that the very most rapid fluctuations have been ironed out. One of the broadest applications of non-equilibrium analysis considers quantum degenerate systems using Martin-Schwinger Green's functions (Phys Rev 115:1342-1373, 1959) as generalized Wigner functions, g^<({p},ω ,{R},T) and g^>({p},ω ,{R},T). This paper describes once again how the quantum kinetic equations for these functions give locally defined conservation laws for mass momentum and energy. In local thermodynamic equilibrium, this kinetic theory enables a reasonable definition of the density of kinetic entropy. However, when the system is outside of local equilibrium, this definition fails. It is speculated that quantum entanglement is the source of this failure.

The third law of thermodynamics and the fractional entropies

NASA Astrophysics Data System (ADS)

Baris Bagci, G.

2016-08-01

We consider the fractal calculus based Ubriaco and Machado entropies and investigate whether they conform to the third law of thermodynamics. The Ubriaco entropy satisfies the third law of thermodynamics in the interval 0 < q ≤ 1 exactly where it is also thermodynamically stable. The Machado entropy, on the other hand, yields diverging inverse temperature in the region 0 < q ≤ 1, albeit with non-vanishing negative entropy values. Therefore, despite the divergent inverse temperature behavior, the Machado entropy fails the third law of thermodynamics. We also show that the aforementioned results are also supported by the one-dimensional Ising model with no external field.

Entropy, complexity, and Markov diagrams for random walk cancer models.

PubMed

Newton, Paul K; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

2014-12-19

The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

Entropy, complexity, and Markov diagrams for random walk cancer models

NASA Astrophysics Data System (ADS)

Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

2014-12-01

The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

Comment on: The cancer Warburg effect may be a testable example of the minimum entropy production rate principle.

PubMed

Sadeghi Ghuchani, Mostafa

2018-02-08

This comment argues against the view that cancer cells produce less entropy than normal cells as stated in a recent paper by Marín and Sabater. The basic principle of estimation of entropy production rate in a living cell is discussed, emphasizing the fact that entropy production depends on both the amount of heat exchange during the metabolism and the entropy difference between products and substrates.

Non-extensive entropy of modified Gaussian quantum dot under polaron effects

NASA Astrophysics Data System (ADS)

Bahramiyan, H.; Khordad, R.; Sedehi, H. R. Rastegar

2018-01-01

The effect of electron-phonon (e-p) interaction on the non-extensive Tsallis entropy of a modified Gaussian quantum dot has been investigated. In this work, the LO-phonons, SO-phonons and LO + SO-phonons have been considered. It is found that the entropy increases with enhancing the confinement potential range and depth. The entropy decreases with considering the electron-phonon interaction. The electron-LO + SO-phonon interaction has the largest contribution to the entropy.

Comment on: The cancer Warburg effect may be a testable example of the minimum entropy production rate principle

NASA Astrophysics Data System (ADS)

Sadeghi Ghuchani, Mostafa

2018-03-01

This comment argues against the view that cancer cells produce less entropy than normal cells as stated in a recent paper by Marín and Sabater. The basic principle of estimation of entropy production rate in a living cell is discussed, emphasizing the fact that entropy production depends on both the amount of heat exchange during the metabolism and the entropy difference between products and substrates.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Helinski, Ryan

This Python package provides high-performance implementations of the functions and examples presented in "BiEntropy - The Approximate Entropy of a Finite Binary String" by Grenville J. Croll, presented at ANPA 34 in 2013. https://arxiv.org/abs/1305.0954 According to the paper, BiEntropy is "a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length" using "a weighted average of the Shannon Entropies of the string and all but the last binary derivative of the string."

Third law of thermodynamics as a key test of generalized entropies.

PubMed

Bento, E P; Viswanathan, G M; da Luz, M G E; Silva, R

2015-02-01

The laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level. The third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium. Conversely, the entropy can vanish only at absolute zero temperature. Here we ask whether or not generalized entropies satisfy this fundamental property. We propose a direct analytical procedure to test if a generalized entropy satisfies the third law, assuming only very general assumptions for the entropy S and energy U of an arbitrary N-level classical system. Mathematically, the method relies on exact calculation of β=dS/dU in terms of the microstate probabilities p(i). To illustrate this approach, we present exact results for the two best known generalizations of statistical mechanics. Specifically, we study the Kaniadakis entropy S(κ), which is additive, and the Tsallis entropy S(q), which is nonadditive. We show that the Kaniadakis entropy correctly satisfies the third law only for -1<κ<+1, thereby shedding light on why κ is conventionally restricted to this interval. Surprisingly, however, the Tsallis entropy violates the third law for q<1. Finally, we give a concrete example of the power of our proposed method by applying it to a paradigmatic system: the one-dimensional ferromagnetic Ising model with nearest-neighbor interactions.

Scaling of the entropy budget with surface temperature in radiative-convective equilibrium

NASA Astrophysics Data System (ADS)

Singh, Martin S.; O'Gorman, Paul A.

2016-09-01

The entropy budget of the atmosphere is examined in simulations of radiative-convective equilibrium with a cloud-system resolving model over a wide range of surface temperatures from 281 to 311 K. Irreversible phase changes and the diffusion of water vapor account for more than half of the irreversible entropy production within the atmosphere, even in the coldest simulation. As the surface temperature is increased, the atmospheric radiative cooling rate increases, driving a greater entropy sink that must be matched by greater irreversible entropy production. The entropy production resulting from irreversible moist processes increases at a similar fractional rate as the entropy sink and at a lower rate than that implied by Clausius-Clapeyron scaling. This allows the entropy production from frictional drag on hydrometeors and on the atmospheric flow to also increase with warming, in contrast to recent results for simulations with global climate models in which the work output decreases with warming. A set of approximate scaling relations is introduced for the terms in the entropy budget as the surface temperature is varied, and many of the terms are found to scale with the mean surface precipitation rate. The entropy budget provides some insight into changes in frictional dissipation in response to warming or changes in model resolution, but it is argued that frictional dissipation is not closely linked to other measures of convective vigor.

DNA entropy reveals a significant difference in complexity between housekeeping and tissue specific gene promoters.

PubMed

Thomas, David; Finan, Chris; Newport, Melanie J; Jones, Susan

2015-10-01

The complexity of DNA can be quantified using estimates of entropy. Variation in DNA complexity is expected between the promoters of genes with different transcriptional mechanisms; namely housekeeping (HK) and tissue specific (TS). The former are transcribed constitutively to maintain general cellular functions, and the latter are transcribed in restricted tissue and cells types for specific molecular events. It is known that promoter features in the human genome are related to tissue specificity, but this has been difficult to quantify on a genomic scale. If entropy effectively quantifies DNA complexity, calculating the entropies of HK and TS gene promoters as profiles may reveal significant differences. Entropy profiles were calculated for a total dataset of 12,003 human gene promoters and for 501 housekeeping (HK) and 587 tissue specific (TS) human gene promoters. The mean profiles show the TS promoters have a significantly lower entropy (p<2.2e-16) than HK gene promoters. The entropy distributions for the 3 datasets show that promoter entropies could be used to identify novel HK genes. Functional features comprise DNA sequence patterns that are non-random and hence they have lower entropies. The lower entropy of TS gene promoters can be explained by a higher density of positive and negative regulatory elements, required for genes with complex spatial and temporary expression. Copyright © 2015 Elsevier Ltd. All rights reserved.

Connectivity in the human brain dissociates entropy and complexity of auditory inputs.

PubMed

Nastase, Samuel A; Iacovella, Vittorio; Davis, Ben; Hasson, Uri

2015-03-01

Complex systems are described according to two central dimensions: (a) the randomness of their output, quantified via entropy; and (b) their complexity, which reflects the organization of a system's generators. Whereas some approaches hold that complexity can be reduced to uncertainty or entropy, an axiom of complexity science is that signals with very high or very low entropy are generated by relatively non-complex systems, while complex systems typically generate outputs with entropy peaking between these two extremes. In understanding their environment, individuals would benefit from coding for both input entropy and complexity; entropy indexes uncertainty and can inform probabilistic coding strategies, whereas complexity reflects a concise and abstract representation of the underlying environmental configuration, which can serve independent purposes, e.g., as a template for generalization and rapid comparisons between environments. Using functional neuroimaging, we demonstrate that, in response to passively processed auditory inputs, functional integration patterns in the human brain track both the entropy and complexity of the auditory signal. Connectivity between several brain regions scaled monotonically with input entropy, suggesting sensitivity to uncertainty, whereas connectivity between other regions tracked entropy in a convex manner consistent with sensitivity to input complexity. These findings suggest that the human brain simultaneously tracks the uncertainty of sensory data and effectively models their environmental generators. Copyright © 2014. Published by Elsevier Inc.

Finite entanglement entropy and spectral dimension in quantum gravity

NASA Astrophysics Data System (ADS)

Arzano, Michele; Calcagni, Gianluca

2017-12-01

What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: (1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; (2) If the spectral dimension of the spatial boundary across which the entropy is calculated is non-negative at all scales, then the entanglement entropy cannot be finite. These conclusions, which we verify in several examples, negatively affect all quantum-gravity models, since their spectral dimension is always positive. Possible ways out are considered, including abandoning the definition of the entanglement entropy in terms of the boundary return probability or admitting an analytic continuation (not a regularization) of the usual definition. In the second case, one can get a finite entanglement entropy density in multi-fractional theories and causal dynamical triangulations.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

NASA Astrophysics Data System (ADS)

Xu, Kaixuan; Wang, Jun

2017-02-01

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model.

Magnetization and isothermal magnetic entropy change of a mixed spin-1 and spin-2 Heisenberg superlattice

NASA Astrophysics Data System (ADS)

Xu, Ping; Du, An

2017-09-01

A superlattice composed of spin-1 and spin-2 with ABAB … structure was described with Heisenberg model. The magnetizations and magnetic entropy changes under different magnetic fields were calculated by the Green's function method. The magnetization compensation phenomenon could be observed by altering the intralayer exchange interactions and the single-ion anisotropies of spins. Along with the temperature increasing, the system in the absence of magnetization compensation shows normal magnetic entropy change and displays a peak near the critical temperature, and yet the system with magnetization compensation shows normal magnetic entropy change near the compensation temperature but inverse magnetic entropy change near the critical temperature. Finally, we illustrated the reasons of different behaviors of magnetic entropy change by analyzing the contributions of two sublattices to the total magnetic entropy change.

Entropy and econophysics

NASA Astrophysics Data System (ADS)

Rosser, J. Barkley

2016-12-01

Entropy is a central concept of statistical mechanics, which is the main branch of physics that underlies econophysics, the application of physics concepts to understand economic phenomena. It enters into econophysics both in an ontological way through the Second Law of Thermodynamics as this drives the world economy from its ecological foundations as solar energy passes through food chains in dissipative process of entropy rising and production fundamentally involving the replacement of lower entropy energy states with higher entropy ones. In contrast the mathematics of entropy as appearing in information theory becomes the basis for modeling financial market dynamics as well as income and wealth distribution dynamics. It also provides the basis for an alternative view of stochastic price equilibria in economics, as well providing a crucial link between econophysics and sociophysics, keeping in mind the essential unity of the various concepts of entropy.

Bispectral index, entropy, and quantitative electroencephalogram during single-agent xenon anesthesia.

PubMed

Laitio, Ruut M; Kaskinoro, Kimmo; Särkelä, Mika O K; Kaisti, Kaike K; Salmi, Elina; Maksimow, Anu; Långsjö, Jaakko W; Aantaa, Riku; Kangas, Katja; Jääskeläinen, Satu; Scheinin, Harry

2008-01-01

The aim was to evaluate the performance of anesthesia depth monitors, Bispectral Index (BIS) and Entropy, during single-agent xenon anesthesia in 17 healthy subjects. After mask induction with xenon and intubation, anesthesia was continued with xenon only. BIS, State Entropy and Response Entropy, and electroencephalogram were monitored throughout induction, steady-state anesthesia, and emergence. The performance of BIS, State Entropy, and Response Entropy were evaluated with prediction probability, sensitivity, and specificity analyses. The power spectrum of the raw electroencephalogram signal was calculated. The mean (SD) xenon concentration during anesthesia was 66.4% (2.4%). BIS, State Entropy, and Response Entropy demonstrated low prediction probability values at loss of response (0.455, 0.656, and 0.619) but 1 min after that the values were high (0.804, 0.941, and 0.929). Thereafter, equally good performance was demonstrated for all indices. At emergence, the prediction probability values to distinguish between steady-state anesthesia and return of response for BIS, State Entropy, and Response Entropy were 0.988, 0.892, and 0.992. No statistical differences between the performances of the monitors were observed. Quantitative electroencephalogram analyses showed generalized increase in total power (P < 0.001), delta (P < 0.001) and theta activity (P < 0.001), and increased alpha activity (P = 0.003) in the frontal brain regions. Electroencephalogram-derived depth of sedation indices BIS and Entropy showed a delay to detect loss of response during induction of xenon anesthesia. Both monitors performed well in distinguishing between conscious and unconscious states during steady-state anesthesia. Xenon-induced changes in electroencephalogram closely resemble those induced by propofol.

Entropy: Order or Information

ERIC Educational Resources Information Center

Ben-Naim, Arieh

2011-01-01

Changes in entropy can "sometimes" be interpreted in terms of changes in disorder. On the other hand, changes in entropy can "always" be interpreted in terms of changes in Shannon's measure of information. Mixing and demixing processes are used to highlight the pitfalls in the association of entropy with disorder. (Contains 3 figures.)

Entropy Is Simple, Qualitatively.

ERIC Educational Resources Information Center

Lambert, Frank L.

2002-01-01

Suggests that qualitatively, entropy is simple. Entropy increase from a macro viewpoint is a measure of the dispersal of energy from localized to spread out at a temperature T. Fundamentally based on statistical and quantum mechanics, this approach is superior to the non-fundamental "disorder" as a descriptor of entropy change. (MM)

Tsallis Entropy and the Transition to Scaling in Fragmentation

NASA Astrophysics Data System (ADS)

Sotolongo-Costa, Oscar; Rodriguez, Arezky H.; Rodgers, G. J.

2000-12-01

By using the maximum entropy principle with Tsallis entropy we obtain a fragment size distribution function which undergoes a transition to scaling. This distribution function reduces to those obtained by other authors using Shannon entropy. The treatment is easily generalisable to any process of fractioning with suitable constraints.

Biologically inspired design of feedback control systems implemented using DNA strand displacement reactions.

PubMed

Foo, Mathias; Sawlekar, Rucha; Kulkarni, Vishwesh V; Bates, Declan G

2016-08-01

The use of abstract chemical reaction networks (CRNs) as a modelling and design framework for the implementation of computing and control circuits using enzyme-free, entropy driven DNA strand displacement (DSD) reactions is starting to garner widespread attention in the area of synthetic biology. Previous work in this area has demonstrated the theoretical plausibility of using this approach to design biomolecular feedback control systems based on classical proportional-integral (PI) controllers, which may be constructed from CRNs implementing gain, summation and integrator operators. Here, we propose an alternative design approach that utilises the abstract chemical reactions involved in cellular signalling cycles to implement a biomolecular controller - termed a signalling-cycle (SC) controller. We compare the performance of the PI and SC controllers in closed-loop with a nonlinear second-order chemical process. Our results show that the SC controller outperforms the PI controller in terms of both performance and robustness, and also requires fewer abstract chemical reactions to implement, highlighting its potential usefulness in the construction of biomolecular control circuits.

Coherent Structure Detection using Persistent Homology and other Topological Tools

NASA Astrophysics Data System (ADS)

Smith, Spencer; Roberts, Eric; Sindi, Suzanne; Mitchell, Kevin

2017-11-01

For non-autonomous, aperiodic fluid flows, coherent structures help organize the dynamics, much as invariant manifolds and periodic orbits do for autonomous or periodic systems. The prevalence of such flows in nature and industry has motivated many successful techniques for defining and detecting coherent structures. However, often these approaches require very fine trajectory data to reconstruct velocity fields and compute Cauchy-Green-tensor-related quantities. We use topological techniques to help detect coherent trajectory sets in relatively sparse 2D advection problems. More specifically, we have developed a homotopy-based algorithm, the ensemble-based topological entropy calculation (E-tec), which assigns to each edge in an initial triangulation of advected points a topologically forced lower bound on its future stretching rate. The triangulation and its weighted edges allow us to analyze flows using persistent homology. This topological data analysis tool detects clusters and loops in the triangulation that are robust in the presence of noise and in this case correspond to coherent trajectory sets.

Thermally-induced first-order phase transition in the (FC6H4C2H4NH3)2[PbI4] photoluminescent organic-inorganic material

NASA Astrophysics Data System (ADS)

Koubaa, M.; Dammak, T.; Garrot, D.; Castro, M.; Codjovi, E.; Mlayah, A.; Abid, Y.; Boukheddaden, K.

2012-03-01

The thermal properties of the perovskite slab alkylammonium lead iodide (FC6H4C2H4NH3)2[PbI4] are investigated using spectroscopic ellipsometry, differential scanning calorimetry, photoluminescence, and Raman spectroscopy. The spectroscopic ellipsometry, performed in the heating mode, clearly evidenced the presence of a singularity at 375 K. This is corroborated by the temperature dependence of the photoluminescence, which pointed out a first-order order-disorder phase transition at ˜375 K, with a hysteresis loop of 40 K width. Raman spectroscopy data suggest that this transition arises from a dynamic rotational disordering of the ammonium headgroups of the alkylammonium chain. In contrast, differential scanning calorimetry measurements on a pellet sample led to an entropy change value ΔS ≈0.39 J/K/mol at the transition, suggesting the existence of a residual short-range order of the NH3+ on cooling from the high temperature phase.

Nonadditive entropy maximization is inconsistent with Bayesian updating

NASA Astrophysics Data System (ADS)

Pressé, Steve

2014-11-01

The maximum entropy method—used to infer probabilistic models from data—is a special case of Bayes's model inference prescription which, in turn, is grounded in basic propositional logic. By contrast to the maximum entropy method, the compatibility of nonadditive entropy maximization with Bayes's model inference prescription has never been established. Here we demonstrate that nonadditive entropy maximization is incompatible with Bayesian updating and discuss the immediate implications of this finding. We focus our attention on special cases as illustrations.

Nonadditive entropy maximization is inconsistent with Bayesian updating.

PubMed

Pressé, Steve

2014-11-01

The maximum entropy method-used to infer probabilistic models from data-is a special case of Bayes's model inference prescription which, in turn, is grounded in basic propositional logic. By contrast to the maximum entropy method, the compatibility of nonadditive entropy maximization with Bayes's model inference prescription has never been established. Here we demonstrate that nonadditive entropy maximization is incompatible with Bayesian updating and discuss the immediate implications of this finding. We focus our attention on special cases as illustrations.

Multiscale Shannon entropy and its application in the stock market

NASA Astrophysics Data System (ADS)

Gu, Rongbao

2017-10-01

In this paper, we perform a multiscale entropy analysis on the Dow Jones Industrial Average Index using the Shannon entropy. The stock index shows the characteristic of multi-scale entropy that caused by noise in the market. The entropy is demonstrated to have significant predictive ability for the stock index in both long-term and short-term, and empirical results verify that noise does exist in the market and can affect stock price. It has important implications on market participants such as noise traders.

Holographic entanglement entropy and cyclic cosmology

NASA Astrophysics Data System (ADS)

Frampton, Paul H.

2018-06-01

We discuss a cyclic cosmology in which the visible universe, or introverse, is all that is accessible to an observer while the extroverse represents the total spacetime originating from the time when the dark energy began to dominate. It is argued that entanglement entropy of the introverse is the more appropriate quantity to render infinitely cyclic, rather than the entropy of the total universe. Since vanishing entanglement entropy implies disconnected spacetimes, at the turnaround when the introverse entropy is zero the disconnected extroverse can be jettisoned with impunity.

Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence.

PubMed

Ryu, Shinsei; Takayanagi, Tadashi

2006-05-12

A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We argue that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to AdS(3). We also compare the entropy computed in AdS(5)XS(5) with that of the free N=4 super Yang-Mills theory.

Computing a Non-trivial Lower Bound on the Joint Entropy between Two Images

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perumalla, Kalyan S.

In this report, a non-trivial lower bound on the joint entropy of two non-identical images is developed, which is greater than the individual entropies of the images. The lower bound is the least joint entropy possible among all pairs of images that have the same histograms as those of the given images. New algorithms are presented to compute the joint entropy lower bound with a computation time proportional to S log S where S is the number of histogram bins of the images. This is faster than the traditional methods of computing the exact joint entropy with a computation timemore » that is quadratic in S .« less

Discrete-time entropy formulation of optimal and adaptive control problems

NASA Technical Reports Server (NTRS)

Tsai, Yweting A.; Casiello, Francisco A.; Loparo, Kenneth A.

1992-01-01

The discrete-time version of the entropy formulation of optimal control of problems developed by G. N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws.

Quantum entropy and uncertainty for two-mode squeezed, coherent and intelligent spin states

NASA Technical Reports Server (NTRS)

Aragone, C.; Mundarain, D.

1993-01-01

We compute the quantum entropy for monomode and two-mode systems set in squeezed states. Thereafter, the quantum entropy is also calculated for angular momentum algebra when the system is either in a coherent or in an intelligent spin state. These values are compared with the corresponding values of the respective uncertainties. In general, quantum entropies and uncertainties have the same minimum and maximum points. However, for coherent and intelligent spin states, it is found that some minima for the quantum entropy turn out to be uncertainty maxima. We feel that the quantum entropy we use provides the right answer, since it is given in an essentially unique way.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Naghavi, S. Shahab; Emery, Antoine A.; Hansen, Heine A.

Previous studies have shown that a large solid-state entropy of reduction increases the thermodynamic efficiency of metal oxides, such as ceria, for two-step thermochemical water splitting cycles. In this context, the configurational entropy arising from oxygen off-stoichiometry in the oxide, has been the focus of most previous work. Here we report a different source of entropy, the onsite electronic configurational entropy, arising from coupling between orbital and spin angular momenta in lanthanide f orbitals. We find that onsite electronic configurational entropy is sizable in all lanthanides, and reaches a maximum value of ≈4.7 k B per oxygen vacancy for Cemore » 4+/Ce 3+ reduction. This unique and large positive entropy source in ceria explains its excellent performance for high-temperature catalytic redox reactions such as water splitting. Our calculations also show that terbium dioxide has a high electronic entropy and thus could also be a potential candidate for solar thermochemical reactions.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dong, Xi

A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Re´nyi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometricmore » prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Re´nyi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Re´nyi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.« less

The increase of the functional entropy of the human brain with age.

PubMed

Yao, Y; Lu, W L; Xu, B; Li, C B; Lin, C P; Waxman, D; Feng, J F

2013-10-09

We use entropy to characterize intrinsic ageing properties of the human brain. Analysis of fMRI data from a large dataset of individuals, using resting state BOLD signals, demonstrated that a functional entropy associated with brain activity increases with age. During an average lifespan, the entropy, which was calculated from a population of individuals, increased by approximately 0.1 bits, due to correlations in BOLD activity becoming more widely distributed. We attribute this to the number of excitatory neurons and the excitatory conductance decreasing with age. Incorporating these properties into a computational model leads to quantitatively similar results to the fMRI data. Our dataset involved males and females and we found significant differences between them. The entropy of males at birth was lower than that of females. However, the entropies of the two sexes increase at different rates, and intersect at approximately 50 years; after this age, males have a larger entropy.

Increased resting-state brain entropy in Alzheimer's disease.

PubMed

Xue, Shao-Wei; Guo, Yonghu

2018-03-07

Entropy analysis of resting-state functional MRI (R-fMRI) is a novel approach to characterize brain temporal dynamics and facilitates the identification of abnormal brain activity caused by several disease conditions. However, Alzheimer's disease (AD)-related brain entropy mapping based on R-fMRI has not been assessed. Here, we measured the sample entropy and voxel-wise connectivity of the network degree centrality (DC) of the intrinsic brain activity acquired by R-fMRI in 26 patients with AD and 26 healthy controls. Compared with the controls, AD patients showed increased entropy in the middle temporal gyrus and the precentral gyrus and also showed decreased DC in the precuneus. Moreover, the magnitude of the negative correlation between local brain activity (entropy) and network connectivity (DC) was increased in AD patients in comparison with healthy controls. These findings provide new evidence on AD-related brain entropy alterations.

Quantum chaos: An entropy approach

NASA Astrophysics Data System (ADS)

Sl/omczyński, Wojciech; Życzkowski, Karol

1994-11-01

A new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics. It generalizes other definitions of entropy, in both the classical and quantum cases. The Kolmogorov-Sinai (KS) entropy is obtained for a classical system and the sharp measurement instrument. For a quantum system and a coherent states instrument, a new quantity, coherent states entropy, is defined. It may be used to measure chaos in quantum mechanics. The following correspondence principle is proved: the upper limit of the coherent states entropy of a quantum map as ℏ→0 is less than or equal to the KS-entropy of the corresponding classical map. ``Chaos umpire sits, And by decision more imbroils the fray By which he reigns: next him high arbiter Chance governs all.'' John Milton, Paradise Lost, Book II

Nonequilibrium Entropy in a Shock

DOE PAGES

Margolin, Len G.

2017-07-19

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies themore » Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.« less

Exploring stability of entropy analysis for signal with different trends

NASA Astrophysics Data System (ADS)

Zhang, Yin; Li, Jin; Wang, Jun

2017-03-01

Considering the effects of environment disturbances and instrument systems, the actual detecting signals always are carrying different trends, which result in that it is difficult to accurately catch signals complexity. So choosing steady and effective analysis methods is very important. In this paper, we applied entropy measures-the base-scale entropy and approximate entropy to analyze signal complexity, and studied the effect of trends on the ideal signal and the heart rate variability (HRV) signals, that is, linear, periodic, and power-law trends which are likely to occur in actual signals. The results show that approximate entropy is unsteady when we embed different trends into the signals, so it is not suitable to analyze signal with trends. However, the base-scale entropy has preferable stability and accuracy for signal with different trends. So the base-scale entropy is an effective method to analyze the actual signals.

The Increase of the Functional Entropy of the Human Brain with Age

PubMed Central

Yao, Y.; Lu, W. L.; Xu, B.; Li, C. B.; Lin, C. P.; Waxman, D.; Feng, J. F.

2013-01-01

We use entropy to characterize intrinsic ageing properties of the human brain. Analysis of fMRI data from a large dataset of individuals, using resting state BOLD signals, demonstrated that a functional entropy associated with brain activity increases with age. During an average lifespan, the entropy, which was calculated from a population of individuals, increased by approximately 0.1 bits, due to correlations in BOLD activity becoming more widely distributed. We attribute this to the number of excitatory neurons and the excitatory conductance decreasing with age. Incorporating these properties into a computational model leads to quantitatively similar results to the fMRI data. Our dataset involved males and females and we found significant differences between them. The entropy of males at birth was lower than that of females. However, the entropies of the two sexes increase at different rates, and intersect at approximately 50 years; after this age, males have a larger entropy. PMID:24103922

Double strand breaks may be a missing link between entropy and aging.

PubMed

Lenart, Peter; Bienertová-Vašků, Julie

2016-07-01

It has been previously suggested that an increase in entropy production leads to aging. However, the mechanisms linking increased entropy production in living mass to aging are currently unclear. Even though entropy cannot be easily associated with any specific molecular damage, the increase of entropy in structural mass may be connected with heat stress, which is known to generate double strand breaks. Double strand breaks, which are in turn known to play an important role in process of aging, are thus connected to both aging and an increase of entropy. In view of these associations, we propose a new model where the increase of entropy leads to the formation of double strand breaks, resulting in an aging phenotype. This not only offers a new perspective on aging research and facilitates experimental validation, but could also serve as a useful explanatory tool. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

A Critical Look at Entropy-Based Gene-Gene Interaction Measures.

PubMed

Lee, Woojoo; Sjölander, Arvid; Pawitan, Yudi

2016-07-01

Several entropy-based measures for detecting gene-gene interaction have been proposed recently. It has been argued that the entropy-based measures are preferred because entropy can better capture the nonlinear relationships between genotypes and traits, so they can be useful to detect gene-gene interactions for complex diseases. These suggested measures look reasonable at intuitive level, but so far there has been no detailed characterization of the interactions captured by them. Here we study analytically the properties of some entropy-based measures for detecting gene-gene interactions in detail. The relationship between interactions captured by the entropy-based measures and those of logistic regression models is clarified. In general we find that the entropy-based measures can suffer from a lack of specificity in terms of target parameters, i.e., they can detect uninteresting signals as interactions. Numerical studies are carried out to confirm theoretical findings. © 2016 WILEY PERIODICALS, INC.

Microscopic insights into the NMR relaxation based protein conformational entropy meter

PubMed Central

Kasinath, Vignesh; Sharp, Kim A.; Wand, A. Joshua

2013-01-01

Conformational entropy is a potentially important thermodynamic parameter contributing to protein function. Quantitative measures of conformational entropy are necessary for an understanding of its role but have been difficult to obtain. An empirical method that utilizes changes in conformational dynamics as a proxy for changes in conformational entropy has recently been introduced. Here we probe the microscopic origins of the link between conformational dynamics and conformational entropy using molecular dynamics simulations. Simulation of seven pro! teins gave an excellent correlation with measures of side-chain motion derived from NMR relaxation. The simulations show that the motion of methyl-bearing side-chains are sufficiently coupled to that of other side chains to serve as excellent reporters of the overall side-chain conformational entropy. These results tend to validate the use of experimentally accessible measures of methyl motion - the NMR-derived generalized order parameters - as a proxy from which to derive changes in protein conformational entropy. PMID:24007504

Nonequilibrium Entropy in a Shock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, Len G.

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies themore » Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.« less

Geometric entropy and edge modes of the electromagnetic field

NASA Astrophysics Data System (ADS)

Donnelly, William; Wall, Aron C.

2016-11-01

We calculate the vacuum entanglement entropy of Maxwell theory in a class of curved spacetimes by Kaluza-Klein reduction of the theory onto a two-dimensional base manifold. Using two-dimensional duality, we express the geometric entropy of the electromagnetic field as the entropy of a tower of scalar fields, constant electric and magnetic fluxes, and a contact term, whose leading-order divergence was discovered by Kabat. The complete contact term takes the form of one negative scalar degree of freedom confined to the entangling surface. We show that the geometric entropy agrees with a statistical definition of entanglement entropy that includes edge modes: classical solutions determined by their boundary values on the entangling surface. This resolves a long-standing puzzle about the statistical interpretation of the contact term in the entanglement entropy. We discuss the implications of this negative term for black hole thermodynamics and the renormalization of Newton's constant.

Secure self-calibrating quantum random-bit generator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fiorentino, M.; Santori, C.; Spillane, S. M.

2007-03-15

Random-bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require 'strong' RBGs that produce high-entropy bit sequences, but traditional software pseudo-RBGs have very low entropy content and therefore are relatively weak for cryptography. Hardware RBGs yield entropy from chaotic or quantum physical systems and therefore are expected to exhibit high entropy, but in current implementations their exact entropy content is unknown. Here we report a quantum random-bit generator (QRBG) that harvests entropy by measuring single-photon and entangled two-photon polarization states. We introduce and implement a quantum tomographicmore » method to measure a lower bound on the 'min-entropy' of the system, and we employ this value to distill a truly random-bit sequence. This approach is secure: even if an attacker takes control of the source of optical states, a secure random sequence can be distilled.« less

Entropy of the Bose-Einstein-condensate ground state: Correlation versus ground-state entropy

NASA Astrophysics Data System (ADS)

Kim, Moochan B.; Svidzinsky, Anatoly; Agarwal, Girish S.; Scully, Marlan O.

2018-01-01

Calculation of the entropy of an ideal Bose-Einstein condensate (BEC) in a three-dimensional trap reveals unusual, previously unrecognized, features of the canonical ensemble. It is found that, for any temperature, the entropy of the Bose gas is equal to the entropy of the excited particles although the entropy of the particles in the ground state is nonzero. We explain this by considering the correlations between the ground-state particles and particles in the excited states. These correlations lead to a correlation entropy which is exactly equal to the contribution from the ground state. The correlations themselves arise from the fact that we have a fixed number of particles obeying quantum statistics. We present results for correlation functions between the ground and excited states in a Bose gas, so as to clarify the role of fluctuations in the system. We also report the sub-Poissonian nature of the ground-state fluctuations.

Computing entropy change in synoptic-scale system

NASA Astrophysics Data System (ADS)

Wu, Y. P.; Hu, Y. Y.; Cao, H. X.; Fu, C. F.; Feng, G. L.

2018-03-01

Thermodynamic entropy is of great importance in the atmospheric physics and chemistry process, because it is a non-conserved state function which making a system's tendency towards spontaneous change. But how the entropy forces a synoptic-scale system is still not well known. In this paper, we analyzed the entropy change in atmosphere system, by calculating several examples of extra tropical cyclones over the Yellow River and its adjacent area in summer. The results show that a strong negative entropy flux appears over the north of a stationary front and the thresholds Fe S ≤ - 280 and ∂s / ∂t ≤ - 50 are satisfied. At the same time, the change of total entropy is smaller than zero. Therefore the cyclone developed quickly and daily precipitation reached 371 mm, which is heaviest rain over the Yellows River area in summer. We suggest the dynamical entropy should be developed to improve the forecasting technique of heavy rainfall event in synoptic-scale.

Psychological Entropy: A Framework for Understanding Uncertainty-Related Anxiety

ERIC Educational Resources Information Center

Hirsh, Jacob B.; Mar, Raymond A.; Peterson, Jordan B.

2012-01-01

Entropy, a concept derived from thermodynamics and information theory, describes the amount of uncertainty and disorder within a system. Self-organizing systems engage in a continual dialogue with the environment and must adapt themselves to changing circumstances to keep internal entropy at a manageable level. We propose the entropy model of…

Discovery and Entropy in the Revision of Technical Reports.

ERIC Educational Resources Information Center

Marder, Daniel

A useful device in revising technical reports is the metaphor of entropy, which refers to the amount of disorder that is present in a system. Applied to communication theory, high entropy would correspond to increased amounts of unfamiliar or useless information in a text. Since entropy in rhetorical systems increases with the unfamiliarity of…

Tachyon condensation and black hole entropy.

PubMed

Dabholkar, Atish

2002-03-04

String propagation on a cone with deficit angle 2pi(1-1 / N) is considered for the purpose of computing the entropy of a large mass black hole. The entropy computed using the recent results on condensation of twisted-sector tachyons in this theory is found to be in precise agreement with the Bekenstein-Hawking entropy.

Content Based Image Retrieval and Information Theory: A General Approach.

ERIC Educational Resources Information Center

Zachary, John; Iyengar, S. S.; Barhen, Jacob

2001-01-01

Proposes an alternative real valued representation of color based on the information theoretic concept of entropy. A theoretical presentation of image entropy is accompanied by a practical description of the merits and limitations of image entropy compared to color histograms. Results suggest that image entropy is a promising approach to image…

Determining Dynamical Path Distributions usingMaximum Relative Entropy

DTIC Science & Technology

2015-05-31

entropy to a one-dimensional continuum labeled by a parameter η. The resulting η-entropies are equivalent to those proposed by Renyi [12] or by Tsallis [13...1995). [12] A. Renyi , “On measures of entropy and information,”Proc. 4th Berkeley Simposium on Mathematical Statistics and Probability, Vol 1, p. 547-461

An Accessible Approach to Understanding Entropy and Change

ERIC Educational Resources Information Center

Johnson, Philip

2018-01-01

This article challenges the notion that entropy is something to be avoided. A line of argument is presented that is accessible to those not having specialist knowledge and that offers a new perspective to those more familiar with the concept. It shows that temperature is better understood by addressing entropy. Entropy change diagrams are…

Entropy for quantum pure states and quantum H theorem

NASA Astrophysics Data System (ADS)

Han, Xizhi; Wu, Biao

2015-06-01

We construct a complete set of Wannier functions that are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability distribution in quantum phase space, we define an entropy for a quantum pure state. We prove an inequality regarding the long-time behavior of our entropy's fluctuation. For a typical initial state, this inequality indicates that our entropy can relax dynamically to a maximized value and stay there most of time with small fluctuations. This result echoes the quantum H theorem proved by von Neumann [Zeitschrift für Physik 57, 30 (1929), 10.1007/BF01339852]. Our entropy is different from the standard von Neumann entropy, which is always zero for quantum pure states. According to our definition, a system always has bigger entropy than its subsystem even when the system is described by a pure state. As the construction of the Wannier basis can be implemented numerically, the dynamical evolution of our entropy is illustrated with an example.

A new one-dimensional radiative equilibrium model for investigating atmospheric radiation entropy flux.

PubMed

Wu, Wei; Liu, Yangang

2010-05-12

A new one-dimensional radiative equilibrium model is built to analytically evaluate the vertical profile of the Earth's atmospheric radiation entropy flux under the assumption that atmospheric longwave radiation emission behaves as a greybody and shortwave radiation as a diluted blackbody. Results show that both the atmospheric shortwave and net longwave radiation entropy fluxes increase with altitude, and the latter is about one order in magnitude greater than the former. The vertical profile of the atmospheric net radiation entropy flux follows approximately that of the atmospheric net longwave radiation entropy flux. Sensitivity study further reveals that a 'darker' atmosphere with a larger overall atmospheric longwave optical depth exhibits a smaller net radiation entropy flux at all altitudes, suggesting an intrinsic connection between the atmospheric net radiation entropy flux and the overall atmospheric longwave optical depth. These results indicate that the overall strength of the atmospheric irreversible processes at all altitudes as determined by the corresponding atmospheric net entropy flux is closely related to the amount of greenhouse gases in the atmosphere.

Driver fatigue detection through multiple entropy fusion analysis in an EEG-based system.

PubMed

Min, Jianliang; Wang, Ping; Hu, Jianfeng

2017-01-01

Driver fatigue is an important contributor to road accidents, and fatigue detection has major implications for transportation safety. The aim of this research is to analyze the multiple entropy fusion method and evaluate several channel regions to effectively detect a driver's fatigue state based on electroencephalogram (EEG) records. First, we fused multiple entropies, i.e., spectral entropy, approximate entropy, sample entropy and fuzzy entropy, as features compared with autoregressive (AR) modeling by four classifiers. Second, we captured four significant channel regions according to weight-based electrodes via a simplified channel selection method. Finally, the evaluation model for detecting driver fatigue was established with four classifiers based on the EEG data from four channel regions. Twelve healthy subjects performed continuous simulated driving for 1-2 hours with EEG monitoring on a static simulator. The leave-one-out cross-validation approach obtained an accuracy of 98.3%, a sensitivity of 98.3% and a specificity of 98.2%. The experimental results verified the effectiveness of the proposed method, indicating that the multiple entropy fusion features are significant factors for inferring the fatigue state of a driver.

Large Eddy Simulation of Entropy Generation in a Turbulent Mixing Layer

NASA Astrophysics Data System (ADS)

Sheikhi, Reza H.; Safari, Mehdi; Hadi, Fatemeh

2013-11-01

Entropy transport equation is considered in large eddy simulation (LES) of turbulent flows. The irreversible entropy generation in this equation provides a more general description of subgrid scale (SGS) dissipation due to heat conduction, mass diffusion and viscosity effects. A new methodology is developed, termed the entropy filtered density function (En-FDF), to account for all individual entropy generation effects in turbulent flows. The En-FDF represents the joint probability density function of entropy, frequency, velocity and scalar fields within the SGS. An exact transport equation is developed for the En-FDF, which is modeled by a system of stochastic differential equations, incorporating the second law of thermodynamics. The modeled En-FDF transport equation is solved by a Lagrangian Monte Carlo method. The methodology is employed to simulate a turbulent mixing layer involving transport of passive scalars and entropy. Various modes of entropy generation are obtained from the En-FDF and analyzed. Predictions are assessed against data generated by direct numerical simulation (DNS). The En-FDF predictions are in good agreements with the DNS data.

Investigation of FeNiCrWMn - a new high entropy alloy

NASA Astrophysics Data System (ADS)

Buluc, G.; Florea, I.; Bălţătescu, O.; Florea, R. M.; Carcea, I.

2015-11-01

The term of high entropy alloys started from the analysis of multicomponent alloys, which were produced at an experimental level since 1995 by developing a new concept related to the development of metallic materials. Recent developments in the field of high-entropy alloys have revealed that they have versatile properties like: ductility, toughness, hardness and corrosion resistance [1]. Up until now, it has been demonstrated that the explored this alloys are feasible to be synthesized, processed and analyzed contrary to the misunderstanding based on traditional experiences. Moreover, there are many opportunities in this field for academic studies and industrial applications [1, 2]. As the combinations of composition and process for producing high entropy alloys are numerous and each high entropy alloy has its own microstructure and properties to be identified and understood, the research work is truly limitless. The novelty of these alloys consists of chemical composition. These alloys have been named high entropy alloys due to the atomic scale mixing entropies higher than traditional alloys. In this paper, I will present the microscopy and the mechanical properties of high entropy alloy FeNiCrWMn.

New Fault Recognition Method for Rotary Machinery Based on Information Entropy and a Probabilistic Neural Network.

PubMed

Jiang, Quansheng; Shen, Yehu; Li, Hua; Xu, Fengyu

2018-01-24

Feature recognition and fault diagnosis plays an important role in equipment safety and stable operation of rotating machinery. In order to cope with the complexity problem of the vibration signal of rotating machinery, a feature fusion model based on information entropy and probabilistic neural network is proposed in this paper. The new method first uses information entropy theory to extract three kinds of characteristics entropy in vibration signals, namely, singular spectrum entropy, power spectrum entropy, and approximate entropy. Then the feature fusion model is constructed to classify and diagnose the fault signals. The proposed approach can combine comprehensive information from different aspects and is more sensitive to the fault features. The experimental results on simulated fault signals verified better performances of our proposed approach. In real two-span rotor data, the fault detection accuracy of the new method is more than 10% higher compared with the methods using three kinds of information entropy separately. The new approach is proved to be an effective fault recognition method for rotating machinery.

Fusion information entropy method of rolling bearing fault diagnosis based on n-dimensional characteristic parameter distance

NASA Astrophysics Data System (ADS)

Ai, Yan-Ting; Guan, Jiao-Yue; Fei, Cheng-Wei; Tian, Jing; Zhang, Feng-Ling

2017-05-01

To monitor rolling bearing operating status with casings in real time efficiently and accurately, a fusion method based on n-dimensional characteristic parameters distance (n-DCPD) was proposed for rolling bearing fault diagnosis with two types of signals including vibration signal and acoustic emission signals. The n-DCPD was investigated based on four information entropies (singular spectrum entropy in time domain, power spectrum entropy in frequency domain, wavelet space characteristic spectrum entropy and wavelet energy spectrum entropy in time-frequency domain) and the basic thought of fusion information entropy fault diagnosis method with n-DCPD was given. Through rotor simulation test rig, the vibration and acoustic emission signals of six rolling bearing faults (ball fault, inner race fault, outer race fault, inner-ball faults, inner-outer faults and normal) are collected under different operation conditions with the emphasis on the rotation speed from 800 rpm to 2000 rpm. In the light of the proposed fusion information entropy method with n-DCPD, the diagnosis of rolling bearing faults was completed. The fault diagnosis results show that the fusion entropy method holds high precision in the recognition of rolling bearing faults. The efforts of this study provide a novel and useful methodology for the fault diagnosis of an aeroengine rolling bearing.

Entropy, complexity, and Markov diagrams for random walk cancer models

PubMed Central

Newton, Paul K.; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

2014-01-01

The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential. PMID:25523357

Entropy Based Genetic Association Tests and Gene-Gene Interaction Tests

PubMed Central

de Andrade, Mariza; Wang, Xin

2011-01-01

In the past few years, several entropy-based tests have been proposed for testing either single SNP association or gene-gene interaction. These tests are mainly based on Shannon entropy and have higher statistical power when compared to standard χ2 tests. In this paper, we extend some of these tests using a more generalized entropy definition, Rényi entropy, where Shannon entropy is a special case of order 1. The order λ (>0) of Rényi entropy weights the events (genotype/haplotype) according to their probabilities (frequencies). Higher λ places more emphasis on higher probability events while smaller λ (close to 0) tends to assign weights more equally. Thus, by properly choosing the λ, one can potentially increase the power of the tests or the p-value level of significance. We conducted simulation as well as real data analyses to assess the impact of the order λ and the performance of these generalized tests. The results showed that for dominant model the order 2 test was more powerful and for multiplicative model the order 1 or 2 had similar power. The analyses indicate that the choice of λ depends on the underlying genetic model and Shannon entropy is not necessarily the most powerful entropy measure for constructing genetic association or interaction tests. PMID:23089811

Correlation as a Determinant of Configurational Entropy in Supramolecular and Protein Systems

PubMed Central

2015-01-01

For biomolecules in solution, changes in configurational entropy are thought to contribute substantially to the free energies of processes like binding and conformational change. In principle, the configurational entropy can be strongly affected by pairwise and higher-order correlations among conformational degrees of freedom. However, the literature offers mixed perspectives regarding the contributions that changes in correlations make to changes in configurational entropy for such processes. Here we take advantage of powerful techniques for simulation and entropy analysis to carry out rigorous in silico studies of correlation in binding and conformational changes. In particular, we apply information-theoretic expansions of the configurational entropy to well-sampled molecular dynamics simulations of a model host–guest system and the protein bovine pancreatic trypsin inhibitor. The results bear on the interpretation of NMR data, as they indicate that changes in correlation are important determinants of entropy changes for biologically relevant processes and that changes in correlation may either balance or reinforce changes in first-order entropy. The results also highlight the importance of main-chain torsions as contributors to changes in protein configurational entropy. As simulation techniques grow in power, the mathematical techniques used here will offer new opportunities to answer challenging questions about complex molecular systems. PMID:24702693

On the Consequences of Clausius-Duhem Inequality for Electrolyte Solutions

NASA Astrophysics Data System (ADS)

Reis, Martina; Bassi, Adalberto Bono Maurizio Sacchi

2014-03-01

Based on the fundamentals of thermo-statics, non-equilibrium thermodynamics theories frequently employ an entropy inequality, where the entropy flux is collinear to the heat flux, and the entropy supply is proportional to the energy supply. Although this assumption is suitable for many material bodies, e.g. heat-conducting viscous fluids, there is a class of materials for which these assumptions are not valid. By assuming that the entropy flux and the entropy supply are constitutive quantities, in this work it is demonstrated that the entropy flux for a reacting ionic mixture of non-volatile solutes presents a non-collinear term due to the diffusive fluxes. The consequences of the collinearity between the entropy flux and the heat flux, as well as the proportionality of the entropy supply and the energy supply on the stability of chemical systems are also investigated. Furthermore, by considering an electrolyte solution of non-volatile solutes in phase equilibrium with water vapor, and the constitutive nature of the entropy flux, the stability of a vapor-electrolyte solution interface is studied. Despite this work only deals with electrolyte solutions, the results presented can be easily extended to more complex chemical reacting systems. The first author acknowledges financial support from CNPq (National Counsel of Technological and Scientific Development).

Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations

PubMed Central

Fogolari, Federico; Corazza, Alessandra; Fortuna, Sara; Soler, Miguel Angel; VanSchouwen, Bryan; Brancolini, Giorgia; Corni, Stefano; Melacini, Giuseppe; Esposito, Gennaro

2015-01-01

Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes. In particular: reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements;the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state;backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy);the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic. PMID:26177039

Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations.

PubMed

Fogolari, Federico; Corazza, Alessandra; Fortuna, Sara; Soler, Miguel Angel; VanSchouwen, Bryan; Brancolini, Giorgia; Corni, Stefano; Melacini, Giuseppe; Esposito, Gennaro

2015-01-01

Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes. In particular: reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements;the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state;backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy);the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic.

Financial time series analysis based on effective phase transfer entropy

NASA Astrophysics Data System (ADS)

Yang, Pengbo; Shang, Pengjian; Lin, Aijing

2017-02-01

Transfer entropy is a powerful technique which is able to quantify the impact of one dynamic system on another system. In this paper, we propose the effective phase transfer entropy method based on the transfer entropy method. We use simulated data to test the performance of this method, and the experimental results confirm that the proposed approach is capable of detecting the information transfer between the systems. We also explore the relationship between effective phase transfer entropy and some variables, such as data size, coupling strength and noise. The effective phase transfer entropy is positively correlated with the data size and the coupling strength. Even in the presence of a large amount of noise, it can detect the information transfer between systems, and it is very robust to noise. Moreover, this measure is indeed able to accurately estimate the information flow between systems compared with phase transfer entropy. In order to reflect the application of this method in practice, we apply this method to financial time series and gain new insight into the interactions between systems. It is demonstrated that the effective phase transfer entropy can be used to detect some economic fluctuations in the financial market. To summarize, the effective phase transfer entropy method is a very efficient tool to estimate the information flow between systems.

Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes

NASA Astrophysics Data System (ADS)

Neri, Izaak; Roldán, Édgar; Jülicher, Frank

2017-01-01

We study the statistics of infima, stopping times, and passage probabilities of entropy production in nonequilibrium steady states, and we show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches a given state for the first time. Our main results are as follows: (i) The distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann's constant; (ii) we find exact expressions for the passage probabilities of entropy production; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production; for example, we derive a relation between the maximal excursion of a molecular motor against the direction of an external force and the infimum of the corresponding entropy-production fluctuations. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follow from our universal results for entropy-production infima.

Entropy method of measuring and evaluating periodicity of quasi-periodic trajectories

NASA Astrophysics Data System (ADS)

Ni, Yanshuo; Turitsyn, Konstantin; Baoyin, Hexi; Junfeng, Li

2018-06-01

This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform (DFT) to the trajectories and analyzing the frequency domain within the concept of entropy. Having introduced the concept of entropy, analytical derivation and numerical results indicate that entropies increase as a logarithmic function of time. Periodic trajectories typically have higher entropies, and trajectories with higher entropies mean the periodicities of the motions are stronger. Theoretical differences between two trajectories expressed as summations of trigonometric functions are also derived analytically. Trajectories in the Henon-Heiles system and the circular restricted three-body problem (CRTBP) are analyzed with the indicator entropy and compared with orthogonal fast Lyapunov indicator (OFLI). The results show that entropy is a better tool for discriminating periodicity in quasiperiodic trajectories than OFLI and can detect periodicity while excluding the spirals that are judged as periodic cases by OFLI. Finally, trajectories in the vicinity of 243 Ida and 6489 Golevka are considered as examples, and the numerical results verify these conclusions. Some trajectories near asteroids look irregular, but their higher entropy values as analyzed by this method serve as evidence of frequency regularity in three directions. Moreover, these results indicate that applying DFT to the trajectories in the vicinity of irregular small bodies and calculating their entropy in the frequency domain provides a useful quantitative analysis method for evaluating orderliness in the periodicity of quasi-periodic trajectories within a given time interval.

Brain entropy and human intelligence: A resting-state fMRI study

PubMed Central

Calderone, Daniel; Morales, Leah J.

2018-01-01

Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns. PMID:29432427

Brain entropy and human intelligence: A resting-state fMRI study.

PubMed

Saxe, Glenn N; Calderone, Daniel; Morales, Leah J

2018-01-01

Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns.

Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen; Magin, Richard L.

2016-07-01

Analytical solutions to the fractional diffusion equation are often obtained by using Laplace and Fourier transforms, which conveniently encode the order of the time and the space derivatives (α and β) as non-integer powers of the conjugate transform variables (s, and k) for the spectral and the spatial frequencies, respectively. This study presents a new solution to the fractional diffusion equation obtained using the Laplace transform and expressed as a Fox's H-function. This result clearly illustrates the kinetics of the underlying stochastic process in terms of the Laplace spectral frequency and entropy. The spectral entropy is numerically calculated by using the direct integration method and the adaptive Gauss-Kronrod quadrature algorithm. Here, the properties of spectral entropy are investigated for the cases of sub-diffusion and super-diffusion. We find that the overall spectral entropy decreases with the increasing α and β, and that the normal or Gaussian case with α = 1 and β = 2, has the lowest spectral entropy (i.e., less information is needed to describe the state of a Gaussian process). In addition, as the neighborhood over which the entropy is calculated increases, the spectral entropy decreases, which implies a spatial averaging or coarse graining of the material properties. Consequently, the spectral entropy is shown to provide a new way to characterize the temporal correlation of anomalous diffusion. Future studies should be designed to examine changes of spectral entropy in physical, chemical and biological systems undergoing phase changes, chemical reactions and tissue regeneration.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sattari, Sulimon, E-mail: ssattari2@ucmerced.edu; Chen, Qianting, E-mail: qchen2@ucmerced.edu; Mitchell, Kevin A., E-mail: kmitchell@ucmerced.edu

Topological approaches to mixing are important tools to understand chaotic fluid flows, ranging from oceanic transport to the design of micro-mixers. Typically, topological entropy, the exponential growth rate of material lines, is used to quantify topological mixing. Computing topological entropy from the direct stretching rate is computationally expensive and sheds little light on the source of the mixing. Earlier approaches emphasized that topological entropy could be viewed as generated by the braiding of virtual, or “ghost,” rods stirring the fluid in a periodic manner. Here, we demonstrate that topological entropy can also be viewed as generated by the braiding ofmore » ghost rods following heteroclinic orbits instead. We use the machinery of homotopic lobe dynamics, which extracts symbolic dynamics from finite-length pieces of stable and unstable manifolds attached to fixed points of the fluid flow. As an example, we focus on the topological entropy of a bounded, chaotic, two-dimensional, double-vortex cavity flow. Over a certain parameter range, the topological entropy is primarily due to the braiding of a period-three orbit. However, this orbit does not explain the topological entropy for parameter values where it does not exist, nor does it explain the excess of topological entropy for the entire range of its existence. We show that braiding by heteroclinic orbits provides an accurate computation of topological entropy when the period-three orbit does not exist, and that it provides an explanation for some of the excess topological entropy when the period-three orbit does exist. Furthermore, the computation of symbolic dynamics using heteroclinic orbits has been automated and can be used to compute topological entropy for a general 2D fluid flow.« less

Entropy of uremia and dialysis technology.

PubMed

Ronco, Claudio

2013-01-01

The second law of thermodynamics applies with local exceptions to patient history and therapy interventions. Living things preserve their low level of entropy throughout time because they receive energy from their surroundings in the form of food. They gain their order at the expense of disordering the nutrients they consume. Death is the thermodynamically favored state: it represents a large increase in entropy as molecular structure yields to chaos. The kidney is an organ dissipating large amounts of energy to maintain the level of entropy of the organism as low as possible. Diseases, and in particular uremia, represent conditions of rapid increase in entropy. Therapeutic strategies are oriented towards a reduction in entropy or at least a decrease in the speed of entropy increase. Uremia is a process accelerating the trend towards randomness and disorder (increase in entropy). Dialysis is a factor external to the patient that tends to reduce the level of entropy caused by kidney disease. Since entropy can only increase in closed systems, energy and work must be spent to limit the entropy of uremia. This energy should be adapted to the system (patient) and be specifically oriented and personalized. This includes a multidimensional effort to achieve an adequate dialysis that goes beyond small molecular weight solute clearance. It includes a biological plan for recovery of homeostasis and a strategy towards long-term rehabilitation of the patient. Such objectives can be achieved with a combination of technology and innovation to answer specific questions that are still present after 60 years of dialysis history. This change in the individual bioentropy may represent a local exception to natural trends as the patient could be considered an isolated universe responding to the classic laws of thermodynamics. Copyright © 2013 S. Karger AG, Basel.

A retrospective analysis of the effect of blood transfusion on cerebral oximetry entropy and acute kidney injury.

PubMed

Engoren, Milo; Brown, Russell R; Dubovoy, Anna

2017-01-01

Acute anemia is associated with both cerebral dysfunction and acute kidney injury and is often treated with red blood cell transfusion. We sought to determine if blood transfusion changed the cerebral oximetry entropy, a measure of the complexity or irregularity of the oximetry values, and if this change was associated with subsequent acute kidney injury. This was a retrospective, case-control study of patients undergoing cardiac surgery with cardiopulmonary bypass at a tertiary care hospital, comparing those who received a red blood cell transfusion to those who did not. Acute kidney injury was defined as a perioperative increase in serum creatinine by ⩾26.4 μmol/L or by ⩾50% increase. Entropy was measured using approximate entropy, sample entropy, forbidden word entropy and basescale4 entropy in 500-point sets. Forty-four transfused patients were matched to 88 randomly selected non-transfused patients. All measures of entropy had small changes in the transfused group, but increased in the non-transfused group (p<0.05, for all comparisons). Thirty-five of 132 patients (27%) suffered acute kidney injury. Based on preoperative factors, patients who suffered kidney injury were similar to those who did not, including baseline cerebral oximetry levels. After analysis with hierarchical logistic regression, the change in basescale4 entropy (odds ratio = 1.609, 95% confidence interval = 1.057-2.450, p = 0.027) and the interaction between basescale entropy and transfusion were significantly associated with subsequent development of acute kidney injury. The transfusion of red blood cells was associated with a smaller rise in entropy values compared to non-transfused patients, suggesting a change in the regulation of cerebral oxygenation, and these changes in cerebral oxygenation are also associated with acute kidney injury.

Noise and Complexity in Human Postural Control: Interpreting the Different Estimations of Entropy

PubMed Central

Rhea, Christopher K.; Silver, Tobin A.; Hong, S. Lee; Ryu, Joong Hyun; Studenka, Breanna E.; Hughes, Charmayne M. L.; Haddad, Jeffrey M.

2011-01-01

Background Over the last two decades, various measures of entropy have been used to examine the complexity of human postural control. In general, entropy measures provide information regarding the health, stability and adaptability of the postural system that is not captured when using more traditional analytical techniques. The purpose of this study was to examine how noise, sampling frequency and time series length influence various measures of entropy when applied to human center of pressure (CoP) data, as well as in synthetic signals with known properties. Such a comparison is necessary to interpret data between and within studies that use different entropy measures, equipment, sampling frequencies or data collection durations. Methods and Findings The complexity of synthetic signals with known properties and standing CoP data was calculated using Approximate Entropy (ApEn), Sample Entropy (SampEn) and Recurrence Quantification Analysis Entropy (RQAEn). All signals were examined at varying sampling frequencies and with varying amounts of added noise. Additionally, an increment time series of the original CoP data was examined to remove long-range correlations. Of the three measures examined, ApEn was the least robust to sampling frequency and noise manipulations. Additionally, increased noise led to an increase in SampEn, but a decrease in RQAEn. Thus, noise can yield inconsistent results between the various entropy measures. Finally, the differences between the entropy measures were minimized in the increment CoP data, suggesting that long-range correlations should be removed from CoP data prior to calculating entropy. Conclusions The various algorithms typically used to quantify the complexity (entropy) of CoP may yield very different results, particularly when sampling frequency and noise are different. The results of this study are discussed within the context of the neural noise and loss of complexity hypotheses. PMID:21437281

An entropy-based analysis of lane changing behavior: An interactive approach.

PubMed

Kosun, Caglar; Ozdemir, Serhan

2017-05-19

As a novelty, this article proposes the nonadditive entropy framework for the description of driver behaviors during lane changing. The authors also state that this entropy framework governs the lane changing behavior in traffic flow in accordance with the long-range vehicular interactions and traffic safety. The nonadditive entropy framework is the new generalized theory of thermostatistical mechanics. Vehicular interactions during lane changing are considered within this framework. The interactive approach for the lane changing behavior of the drivers is presented in the traffic flow scenarios presented in the article. According to the traffic flow scenarios, 4 categories of traffic flow and driver behaviors are obtained. Through the scenarios, comparative analyses of nonadditive and additive entropy domains are also provided. Two quadrants of the categories belong to the nonadditive entropy; the rest are involved in the additive entropy domain. Driving behaviors are extracted and the scenarios depict that nonadditivity matches safe driving well, whereas additivity corresponds to unsafe driving. Furthermore, the cooperative traffic system is considered in nonadditivity where the long-range interactions are present. However, the uncooperative traffic system falls into the additivity domain. The analyses also state that there would be possible traffic flow transitions among the quadrants. This article shows that lane changing behavior could be generalized as nonadditive, with additivity as a special case, based on the given traffic conditions. The nearest and close neighbor models are well within the conventional additive entropy framework. In this article, both the long-range vehicular interactions and safe driving behavior in traffic are handled in the nonadditive entropy domain. It is also inferred that the Tsallis entropy region would correspond to mandatory lane changing behavior, whereas additive and either the extensive or nonextensive entropy region would match discretionary lane changing behavior. This article states that driver behaviors would be in the nonadditive entropy domain to provide a safe traffic stream and hence with vehicle accident prevention in mind.

Two aspects of black hole entropy in Lanczos-Lovelock models of gravity

NASA Astrophysics Data System (ADS)

Kolekar, Sanved; Kothawala, Dawood; Padmanabhan, T.

2012-03-01

We consider two specific approaches to evaluate the black hole entropy which are known to produce correct results in the case of Einstein’s theory and generalize them to Lanczos-Lovelock models. In the first approach (which could be called extrinsic), we use a procedure motivated by earlier work by Pretorius, Vollick, and Israel, and by Oppenheim, and evaluate the entropy of a configuration of densely packed gravitating shells on the verge of forming a black hole in Lanczos-Lovelock theories of gravity. We find that this matter entropy is not equal to (it is less than) Wald entropy, except in the case of Einstein theory, where they are equal. The matter entropy is proportional to the Wald entropy if we consider a specific mth-order Lanczos-Lovelock model, with the proportionality constant depending on the spacetime dimensions D and the order m of the Lanczos-Lovelock theory as (D-2m)/(D-2). Since the proportionality constant depends on m, the proportionality between matter entropy and Wald entropy breaks down when we consider a sum of Lanczos-Lovelock actions involving different m. In the second approach (which could be called intrinsic), we generalize a procedure, previously introduced by Padmanabhan in the context of general relativity, to study off-shell entropy of a class of metrics with horizon using a path integral method. We consider the Euclidean action of Lanczos-Lovelock models for a class of metrics off shell and interpret it as a partition function. We show that in the case of spherically symmetric metrics, one can interpret the Euclidean action as the free energy and read off both the entropy and energy of a black hole spacetime. Surprisingly enough, this leads to exactly the Wald entropy and the energy of the spacetime in Lanczos-Lovelock models obtained by other methods. We comment on possible implications of the result.

Bubble Entropy: An Entropy Almost Free of Parameters.

PubMed

Manis, George; Aktaruzzaman, Md; Sassi, Roberto

2017-11-01

Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors. Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors.

Enumeration of spanning trees in planar unclustered networks

NASA Astrophysics Data System (ADS)

Xiao, Yuzhi; Zhao, Haixing; Hu, Guona; Ma, Xiujuan

2014-07-01

Among a variety of subgraphs, spanning trees are one of the most important and fundamental categories. They are relevant to diverse aspects of networks, including reliability, transport, self-organized criticality, loop-erased random walks and so on. In this paper, we introduce a family of modular, self-similar planar networks with zero clustering. Relevant properties of this family are comparable to those networks associated with technological systems having low clustering, like power grids, some electronic circuits, the Internet and some biological systems. So, it is very significant to research on spanning trees of planar networks. However, for a large network, evaluating the relevant determinant is intractable. In this paper, we propose a fairly generic linear algorithm for counting the number of spanning trees of a planar network. Using the algorithm, we derive analytically the exact numbers of spanning trees in planar networks. Our result shows that the computational complexity is O(t) , which is better than that of the matrix tree theorem with O(m2t2) , where t is the number of steps and m is the girth of the planar network. We also obtain the entropy for the spanning trees of a given planar network. We find that the entropy of spanning trees in the studied network is small, which is in sharp contrast to the previous result for planar networks with the same average degree. We also determine an upper bound and a lower bound for the numbers of spanning trees in the family of planar networks by the algorithm. As another application of the algorithm, we give a formula for the number of spanning trees in an outerplanar network with small-world features.

Microstructural stability and mechanical behavior of FeNiMnCr high entropy alloy under ion irradiation

DOE PAGES

Leonard, Keith J.; Bei, Hongbin; Zinkle, Steven J.; ...

2016-05-13

In recent years, high entropy alloys (HEAs) have attracted significant attention due to their excellent mechanical properties and good corrosion resistance, making them potential candidates for high temperature fission and fusion structural applications. However there is very little known about their radiation resistance, particularly at elevated temperatures relevant for energy applications. In the present study, a single phase (face centered cubic) concentrated solid solution alloy of composition 27%Fe-28%Ni-27%Mn-18%Cr was irradiated with 3 or 5.8 MeV Ni ions at temperatures ranging from room temperature to 700 °C and midrange doses from 0.03 to 10 displacements per atom (dpa). Transmission electron microscopymore » (TEM), scanning transmission electron microscopy with energy dispersive x-ray spectrometry (STEM/EDS) and X-ray diffraction (XRD) were used to characterize the radiation defects and microstructural changes. Irradiation at higher temperatures showed evidence of relatively sluggish solute diffusion with limited solute depletion or enrichment at grain boundaries. The main microstructural feature at all temperatures was high-density small dislocation loops. Voids were not observed at any irradiation condition. Nano-indentation tests on specimens irradiated at room temperature showed a rapid increase in hardness ~35% and ~80% higher than the unirradiated value at 0.03 and 0.3 dpa midrange doses, respectively. The irradiation-induced hardening was less pronounced for 500 °C irradiations (<20% increase after 3 dpa). Overall, the examined HEA material exhibits superior radiation resistance compared to conventional single phase Fe-Cr-Ni austenitic alloys such as stainless steels. Furthermore, the present study provides insight on the fundamental irradiation behavior of a single phase HEA material over a broad range of irradiation temperatures.« less

An Entropy-Based Measure for Assessing Fuzziness in Logistic Regression

ERIC Educational Resources Information Center

Weiss, Brandi A.; Dardick, William

2016-01-01

This article introduces an entropy-based measure of data-model fit that can be used to assess the quality of logistic regression models. Entropy has previously been used in mixture-modeling to quantify how well individuals are classified into latent classes. The current study proposes the use of entropy for logistic regression models to quantify…

A Maximal Entropy Distribution Derivation of the Sharma-Taneja-Mittal Entropic Form

NASA Astrophysics Data System (ADS)

Scarfone, Antonio M.

In this letter we derive the distribution maximizing the Sharma-Taneja-Mittal entropy under certain constrains by using an information inequality satisfied by the Br`egman divergence associated to this entropic form. The resulting maximal entropy distribution coincides with the one derived from the calculus according to the maximal entropy principle à la Jaynes.

Entropy-based goodness-of-fit test: Application to the Pareto distribution

NASA Astrophysics Data System (ADS)

Lequesne, Justine

2013-08-01

Goodness-of-fit tests based on entropy have been introduced in [13] for testing normality. The maximum entropy distribution in a class of probability distributions defined by linear constraints induces a Pythagorean equality between the Kullback-Leibler information and an entropy difference. This allows one to propose a goodness-of-fit test for maximum entropy parametric distributions which is based on the Kullback-Leibler information. We will focus on the application of the method to the Pareto distribution. The power of the proposed test is computed through Monte Carlo simulation.

RED: a set of molecular descriptors based on Renyi entropy.

PubMed

Delgado-Soler, Laura; Toral, Raul; Tomás, M Santos; Rubio-Martinez, Jaime

2009-11-01

New molecular descriptors, RED (Renyi entropy descriptors), based on the generalized entropies introduced by Renyi are presented. Topological descriptors based on molecular features have proven to be useful for describing molecular profiles. Renyi entropy is used as a variability measure to contract a feature-pair distribution composing the descriptor vector. The performance of RED descriptors was tested for the analysis of different sets of molecular distances, virtual screening, and pharmacological profiling. A free parameter of the Renyi entropy has been optimized for all the considered applications.

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

Entropy as a measure of diffusion

NASA Astrophysics Data System (ADS)

Aghamohammadi, Amir; Fatollahi, Amir H.; Khorrami, Mohammad; Shariati, Ahmad

2013-10-01

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

Entropic inequalities for a class of quantum secret-sharing states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sarvepalli, Pradeep

It is well known that von Neumann entropy is nonmonotonic, unlike Shannon entropy (which is monotonically nondecreasing). Consequently, it is difficult to relate the entropies of the subsystems of a given quantum state. In this paper, we show that if we consider quantum secret-sharing states arising from a class of monotone span programs, then we can partially recover the monotonicity of entropy for the so-called unauthorized sets. Furthermore, we can show for these quantum states that the entropy of the authorized sets is monotonically nonincreasing.

Entropy of a (1+1)-dimensional charged black hole to all orders in the Planck length

NASA Astrophysics Data System (ADS)

Kim, Yong-Wan; Park, Young-Jai

2013-02-01

We study the statistical entropy of a scalar field on the (1+1)-dimensional Maxwell-dilaton background without an artificial cutoff by considering corrections to all orders in the Planck length obtained from a generalized uncertainty principle applied to the quantum state density. In contrast to the previous results for d ≥ 3 dimensional cases, we obtain an unadjustable entropy due to the independence of the minimal length, which plays the role of an adjustable parameter. However, this entropy is still proportional to the Bekenstein-Hawking entropy.

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

NASA Astrophysics Data System (ADS)

Cofré, Rodrigo; Maldonado, Cesar

2018-01-01

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

High Entropy Alloys: Criteria for Stable Structure

NASA Astrophysics Data System (ADS)

Tripathy, Snehashish; Gupta, Gaurav; Chowdhury, Sandip Ghosh

2018-01-01

An effort has been made to reassess the phase predicting capability of various thermodynamic and topological parameters across a wide range of HEA systems. These parameters are valence electron concentration, atomic mismatch ( δ), electronegativity difference (Δ χ), mixing entropy (Δ S mix), entropy of fusion (Δ S f), and mismatch entropy ( S σ ). In continuation of that, two new parameters (a) Modified Darken-Gurry parameter ( A = Sσ * χ) and (b) Modified Mismatch Entropy parameter ( B = δ* Sσ) have been designed to predict the stable crystal structure that would form in the HEA systems considered for assessment.

Entropy in the interior of a higher-dimensional black hole

NASA Astrophysics Data System (ADS)

Yang, Jian-Zhi; Liu, Wen-Biao

2018-07-01

Recently Christodoulou and Rovelli brought out a sensible description for the black hole volume as the largest volume. Later the entropy related to this volume in a 4-dimensional Schwarzschild black hole was investigated, which showed that such entropy is proportional to the surface area of the black hole. We will probe into these issues in the context of higher-dimensional case. It is found that the proportion between this entropy and the Bekenstein-Hawking entropy will go down through dramatic change along with the increase of spacetime dimension.

Entropy production and nonlinear Fokker-Planck equations.

PubMed

Casas, G A; Nobre, F D; Curado, E M F

2012-12-01

The entropy time rate of systems described by nonlinear Fokker-Planck equations--which are directly related to generalized entropic forms--is analyzed. Both entropy production, associated with irreversible processes, and entropy flux from the system to its surroundings are studied. Some examples of known generalized entropic forms are considered, and particularly, the flux and production of the Boltzmann-Gibbs entropy, obtained from the linear Fokker-Planck equation, are recovered as particular cases. Since nonlinear Fokker-Planck equations are appropriate for the dynamical behavior of several physical phenomena in nature, like many within the realm of complex systems, the present analysis should be applicable to irreversible processes in a large class of nonlinear systems, such as those described by Tsallis and Kaniadakis entropies.

The performance evaluation model of mining project founded on the weight optimization entropy value method

NASA Astrophysics Data System (ADS)

Mao, Chao; Chen, Shou

2017-01-01

According to the traditional entropy value method still have low evaluation accuracy when evaluating the performance of mining projects, a performance evaluation model of mineral project founded on improved entropy is proposed. First establish a new weight assignment model founded on compatible matrix analysis of analytic hierarchy process (AHP) and entropy value method, when the compatibility matrix analysis to achieve consistency requirements, if it has differences between subjective weights and objective weights, moderately adjust both proportions, then on this basis, the fuzzy evaluation matrix for performance evaluation. The simulation experiments show that, compared with traditional entropy and compatible matrix analysis method, the proposed performance evaluation model of mining project based on improved entropy value method has higher accuracy assessment.

Application of a Real-Time, Calculable Limiting Form of the Renyi Entropy for Molecular Imaging of Tumors

PubMed Central

Marsh, J. N.; Wallace, K. D.; McCarthy, J. E.; Wickerhauser, M. V.; Maurizi, B. N.; Lanza, G. M.; Wickline, S. A.; Hughes, M. S.

2011-01-01

Previously, we reported new methods for ultrasound signal characterization using entropy, Hf; a generalized entropy, the Renyi entropy, If(r); and a limiting form of Renyi entropy suitable for real-time calculation, If,∞. All of these quantities demonstrated significantly more sensitivity to subtle changes in scattering architecture than energy-based methods in certain settings. In this study, the real-time calculable limit of the Renyi entropy, If,∞, is applied for the imaging of angiogenic murine neovasculature in a breast cancer xenograft using a targeted contrast agent. It is shown that this approach may be used to detect reliably the accumulation of targeted nanoparticles at five minutes post-injection in this in vivo model. PMID:20679020

Sharpening the second law of thermodynamics with the quantum Bayes theorem.

PubMed

Gharibyan, Hrant; Tegmark, Max

2014-09-01

We prove a generalization of the classic Groenewold-Lindblad entropy inequality, combining decoherence and the quantum Bayes theorem into a simple unified picture where decoherence increases entropy while observation decreases it. This provides a rigorous quantum-mechanical version of the second law of thermodynamics, governing how the entropy of a system (the entropy of its density matrix, partial-traced over the environment and conditioned on what is known) evolves under general decoherence and observation. The powerful tool of spectral majorization enables both simple alternative proofs of the classic Lindblad and Holevo inequalities without using strong subadditivity, and also novel inequalities for decoherence and observation that hold not only for von Neumann entropy, but also for arbitrary concave entropies.

Invariant quantities in the scalar-tensor theories of gravitation

NASA Astrophysics Data System (ADS)

Järv, Laur; Kuusk, Piret; Saal, Margus; Vilson, Ott

2015-01-01

We consider the general scalar-tensor gravity without derivative couplings. By rescaling of the metric and reparametrization of the scalar field, the theory can be presented in different conformal frames and parametrizations. In this work we argue that while due to the freedom to transform the metric and the scalar field, the scalar field itself does not carry a physical meaning (in a generic parametrization), there are functions of the scalar field and its derivatives which remain invariant under the transformations. We put forward a scheme to construct these invariants, discuss how to formulate the theory in terms of the invariants, and show how the observables like parametrized post-Newtonian parameters and characteristics of the cosmological solutions can be neatly expressed in terms of the invariants. In particular, we describe the scalar field solutions in Friedmann-Lemaître-Robertson-Walker cosmology in Einstein and Jordan frames and explain their correspondence despite the approximate equations turning out to be linear and nonlinear in different frames.

Correlation and agreement between the bispectral index vs. state entropy during hypothermic cardio-pulmonary bypass.

PubMed

Meybohm, P; Gruenewald, M; Höcker, J; Renner, J; Graesner, J-T; Ilies, C; Scholz, J; Bein, B

2010-02-01

The bispectral index (BIS) and spectral entropy enable monitoring the depth of anaesthesia. Mild hypothermia has been shown to affect the ability of electroencephalography monitors to reflect the anaesthetic drug effect. The purpose of this study was to investigate the effect of hypothermia during a cardio-pulmonary bypass on the correlation and agreement between the BIS and entropy variables compared with normothermic conditions. This prospective clinical study included coronary artery bypass grafting patients (n=25) evaluating correlation and agreement (Bland-Altman analysis) between the BIS and both spectral and response entropy during a hypothermic cardio-pulmonary bypass (31-34 degrees C) compared with nomothermic conditions (34-37.5 degrees C). Anaesthesia was maintained with propofol and sufentanil and adjusted clinically, while the anaesthetist was blinded to the monitors. The BIS and entropy values decreased during cooling (P<0.05), but the decrease was more pronounced for entropy variables compared with BIS (P<0.05). The correlation coefficients (bias+/-SD; percentage error) between the BIS vs. spectral state entropy and response entropy were r(2)=0.56 (1+/-11; 42%) and r(2)=0.58 (-2+/-11; 43%) under normothermic conditions, and r(2)=0.17 (10+/-12; 77%) and r(2)=0.18 (9+/-11; 68%) under hypothermic conditions, respectively. Bias was significantly increased under hypothermic conditions (P<0.001 vs. normothermia). Acceptable agreement was observed between the BIS and entropy variables under normothermic but not under hypothermic conditions. The BIS and entropy variables may therefore not be interchangeable during a hypothermic cardio-pulmonary bypass.

Dynamic approximate entropy electroanatomic maps detect rotors in a simulated atrial fibrillation model.

PubMed

Ugarte, Juan P; Orozco-Duque, Andrés; Tobón, Catalina; Kremen, Vaclav; Novak, Daniel; Saiz, Javier; Oesterlein, Tobias; Schmitt, Clauss; Luik, Armin; Bustamante, John

2014-01-01

There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping.

From atomic structure to excess entropy: a neutron diffraction and density functional theory study of CaO-Al2O3-SiO2 melts

NASA Astrophysics Data System (ADS)

Liu, Maoyuan; Jacob, Aurélie; Schmetterer, Clemens; Masset, Patrick J.; Hennet, Louis; Fischer, Henry E.; Kozaily, Jad; Jahn, Sandro; Gray-Weale, Angus

2016-04-01

Calcium aluminosilicate \\text{CaO}-\\text{A}{{\\text{l}}2}{{\\text{O}}3}-\\text{Si}{{\\text{O}}2} (CAS) melts with compositions {{≤ft(\\text{CaO}-\\text{Si}{{\\text{O}}2}\\right)}x}{{≤ft(\\text{A}{{\\text{l}}2}{{\\text{O}}3}\\right)}1-x} for x  <  0.5 and {{≤ft(\\text{A}{{\\text{l}}2}{{\\text{O}}3}\\right)}x}{{≤ft(\\text{Si}{{\\text{O}}2}\\right)}1-x} for x≥slant 0.5 are studied using neutron diffraction with aerodynamic levitation and density functional theory molecular dynamics modelling. Simulated structure factors are found to be in good agreement with experimental structure factors. Local atomic structures from simulations reveal the role of calcium cations as a network modifier, and aluminium cations as a non-tetrahedral network former. Distributions of tetrahedral order show that an increasing concentration of the network former Al increases entropy, while an increasing concentration of the network modifier Ca decreases entropy. This trend is opposite to the conventional understanding that increasing amounts of network former should increase order in the network liquid, and so decrease entropy. The two-body correlation entropy S 2 is found to not correlate with the excess entropy values obtained from thermochemical databases, while entropies including higher-order correlations such as tetrahedral order, O-M-O or M-O-M bond angles and Q N environments show a clear linear correlation between computed entropy and database excess entropy. The possible relationship between atomic structures and excess entropy is discussed.

Influence of hypobaric hypoxia on bispectral index and spectral entropy in volunteers.

PubMed

Ikeda, T; Yamada, S; Imada, T; Matsuda, H; Kazama, T

2009-08-01

Hypoxia has been shown to change electroencephalogram parameters including frequency and amplitude, and may thus change bispectral index (BIS) and spectral entropy values. If hypoxia per se changes BIS and spectral entropy values, BIS and spectral entropy values may not correctly reflect the depth of anaesthesia during hypoxia. The aim of this study was to examine the changes in BIS and spectral entropy values during hypobaric hypoxia in volunteers. The study was conducted in a high-altitude chamber with 11 volunteers. After the subjects breathed 100% oxygen for 15 min at the ground level, the simulated altitude increased gradually to the 7620 m (25,000 ft) level while the subjects continued to breathe oxygen. Then, the subjects discontinued to breath oxygen and breathed room air at the 7620 m level for up to 5 min until they requested to stop hypoxic exposure. Oxygen saturation (SpO2), heart rate, 95% spectral edge frequency (SEF), BIS, response entropy (RE), and state entropy (SE) of spectral entropy were recorded throughout the study period. Of the 11 subjects, seven subjects who underwent hypoxic exposure for 4 min were analysed. SpO2 decreased to 69% at the 7620 m level without oxygen. However, SEF, BIS, RE, and SE before and during hypoxic exposure were almost identical. These data suggest that hypoxia of oxygen saturation around 70% does not have a strong effect on BIS and spectral entropy.

Formulating the shear stress distribution in circular open channels based on the Renyi entropy

NASA Astrophysics Data System (ADS)

Khozani, Zohreh Sheikh; Bonakdari, Hossein

2018-01-01

The principle of maximum entropy is employed to derive the shear stress distribution by maximizing the Renyi entropy subject to some constraints and by assuming that dimensionless shear stress is a random variable. A Renyi entropy-based equation can be used to model the shear stress distribution along the entire wetted perimeter of circular channels and circular channels with flat beds and deposited sediments. A wide range of experimental results for 12 hydraulic conditions with different Froude numbers (0.375 to 1.71) and flow depths (20.3 to 201.5 mm) were used to validate the derived shear stress distribution. For circular channels, model performance enhanced with increasing flow depth (mean relative error (RE) of 0.0414) and only deteriorated slightly at the greatest flow depth (RE of 0.0573). For circular channels with flat beds, the Renyi entropy model predicted the shear stress distribution well at lower sediment depth. The Renyi entropy model results were also compared with Shannon entropy model results. Both models performed well for circular channels, but for circular channels with flat beds the Renyi entropy model displayed superior performance in estimating the shear stress distribution. The Renyi entropy model was highly precise and predicted the shear stress distribution in a circular channel with RE of 0.0480 and in a circular channel with a flat bed with RE of 0.0488.

Maximum and minimum entropy states yielding local continuity bounds

NASA Astrophysics Data System (ADS)

Hanson, Eric P.; Datta, Nilanjana

2018-04-01

Given an arbitrary quantum state (σ), we obtain an explicit construction of a state ρɛ * ( σ ) [respectively, ρ * , ɛ ( σ ) ] which has the maximum (respectively, minimum) entropy among all states which lie in a specified neighborhood (ɛ-ball) of σ. Computing the entropy of these states leads to a local strengthening of the continuity bound of the von Neumann entropy, i.e., the Audenaert-Fannes inequality. Our bound is local in the sense that it depends on the spectrum of σ. The states ρɛ * ( σ ) and ρ * , ɛ (σ) depend only on the geometry of the ɛ-ball and are in fact optimizers for a larger class of entropies. These include the Rényi entropy and the minimum- and maximum-entropies, providing explicit formulas for certain smoothed quantities. This allows us to obtain local continuity bounds for these quantities as well. In obtaining this bound, we first derive a more general result which may be of independent interest, namely, a necessary and sufficient condition under which a state maximizes a concave and Gâteaux-differentiable function in an ɛ-ball around a given state σ. Examples of such a function include the von Neumann entropy and the conditional entropy of bipartite states. Our proofs employ tools from the theory of convex optimization under non-differentiable constraints, in particular Fermat's rule, and majorization theory.

An Extension to Deng's Entropy in the Open World Assumption with an Application in Sensor Data Fusion.

PubMed

Tang, Yongchuan; Zhou, Deyun; Chan, Felix T S

2018-06-11

Quantification of uncertain degree in the Dempster-Shafer evidence theory (DST) framework with belief entropy is still an open issue, even a blank field for the open world assumption. Currently, the existed uncertainty measures in the DST framework are limited to the closed world where the frame of discernment (FOD) is assumed to be complete. To address this issue, this paper focuses on extending a belief entropy to the open world by considering the uncertain information represented as the FOD and the nonzero mass function of the empty set simultaneously. An extension to Deng’s entropy in the open world assumption (EDEOW) is proposed as a generalization of the Deng’s entropy and it can be degenerated to the Deng entropy in the closed world wherever necessary. In order to test the reasonability and effectiveness of the extended belief entropy, an EDEOW-based information fusion approach is proposed and applied to sensor data fusion under uncertainty circumstance. The experimental results verify the usefulness and applicability of the extended measure as well as the modified sensor data fusion method. In addition, a few open issues still exist in the current work: the necessary properties for a belief entropy in the open world assumption, whether there exists a belief entropy that satisfies all the existed properties, and what is the most proper fusion frame for sensor data fusion under uncertainty.

Entropy Generation and Human Aging: Lifespan Entropy and Effect of Physical Activity Level

NASA Astrophysics Data System (ADS)

Silva, Carlos; Annamalai, Kalyan

2008-06-01

The first and second laws of thermodynamics were applied to biochemical reactions typical of human metabolism. An open-system model was used for a human body. Energy conservation, availability and entropy balances were performed to obtain the entropy generated for the main food components. Quantitative results for entropy generation were obtained as a function of age using the databases from the U.S. Food and Nutrition Board (FNB) and Centers for Disease Control and Prevention (CDC), which provide energy requirements and food intake composition as a function of age, weight and stature. Numerical integration was performed through human lifespan for different levels of physical activity. Results were presented and analyzed. Entropy generated over the lifespan of average individuals (natural death) was found to be 11,404 kJ/ºK per kg of body mass with a rate of generation three times higher on infants than on the elderly. The entropy generated predicts a life span of 73.78 and 81.61 years for the average U.S. male and female individuals respectively, which are values that closely match the average lifespan from statistics (74.63 and 80.36 years). From the analysis of the effect of different activity levels, it is shown that entropy generated increases with physical activity, suggesting that exercise should be kept to a “healthy minimum” if entropy generation is to be minimized.

Entropy Analysis of Kinetic Flux Vector Splitting Schemes for the Compressible Euler Equations

NASA Technical Reports Server (NTRS)

Shiuhong, Lui; Xu, Jun

1999-01-01

Flux Vector Splitting (FVS) scheme is one group of approximate Riemann solvers for the compressible Euler equations. In this paper, the discretized entropy condition of the Kinetic Flux Vector Splitting (KFVS) scheme based on the gas-kinetic theory is proved. The proof of the entropy condition involves the entropy definition difference between the distinguishable and indistinguishable particles.

Comparing Postural Stability Entropy Analyses to Differentiate Fallers and Non-Fallers

PubMed Central

Fino, Peter C.; Mojdehi, Ahmad R.; Adjerid, Khaled; Habibi, Mohammad; Lockhart, Thurmon E.; Ross, Shane D.

2015-01-01

The health and financial cost of falls has spurred research to differentiate the characteristics of fallers and non-fallers. Postural stability has received much of the attention with recent studies exploring various measures of entropy. This study compared the discriminatory ability of several entropy methods at differentiating two paradigms in the center-of-pressure (COP) of elderly individuals: 1.) eyes open (EO) versus eyes closed (EC) and 2.) fallers (F) versus non-fallers (NF). Methods were compared using the area under the curve (AUC) of the receiver-operating characteristic (ROC) curves developed from logistic regression models. Overall, multiscale entropy (MSE) and composite multiscale entropy (CompMSE) performed the best with AUCs of 0.71 for EO/EC and 0.77 for F/NF. When methods were combined together to maximize the AUC, the entropy classifier had an AUC of for 0.91 the F/NF comparison. These results suggest researchers and clinicians attempting to create clinical tests to identify fallers should consider a combination of every entropy method when creating a classifying test. Additionally, MSE and CompMSE classifiers using polar coordinate data outperformed rectangular coordinate data, encouraging more research into the most appropriate time series for postural stability entropy analysis. PMID:26464267

Ecosystem functioning and maximum entropy production: a quantitative test of hypotheses.

PubMed

Meysman, Filip J R; Bruers, Stijn

2010-05-12

The idea that entropy production puts a constraint on ecosystem functioning is quite popular in ecological thermodynamics. Yet, until now, such claims have received little quantitative verification. Here, we examine three 'entropy production' hypotheses that have been forwarded in the past. The first states that increased entropy production serves as a fingerprint of living systems. The other two hypotheses invoke stronger constraints. The state selection hypothesis states that when a system can attain multiple steady states, the stable state will show the highest entropy production rate. The gradient response principle requires that when the thermodynamic gradient increases, the system's new stable state should always be accompanied by a higher entropy production rate. We test these three hypotheses by applying them to a set of conventional food web models. Each time, we calculate the entropy production rate associated with the stable state of the ecosystem. This analysis shows that the first hypothesis holds for all the food webs tested: the living state shows always an increased entropy production over the abiotic state. In contrast, the state selection and gradient response hypotheses break down when the food web incorporates more than one trophic level, indicating that they are not generally valid.

Atomic and electronic basis for the serrations of refractory high-entropy alloys

NASA Astrophysics Data System (ADS)

Wang, William Yi; Shang, Shun Li; Wang, Yi; Han, Fengbo; Darling, Kristopher A.; Wu, Yidong; Xie, Xie; Senkov, Oleg N.; Li, Jinshan; Hui, Xi Dong; Dahmen, Karin A.; Liaw, Peter K.; Kecskes, Laszlo J.; Liu, Zi-Kui

2017-06-01

Refractory high-entropy alloys present attractive mechanical properties, i.e., high yield strength and fracture toughness, making them potential candidates for structural applications. Understandings of atomic and electronic interactions are important to reveal the origins for the formation of high-entropy alloys and their structure-dominated mechanical properties, thus enabling the development of a predictive approach for rapidly designing advanced materials. Here, we report the atomic and electronic basis for the valence-electron-concentration-categorized principles and the observed serration behavior in high-entropy alloys and high-entropy metallic glass, including MoNbTaW, MoNbVW, MoTaVW, HfNbTiZr, and Vitreloy-1 MG (Zr41Ti14Cu12.5Ni10Be22.5). We find that the yield strengths of high-entropy alloys and high-entropy metallic glass are a power-law function of the electron-work function, which is dominated by local atomic arrangements. Further, a reliance on the bonding-charge density provides a groundbreaking insight into the nature of loosely bonded spots in materials. The presence of strongly bonded clusters and weakly bonded glue atoms imply a serrated deformation of high-entropy alloys, resulting in intermittent avalanches of defects movement.

Exact solutions for the entropy production rate of several irreversible processes.

PubMed

Ross, John; Vlad, Marcel O

2005-11-24

We investigate thermal conduction described by Newton's law of cooling and by Fourier's transport equation and chemical reactions based on mass action kinetics where we detail a simple example of a reaction mechanism with one intermediate. In these cases we derive exact expressions for the entropy production rate and its differential. We show that at a stationary state the entropy production rate is an extremum if and only if the stationary state is a state of thermodynamic equilibrium. These results are exact and independent of any expansions of the entropy production rate. In the case of thermal conduction we compare our exact approach with the conventional approach based on the expansion of the entropy production rate near equilibrium. If we expand the entropy production rate in a series and keep terms up to the third order in the deviation variables and then differentiate, we find out that the entropy production rate is not an extremum at a nonequilibrium steady state. If there is a strict proportionality between fluxes and forces, then the entropy production rate is an extremum at the stationary state even if the stationary state is far away from equilibrium.

A new entropy based on a group-theoretical structure

NASA Astrophysics Data System (ADS)

Curado, Evaldo M. F.; Tempesta, Piergiulio; Tsallis, Constantino

2016-03-01

A multi-parametric version of the nonadditive entropy Sq is introduced. This new entropic form, denoted by S a , b , r, possesses many interesting statistical properties, and it reduces to the entropy Sq for b = 0, a = r : = 1 - q (hence Boltzmann-Gibbs entropy SBG for b = 0, a = r → 0). The construction of the entropy S a , b , r is based on a general group-theoretical approach recently proposed by one of us, Tempesta (2016). Indeed, essentially all the properties of this new entropy are obtained as a consequence of the existence of a rational group law, which expresses the structure of S a , b , r with respect to the composition of statistically independent subsystems. Depending on the choice of the parameters, the entropy S a , b , r can be used to cover a wide range of physical situations, in which the measure of the accessible phase space increases say exponentially with the number of particles N of the system, or even stabilizes, by increasing N, to a limiting value. This paves the way to the use of this entropy in contexts where the size of the phase space does not increase as fast as the number of its constituting particles (or subsystems) increases.

Towards operational interpretations of generalized entropies

NASA Astrophysics Data System (ADS)

Topsøe, Flemming

2010-12-01

The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.

Rényi entropy of the totally asymmetric exclusion process

NASA Astrophysics Data System (ADS)

Wood, Anthony J.; Blythe, Richard A.; Evans, Martin R.

2017-11-01

The Rényi entropy is a generalisation of the Shannon entropy that is sensitive to the fine details of a probability distribution. We present results for the Rényi entropy of the totally asymmetric exclusion process (TASEP). We calculate explicitly an entropy whereby the squares of configuration probabilities are summed, using the matrix product formalism to map the problem to one involving a six direction lattice walk in the upper quarter plane. We derive the generating function across the whole phase diagram, using an obstinate kernel method. This gives the leading behaviour of the Rényi entropy and corrections in all phases of the TASEP. The leading behaviour is given by the result for a Bernoulli measure and we conjecture that this holds for all Rényi entropies. Within the maximal current phase the correction to the leading behaviour is logarithmic in the system size. Finally, we remark upon a special property of equilibrium systems whereby discontinuities in the Rényi entropy arise away from phase transitions, which we refer to as secondary transitions. We find no such secondary transition for this nonequilibrium system, supporting the notion that these are specific to equilibrium cases.

On variational expressions for quantum relative entropies

NASA Astrophysics Data System (ADS)

Berta, Mario; Fawzi, Omar; Tomamichel, Marco

2017-12-01

Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the Kullback-Leibler divergence over projective measurement statistics, is strictly smaller than Umegaki's quantum relative entropy whenever the states do not commute. We extend this result in two ways. First, we show that Petz' conclusion remains true if we allow general positive operator-valued measures. Second, we extend the result to Rényi relative entropies and show that for non-commuting states the sandwiched Rényi relative entropy is strictly larger than the measured Rényi relative entropy for α \\in (1/2, \\infty ) and strictly smaller for α \\in [0,1/2). The latter statement provides counterexamples for the data processing inequality of the sandwiched Rényi relative entropy for α < 1/2. Our main tool is a new variational expression for the measured Rényi relative entropy, which we further exploit to show that certain lower bounds on quantum conditional mutual information are superadditive.

Comparing Postural Stability Entropy Analyses to Differentiate Fallers and Non-fallers.

PubMed

Fino, Peter C; Mojdehi, Ahmad R; Adjerid, Khaled; Habibi, Mohammad; Lockhart, Thurmon E; Ross, Shane D

2016-05-01

The health and financial cost of falls has spurred research to differentiate the characteristics of fallers and non-fallers. Postural stability has received much of the attention with recent studies exploring various measures of entropy. This study compared the discriminatory ability of several entropy methods at differentiating two paradigms in the center-of-pressure of elderly individuals: (1) eyes open (EO) vs. eyes closed (EC) and (2) fallers (F) vs. non-fallers (NF). Methods were compared using the area under the curve (AUC) of the receiver-operating characteristic curves developed from logistic regression models. Overall, multiscale entropy (MSE) and composite multiscale entropy (CompMSE) performed the best with AUCs of 0.71 for EO/EC and 0.77 for F/NF. When methods were combined together to maximize the AUC, the entropy classifier had an AUC of for 0.91 the F/NF comparison. These results suggest researchers and clinicians attempting to create clinical tests to identify fallers should consider a combination of every entropy method when creating a classifying test. Additionally, MSE and CompMSE classifiers using polar coordinate data outperformed rectangular coordinate data, encouraging more research into the most appropriate time series for postural stability entropy analysis.

Harvesting Entropy for Random Number Generation for Internet of Things Constrained Devices Using On-Board Sensors

PubMed Central

Pawlowski, Marcin Piotr; Jara, Antonio; Ogorzalek, Maciej

2015-01-01

Entropy in computer security is associated with the unpredictability of a source of randomness. The random source with high entropy tends to achieve a uniform distribution of random values. Random number generators are one of the most important building blocks of cryptosystems. In constrained devices of the Internet of Things ecosystem, high entropy random number generators are hard to achieve due to hardware limitations. For the purpose of the random number generation in constrained devices, this work proposes a solution based on the least-significant bits concatenation entropy harvesting method. As a potential source of entropy, on-board integrated sensors (i.e., temperature, humidity and two different light sensors) have been analyzed. Additionally, the costs (i.e., time and memory consumption) of the presented approach have been measured. The results obtained from the proposed method with statistical fine tuning achieved a Shannon entropy of around 7.9 bits per byte of data for temperature and humidity sensors. The results showed that sensor-based random number generators are a valuable source of entropy with very small RAM and Flash memory requirements for constrained devices of the Internet of Things. PMID:26506357

Population entropies estimates of proteins

NASA Astrophysics Data System (ADS)

Low, Wai Yee

2017-05-01

The Shannon entropy equation provides a way to estimate variability of amino acids sequences in a multiple sequence alignment of proteins. Knowledge of protein variability is useful in many areas such as vaccine design, identification of antibody binding sites, and exploration of protein 3D structural properties. In cases where the population entropies of a protein are of interest but only a small sample size can be obtained, a method based on linear regression and random subsampling can be used to estimate the population entropy. This method is useful for comparisons of entropies where the actual sequence counts differ and thus, correction for alignment size bias is needed. In the current work, an R based package named EntropyCorrect that enables estimation of population entropy is presented and an empirical study on how well this new algorithm performs on simulated dataset of various combinations of population and sample sizes is discussed. The package is available at https://github.com/lloydlow/EntropyCorrect. This article, which was originally published online on 12 May 2017, contained an error in Eq. (1), where the summation sign was missing. The corrected equation appears in the Corrigendum attached to the pdf.

Driver fatigue detection through multiple entropy fusion analysis in an EEG-based system

PubMed Central

Min, Jianliang; Wang, Ping

2017-01-01

Driver fatigue is an important contributor to road accidents, and fatigue detection has major implications for transportation safety. The aim of this research is to analyze the multiple entropy fusion method and evaluate several channel regions to effectively detect a driver's fatigue state based on electroencephalogram (EEG) records. First, we fused multiple entropies, i.e., spectral entropy, approximate entropy, sample entropy and fuzzy entropy, as features compared with autoregressive (AR) modeling by four classifiers. Second, we captured four significant channel regions according to weight-based electrodes via a simplified channel selection method. Finally, the evaluation model for detecting driver fatigue was established with four classifiers based on the EEG data from four channel regions. Twelve healthy subjects performed continuous simulated driving for 1–2 hours with EEG monitoring on a static simulator. The leave-one-out cross-validation approach obtained an accuracy of 98.3%, a sensitivity of 98.3% and a specificity of 98.2%. The experimental results verified the effectiveness of the proposed method, indicating that the multiple entropy fusion features are significant factors for inferring the fatigue state of a driver. PMID:29220351

Harvesting entropy for random number generation for internet of things constrained devices using on-board sensors.

PubMed

Pawlowski, Marcin Piotr; Jara, Antonio; Ogorzalek, Maciej

2015-10-22

Entropy in computer security is associated with the unpredictability of a source of randomness. The random source with high entropy tends to achieve a uniform distribution of random values. Random number generators are one of the most important building blocks of cryptosystems. In constrained devices of the Internet of Things ecosystem, high entropy random number generators are hard to achieve due to hardware limitations. For the purpose of the random number generation in constrained devices, this work proposes a solution based on the least-significant bits concatenation entropy harvesting method. As a potential source of entropy, on-board integrated sensors (i.e., temperature, humidity and two different light sensors) have been analyzed. Additionally, the costs (i.e., time and memory consumption) of the presented approach have been measured. The results obtained from the proposed method with statistical fine tuning achieved a Shannon entropy of around 7.9 bits per byte of data for temperature and humidity sensors. The results showed that sensor-based random number generators are a valuable source of entropy with very small RAM and Flash memory requirements for constrained devices of the Internet of Things.

Entropy, matter, and cosmology.

PubMed

Prigogine, I; Géhéniau, J

1986-09-01

The role of irreversible processes corresponding to creation of matter in general relativity is investigated. The use of Landau-Lifshitz pseudotensors together with conformal (Minkowski) coordinates suggests that this creation took place in the early universe at the stage of the variation of the conformal factor. The entropy production in this creation process is calculated. It is shown that these dissipative processes lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy. Gravitational entropy takes a simple meaning as associated to the entropy that is necessary to produce matter. This leads to an extension of the third law of thermodynamics, as now the zero point of entropy becomes the space-time structure out of which matter is generated. The theory can be put into a convenient form using a supplementary "C" field in Einstein's field equations. The role of the C field is to express the coupling between gravitation and matter leading to irreversible entropy production.

Wavelet Packet Entropy for Heart Murmurs Classification

PubMed Central

Safara, Fatemeh; Doraisamy, Shyamala; Azman, Azreen; Jantan, Azrul; Ranga, Sri

2012-01-01

Heart murmurs are the first signs of cardiac valve disorders. Several studies have been conducted in recent years to automatically differentiate normal heart sounds, from heart sounds with murmurs using various types of audio features. Entropy was successfully used as a feature to distinguish different heart sounds. In this paper, new entropy was introduced to analyze heart sounds and the feasibility of using this entropy in classification of five types of heart sounds and murmurs was shown. The entropy was previously introduced to analyze mammograms. Four common murmurs were considered including aortic regurgitation, mitral regurgitation, aortic stenosis, and mitral stenosis. Wavelet packet transform was employed for heart sound analysis, and the entropy was calculated for deriving feature vectors. Five types of classification were performed to evaluate the discriminatory power of the generated features. The best results were achieved by BayesNet with 96.94% accuracy. The promising results substantiate the effectiveness of the proposed wavelet packet entropy for heart sounds classification. PMID:23227043

Entropy Production in Chemical Reactors

NASA Astrophysics Data System (ADS)

Kingston, Diego; Razzitte, Adrián C.

2017-06-01

We have analyzed entropy production in chemically reacting systems and extended previous results to the two limiting cases of ideal reactors, namely continuous stirred tank reactor (CSTR) and plug flow reactor (PFR). We have found upper and lower bounds for the entropy production in isothermal systems and given expressions for non-isothermal operation and analyzed the influence of pressure and temperature in entropy generation minimization in reactors with a fixed volume and production. We also give a graphical picture of entropy production in chemical reactions subject to constant volume, which allows us to easily assess different options. We show that by dividing a reactor into two smaller ones, operating at different temperatures, the entropy production is lowered, going as near as 48 % less in the case of a CSTR and PFR in series, and reaching 58 % with two CSTR. Finally, we study the optimal pressure and temperature for a single isothermal PFR, taking into account the irreversibility introduced by a compressor and a heat exchanger, decreasing the entropy generation by as much as 30 %.

Gradient Dynamics and Entropy Production Maximization

NASA Astrophysics Data System (ADS)

Janečka, Adam; Pavelka, Michal

2018-01-01

We compare two methods for modeling dissipative processes, namely gradient dynamics and entropy production maximization. Both methods require similar physical inputs-how energy (or entropy) is stored and how it is dissipated. Gradient dynamics describes irreversible evolution by means of dissipation potential and entropy, it automatically satisfies Onsager reciprocal relations as well as their nonlinear generalization (Maxwell-Onsager relations), and it has statistical interpretation. Entropy production maximization is based on knowledge of free energy (or another thermodynamic potential) and entropy production. It also leads to the linear Onsager reciprocal relations and it has proven successful in thermodynamics of complex materials. Both methods are thermodynamically sound as they ensure approach to equilibrium, and we compare them and discuss their advantages and shortcomings. In particular, conditions under which the two approaches coincide and are capable of providing the same constitutive relations are identified. Besides, a commonly used but not often mentioned step in the entropy production maximization is pinpointed and the condition of incompressibility is incorporated into gradient dynamics.

Binding stability of peptides on major histocompatibility complex class I proteins: role of entropy and dynamics.

PubMed

Gul, Ahmet; Erman, Burak

2018-01-16

Prediction of peptide binding on specific human leukocyte antigens (HLA) has long been studied with successful results. We herein describe the effects of entropy and dynamics by investigating the binding stabilities of 10 nanopeptides on various HLA Class I alleles using a theoretical model based on molecular dynamics simulations. The fluctuational entropies of the peptides are estimated over a temperature range of 310-460 K. The estimated entropies correlate well with experimental binding affinities of the peptides: peptides that have higher binding affinities have lower entropies compared to non-binders, which have significantly larger entropies. The computation of the entropies is based on a simple model that requires short molecular dynamics trajectories and allows for approximate but rapid determination. The paper draws attention to the long neglected dynamic aspects of peptide binding, and provides a fast computation scheme that allows for rapid scanning of large numbers of peptides on selected HLA antigens, which may be useful in defining the right peptides for personal immunotherapy.

Entropy generation in biophysical systems

NASA Astrophysics Data System (ADS)

Lucia, U.; Maino, G.

2013-03-01

Recently, in theoretical biology and in biophysical engineering the entropy production has been verified to approach asymptotically its maximum rate, by using the probability of individual elementary modes distributed in accordance with the Boltzmann distribution. The basis of this approach is the hypothesis that the entropy production rate is maximum at the stationary state. In the present work, this hypothesis is explained and motivated, starting from the entropy generation analysis. This latter quantity is obtained from the entropy balance for open systems considering the lifetime of the natural real process. The Lagrangian formalism is introduced in order to develop an analytical approach to the thermodynamic analysis of the open irreversible systems. The stationary conditions of the open systems are thus obtained in relation to the entropy generation and the least action principle. Consequently, the considered hypothesis is analytically proved and it represents an original basic approach in theoretical and mathematical biology and also in biophysical engineering. It is worth remarking that the present results show that entropy generation not only increases but increases as fast as possible.

Neuronal Entropy-Rate Feature of Entopeduncular Nucleus in Rat Model of Parkinson's Disease.

PubMed

Darbin, Olivier; Jin, Xingxing; Von Wrangel, Christof; Schwabe, Kerstin; Nambu, Atsushi; Naritoku, Dean K; Krauss, Joachim K; Alam, Mesbah

2016-03-01

The function of the nigro-striatal pathway on neuronal entropy in the basal ganglia (BG) output nucleus, i.e. the entopeduncular nucleus (EPN) was investigated in the unilaterally 6-hyroxydopamine (6-OHDA)-lesioned rat model of Parkinson's disease (PD). In both control subjects and subjects with 6-OHDA lesion of dopamine (DA) the nigro-striatal pathway, a histological hallmark for parkinsonism, neuronal entropy in EPN was maximal in neurons with firing rates ranging between 15 and 25 Hz. In 6-OHDA lesioned rats, neuronal entropy in the EPN was specifically higher in neurons with firing rates above 25 Hz. Our data establishes that the nigro-striatal pathway controls neuronal entropy in motor circuitry and that the parkinsonian condition is associated with abnormal relationship between firing rate and neuronal entropy in BG output nuclei. The neuronal firing rates and entropy relationship provide putative relevant electrophysiological information to investigate the sensory-motor processing in normal condition and conditions such as movement disorders.

Ergodicity, configurational entropy and free energy in pigment solutions and plant photosystems: influence of excited state lifetime.

PubMed

Jennings, Robert C; Zucchelli, Giuseppe

2014-01-01

We examine ergodicity and configurational entropy for a dilute pigment solution and for a suspension of plant photosystem particles in which both ground and excited state pigments are present. It is concluded that the pigment solution, due to the extreme brevity of the excited state lifetime, is non-ergodic and the configurational entropy approaches zero. Conversely, due to the rapid energy transfer among pigments, each photosystem is ergodic and the configurational entropy is positive. This decreases the free energy of the single photosystem pigment array by a small amount. On the other hand, the suspension of photosystems is non-ergodic and the configurational entropy approaches zero. The overall configurational entropy which, in principle, includes contributions from both the single excited photosystems and the suspension which contains excited photosystems, also approaches zero. Thus the configurational entropy upon photon absorption by either a pigment solution or a suspension of photosystem particles is approximately zero. Copyright © 2014 Elsevier B.V. All rights reserved.

Prediction of Protein Configurational Entropy (Popcoen).

PubMed

Goethe, Martin; Gleixner, Jan; Fita, Ignacio; Rubi, J Miguel

2018-03-13

A knowledge-based method for configurational entropy prediction of proteins is presented; this methodology is extremely fast, compared to previous approaches, because it does not involve any type of configurational sampling. Instead, the configurational entropy of a query fold is estimated by evaluating an artificial neural network, which was trained on molecular-dynamics simulations of ∼1000 proteins. The predicted entropy can be incorporated into a large class of protein software based on cost-function minimization/evaluation, in which configurational entropy is currently neglected for performance reasons. Software of this type is used for all major protein tasks such as structure predictions, proteins design, NMR and X-ray refinement, docking, and mutation effect predictions. Integrating the predicted entropy can yield a significant accuracy increase as we show exemplarily for native-state identification with the prominent protein software FoldX. The method has been termed Popcoen for Prediction of Protein Configurational Entropy. An implementation is freely available at http://fmc.ub.edu/popcoen/ .

Binding stability of peptides on major histocompatibility complex class I proteins: role of entropy and dynamics

NASA Astrophysics Data System (ADS)

Gul, Ahmet; Erman, Burak

2018-03-01

Prediction of peptide binding on specific human leukocyte antigens (HLA) has long been studied with successful results. We herein describe the effects of entropy and dynamics by investigating the binding stabilities of 10 nanopeptides on various HLA Class I alleles using a theoretical model based on molecular dynamics simulations. The fluctuational entropies of the peptides are estimated over a temperature range of 310-460 K. The estimated entropies correlate well with experimental binding affinities of the peptides: peptides that have higher binding affinities have lower entropies compared to non-binders, which have significantly larger entropies. The computation of the entropies is based on a simple model that requires short molecular dynamics trajectories and allows for approximate but rapid determination. The paper draws attention to the long neglected dynamic aspects of peptide binding, and provides a fast computation scheme that allows for rapid scanning of large numbers of peptides on selected HLA antigens, which may be useful in defining the right peptides for personal immunotherapy.

RELATIONSHIP BETWEEN ENTROPY OF SPIKE TIMING AND FIRING RATE IN ENTOPEDUNCULAR NUCLEUS NEURONS IN ANESTHETIZED RATS: FUNCTION OF THE NIGRO-STRIATAL PATHWAY

PubMed Central

Darbin, Olivier; Jin, Xingxing; von Wrangel, Christof; Schwabe, Kerstin; Nambu, Atsushi; Naritoku, Dean K; Krauss, Joachim K.; Alam, Mesbah

2016-01-01

The function of the nigro-striatal pathway on neuronal entropy in the basal ganglia (BG) output nucleus (entopeduncular nucleus, EPN) was investigated in the unilaterally 6-hyroxydopamine (6-OHDA)-lesioned rat model of Parkinson’s disease (PD). In both control subjects and subjects with 6-OHDA lesion of the nigro-striatal pathway, a histological hallmark for parkinsonism, neuronal entropy in EPN was maximal in neurons with firing rates ranging between 15Hz and 25 Hz. In 6-OHDA lesioned rats, neuronal entropy in the EPN was specifically higher in neurons with firing rates above 25Hz. Our data establishes that nigro-striatal pathway controls neuronal entropy in motor circuitry and that the parkinsonian condition is associated with abnormal relationship between firing rate and neuronal entropy in BG output nuclei. The neuronal firing rates and entropy relationship provide putative relevant electrophysiological information to investigate the sensory-motor processing in normal condition and conditions with movement disorders. PMID:26711712

Random versus maximum entropy models of neural population activity

NASA Astrophysics Data System (ADS)

Ferrari, Ulisse; Obuchi, Tomoyuki; Mora, Thierry

2017-04-01

The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions underlying maximum entropy are intuitive and appealing, its adequacy for describing complex empirical data has been little studied in comparison to alternative approaches. Here, data from the collective spiking activity of retinal neurons is reanalyzed. The accuracy of the maximum entropy distribution constrained by mean firing rates and pairwise correlations is compared to a random ensemble of distributions constrained by the same observables. For most of the tested networks, maximum entropy approximates the true distribution better than the typical or mean distribution from that ensemble. This advantage improves with population size, with groups as small as eight being almost always better described by maximum entropy. Failure of maximum entropy to outperform random models is found to be associated with strong correlations in the population.

Entropy of hydrological systems under small samples: Uncertainty and variability

NASA Astrophysics Data System (ADS)

Liu, Dengfeng; Wang, Dong; Wang, Yuankun; Wu, Jichun; Singh, Vijay P.; Zeng, Xiankui; Wang, Lachun; Chen, Yuanfang; Chen, Xi; Zhang, Liyuan; Gu, Shenghua

2016-01-01

Entropy theory has been increasingly applied in hydrology in both descriptive and inferential ways. However, little attention has been given to the small-sample condition widespread in hydrological practice, where either hydrological measurements are limited or are even nonexistent. Accordingly, entropy estimated under this condition may incur considerable bias. In this study, small-sample condition is considered and two innovative entropy estimators, the Chao-Shen (CS) estimator and the James-Stein-type shrinkage (JSS) estimator, are introduced. Simulation tests are conducted with common distributions in hydrology, that lead to the best-performing JSS estimator. Then, multi-scale moving entropy-based hydrological analyses (MM-EHA) are applied to indicate the changing patterns of uncertainty of streamflow data collected from the Yangtze River and the Yellow River, China. For further investigation into the intrinsic property of entropy applied in hydrological uncertainty analyses, correlations of entropy and other statistics at different time-scales are also calculated, which show connections between the concept of uncertainty and variability.

Entanglement entropy in a boundary impurity model.

PubMed

Levine, G C

2004-12-31

Boundary impurities are known to dramatically alter certain bulk properties of (1+1)-dimensional strongly correlated systems. The entanglement entropy of a zero temperature Luttinger liquid bisected by a single impurity is computed using a novel finite size scaling or bosonization scheme. For a Luttinger liquid of length 2L and UV cutoff epsilon, the boundary impurity correction (deltaSimp) to the logarithmic entanglement entropy (Sent proportional, variant lnL/epsilon scales as deltaSimp approximately yrlnL/epsilon, where yr is the renormalized backscattering coupling constant. In this way, the entanglement entropy within a region is related to scattering through the region's boundary. In the repulsive case (g<1), deltaSimp diverges (negatively) suggesting that the entropy vanishes. Our results are consistent with the recent conjecture that entanglement entropy decreases irreversibly along renormalization group flow.

Quantitative characterization of brazing performance for Sn-plated silver alloy fillers

NASA Astrophysics Data System (ADS)

Wang, Xingxing; Peng, Jin; Cui, Datian

2017-12-01

Two types of AgCuZnSn fillers were prepared based on BAg50CuZn and BAg34CuZnSn alloy through a combinative process of electroplating and thermal diffusion. The models of wetting entropy and joint strength entropy of AgCuZnSn filler metals were established. The wetting entropy of the Sn-plated silver brazing alloys are lower than the traditional fillers, and its joint strength entropy value is slightly higher than the latter. The wetting entropy value of the Sn-plated brazing alloys and traditional filler metal are similar to the change trend of the wetting area. The trend of the joint strength entropy value with those fillers are consisted with the tensile strength of the stainless steel joints with the increase of Sn content.

Application of a real-time, calculable limiting form of the Renyi entropy for molecular imaging of tumors.

PubMed

Marsh, Jon N; Wallace, Kirk D; McCarthy, John E; Wickerhauser, Mladen V; Maurizi, Brian N; Lanza, Gregory M; Wickline, Samuel A; Hughes, Michael S

2010-08-01

Previously, we reported new methods for ultrasound signal characterization using entropy, H(f); a generalized entropy, the Renyi entropy, I(f)(r); and a limiting form of Renyi entropy suitable for real-time calculation, I(f),(infinity). All of these quantities demonstrated significantly more sensitivity to subtle changes in scattering architecture than energy-based methods in certain settings. In this study, the real-time calculable limit of the Renyi entropy, I(f),(infinity), is applied for the imaging of angiogenic murine neovasculature in a breast cancer xenograft using a targeted contrast agent. It is shown that this approach may be used to reliably detect the accumulation of targeted nanoparticles at five minutes post-injection in this in vivo model.

Low Streamflow Forcasting using Minimum Relative Entropy

NASA Astrophysics Data System (ADS)

Cui, H.; Singh, V. P.

2013-12-01

Minimum relative entropy spectral analysis is derived in this study, and applied to forecast streamflow time series. Proposed method extends the autocorrelation in the manner that the relative entropy of underlying process is minimized so that time series data can be forecasted. Different prior estimation, such as uniform, exponential and Gaussian assumption, is taken to estimate the spectral density depending on the autocorrelation structure. Seasonal and nonseasonal low streamflow series obtained from Colorado River (Texas) under draught condition is successfully forecasted using proposed method. Minimum relative entropy determines spectral of low streamflow series with higher resolution than conventional method. Forecasted streamflow is compared to the prediction using Burg's maximum entropy spectral analysis (MESA) and Configurational entropy. The advantage and disadvantage of each method in forecasting low streamflow is discussed.

An efficient algorithm for automatic phase correction of NMR spectra based on entropy minimization

NASA Astrophysics Data System (ADS)

Chen, Li; Weng, Zhiqiang; Goh, LaiYoong; Garland, Marc

2002-09-01

A new algorithm for automatic phase correction of NMR spectra based on entropy minimization is proposed. The optimal zero-order and first-order phase corrections for a NMR spectrum are determined by minimizing entropy. The objective function is constructed using a Shannon-type information entropy measure. Entropy is defined as the normalized derivative of the NMR spectral data. The algorithm has been successfully applied to experimental 1H NMR spectra. The results of automatic phase correction are found to be comparable to, or perhaps better than, manual phase correction. The advantages of this automatic phase correction algorithm include its simple mathematical basis and the straightforward, reproducible, and efficient optimization procedure. The algorithm is implemented in the Matlab program ACME—Automated phase Correction based on Minimization of Entropy.

Effect of electron count and chemical complexity in the Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor.

PubMed

von Rohr, Fabian; Winiarski, Michał J; Tao, Jing; Klimczuk, Tomasz; Cava, Robert Joseph

2016-11-15

High-entropy alloys are made from random mixtures of principal elements on simple lattices, stabilized by a high mixing entropy. The recently discovered body-centered cubic (BCC) Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor appears to display properties of both simple crystalline intermetallics and amorphous materials; e.g., it has a well-defined superconducting transition along with an exceptional robustness against disorder. Here we show that the valence electron count dependence of the superconducting transition temperature in the high-entropy alloy falls between those of analogous simple solid solutions and amorphous materials and test the effect of alloy complexity on the superconductivity. We propose high-entropy alloys as excellent intermediate systems for studying superconductivity as it evolves between crystalline and amorphous materials.

An alternative expression to the Sackur-Tetrode entropy formula for an ideal gas

NASA Astrophysics Data System (ADS)

Nagata, Shoichi

2018-03-01

An expression for the entropy of a monoatomic classical ideal gas is known as the Sackur-Tetrode equation. This pioneering investigation about 100 years ago incorporates quantum considerations. The purpose of this paper is to provide an alternative expression for the entropy in terms of the Heisenberg uncertainty relation. The analysis is made on the basis of fluctuation theory, for a canonical system in thermal equilibrium at temperature T. This new formula indicates manifestly that the entropy of macroscopic world is recognized as a measure of uncertainty in microscopic quantum world. The entropy in the Sackur-Tetrode equation can be re-interpreted from a different perspective viewpoint. The emphasis is on the connection between the entropy and the uncertainty relation in quantum consideration.

General monogamy of Tsallis q -entropy entanglement in multiqubit systems

NASA Astrophysics Data System (ADS)

Luo, Yu; Tian, Tian; Shao, Lian-He; Li, Yongming

2016-06-01

In this paper, we study the monogamy inequality of Tsallis q -entropy entanglement. We first provide an analytic formula of Tsallis q -entropy entanglement in two-qubit systems for 5/-√{13 } 2 ≤q ≤5/+√{13 } 2 . The analytic formula of Tsallis q -entropy entanglement in 2 ⊗d system is also obtained and we show that Tsallis q -entropy entanglement satisfies a set of hierarchical monogamy equalities. Furthermore, we prove the squared Tsallis q -entropy entanglement follows a general inequality in the qubit systems. Based on the monogamy relations, a set of multipartite entanglement indicators is constructed, which can detect all genuine multiqubit entangled states even in the case of N -tangle vanishes. Moreover, we study some examples in multipartite higher-dimensional system for the monogamy inequalities.

Quantum thermodynamics and quantum entanglement entropies in an expanding universe

NASA Astrophysics Data System (ADS)

Farahmand, Mehrnoosh; Mohammadzadeh, Hosein; Mehri-Dehnavi, Hossein

2017-05-01

We investigate an asymptotically spatially flat Robertson-Walker space-time from two different perspectives. First, using von Neumann entropy, we evaluate the entanglement generation due to the encoded information in space-time. Then, we work out the entropy of particle creation based on the quantum thermodynamics of the scalar field on the underlying space-time. We show that the general behavior of both entropies are the same. Therefore, the entanglement can be applied to the customary quantum thermodynamics of the universe. Also, using these entropies, we can recover some information about the parameters of space-time.

Defining chaos.

PubMed

Hunt, Brian R; Ott, Edward

2015-09-01

In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy," and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.

Entropy Generation in Regenerative Systems

NASA Technical Reports Server (NTRS)

Kittel, Peter

1995-01-01

Heat exchange to the oscillating flows in regenerative coolers generates entropy. These flows are characterized by oscillating mass flows and oscillating temperatures. Heat is transferred between the flow and heat exchangers and regenerators. In the former case, there is a steady temperature difference between the flow and the heat exchangers. In the latter case, there is no mean temperature difference. In this paper a mathematical model of the entropy generated is developed for both cases. Estimates of the entropy generated by this process are given for oscillating flows in heat exchangers and in regenerators. The practical significance of this entropy is also discussed.

On the dispute between Boltzmann and Gibbs entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buonsante, Pierfrancesco; Franzosi, Roberto, E-mail: roberto.franzosi@ino.it; Smerzi, Augusto

2016-12-15

The validity of the concept of negative temperature has been recently challenged by arguing that the Boltzmann entropy (that allows negative temperatures) is inconsistent from a mathematical and statistical point of view, whereas the Gibbs entropy (that does not admit negative temperatures) provides the correct definition for the microcanonical entropy. Here we prove that the Boltzmann entropy is thermodynamically and mathematically consistent. Analytical results on two systems supporting negative temperatures illustrate the scenario we propose. In addition we numerically study a lattice system to show that negative temperature equilibrium states are accessible and obey standard statistical mechanics prediction.

Measuring Gaussian quantum information and correlations using the Rényi entropy of order 2.

PubMed

Adesso, Gerardo; Girolami, Davide; Serafini, Alessio

2012-11-09

We demonstrate that the Rényi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of the state. We prove that, in the Gaussian scenario, such an entropy satisfies the strong subadditivity inequality, a key requirement for quantum information theory. This allows us to define and analyze measures of Gaussian entanglement and more general quantum correlations based on such an entropy, which are shown to satisfy relevant properties such as monogamy.

First law of entanglement entropy in topologically massive gravity

NASA Astrophysics Data System (ADS)

Cheng, Long; Hung, Ling-Yan; Liu, Si-Nong; Zhou, Hong-Zhe

2016-09-01

In this paper we explore the validity of the first law of entanglement entropy in the context of topologically massive gravity (TMG). We find that the variation of the holographic entanglement entropy under perturbation from the pure anti-de Sitter background satisfies the first law upon imposing the bulk equations of motion in a given time slice, despite the appearance of instabilities in the bulk for generic gravitational Chern-Simons coupling μ . The Noether-Wald entropy is different from the holographic entanglement entropy in a general boosted frame. However, this discrepancy does not affect the entanglement first law.

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Fisher, Travis C.

2013-01-01

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

Nonequilibrium Thermodynamics in Biological Systems

NASA Astrophysics Data System (ADS)

Aoki, I.

2005-12-01

1. Respiration Oxygen-uptake by respiration in organisms decomposes macromolecules such as carbohydrate, protein and lipid and liberates chemical energy of high quality, which is then used to chemical reactions and motions of matter in organisms to support lively order in structure and function in organisms. Finally, this chemical energy becomes heat energy of low quality and is discarded to the outside (dissipation function). Accompanying this heat energy, entropy production which inevitably occurs by irreversibility also is discarded to the outside. Dissipation function and entropy production are estimated from data of respiration. 2. Human body From the observed data of respiration (oxygen absorption), the entropy production in human body can be estimated. Entropy production from 0 to 75 years old human has been obtained, and extrapolated to fertilized egg (beginning of human life) and to 120 years old (maximum period of human life). Entropy production show characteristic behavior in human life span : early rapid increase in short growing phase and later slow decrease in long aging phase. It is proposed that this tendency is ubiquitous and constitutes a Principle of Organization in complex biotic systems. 3. Ecological communities From the data of respiration of eighteen aquatic communities, specific (i.e. per biomass) entropy productions are obtained. They show two phase character with respect to trophic diversity : early increase and later decrease with the increase of trophic diversity. The trophic diversity in these aquatic ecosystems is shown to be positively correlated with the degree of eutrophication, and the degree of eutrophication is an "arrow of time" in the hierarchy of aquatic ecosystems. Hence specific entropy production has the two phase: early increase and later decrease with time. 4. Entropy principle for living systems The Second Law of Thermodynamics has been expressed as follows. 1) In isolated systems, entropy increases with time and approaches to a maximum value. This is well-known classical Clausius principle. 2) In open systems near equilibrium entropy production always decreases with time approaching a minimum stationary level. This is the minimum entropy production principle by Prigogine. These two principle are established ones. However, living systems are not isolated and not near to equilibrium. Hence, these two principles can not be applied to living systems. What is entropy principle for living systems? Answer: Entropy production in living systems consists of multi-stages with time: early increasing, later decreasing and/or intermediate stages. This tendency is supported by various living systems.

Psychoacoustic entropy theory and its implications for performance practice

NASA Astrophysics Data System (ADS)

Strohman, Gregory J.

This dissertation attempts to motivate, derive and imply potential uses for a generalized perceptual theory of musical harmony called psychoacoustic entropy theory. This theory treats the human auditory system as a physical system which takes acoustic measurements. As a result, the human auditory system is subject to all the appropriate uncertainties and limitations of other physical measurement systems. This is the theoretic basis for defining psychoacoustic entropy. Psychoacoustic entropy is a numerical quantity which indexes the degree to which the human auditory system perceives instantaneous disorder within a sound pressure wave. Chapter one explains the importance of harmonic analysis as a tool for performance practice. It also outlines the critical limitations for many of the most influential historical approaches to modeling harmonic stability, particularly when compared to available scientific research in psychoacoustics. Rather than analyze a musical excerpt, psychoacoustic entropy is calculated directly from sound pressure waves themselves. This frames psychoacoustic entropy theory in the most general possible terms as a theory of musical harmony, enabling it to be invoked for any perceivable sound. Chapter two provides and examines many widely accepted mathematical models of the acoustics and psychoacoustics of these sound pressure waves. Chapter three introduces entropy as a precise way of measuring perceived uncertainty in sound pressure waves. Entropy is used, in combination with the acoustic and psychoacoustic models introduced in chapter two, to motivate the mathematical formulation of psychoacoustic entropy theory. Chapter four shows how to use psychoacoustic entropy theory to analyze the certain types of musical harmonies, while chapter five applies the analytical tools developed in chapter four to two short musical excerpts to influence their interpretation. Almost every form of harmonic analysis invokes some degree of mathematical reasoning. However, the limited scope of most harmonic systems used for Western common practice music greatly simplifies the necessary level of mathematical detail. Psychoacoustic entropy theory requires a greater deal of mathematical complexity due to its sheer scope as a generalized theory of musical harmony. Fortunately, under specific assumptions the theory can take on vastly simpler forms. Psychoacoustic entropy theory appears to be highly compatible with the latest scientific research in psychoacoustics. However, the theory itself should be regarded as a hypothesis and this dissertation an experiment in progress. The evaluation of psychoacoustic entropy theory as a scientific theory of human sonic perception must wait for more rigorous future research.

Entropy of electromyography time series

NASA Astrophysics Data System (ADS)

Kaufman, Miron; Zurcher, Ulrich; Sung, Paul S.

2007-12-01

A nonlinear analysis based on Renyi entropy is applied to electromyography (EMG) time series from back muscles. The time dependence of the entropy of the EMG signal exhibits a crossover from a subdiffusive regime at short times to a plateau at longer times. We argue that this behavior characterizes complex biological systems. The plateau value of the entropy can be used to differentiate between healthy and low back pain individuals.

Entanglement distribution in multi-particle systems in terms of unified entropy.

PubMed

Luo, Yu; Zhang, Fu-Gang; Li, Yongming

2017-04-25

We investigate the entanglement distribution in multi-particle systems in terms of unified (q, s)-entropy. We find that for any tripartite mixed state, the unified (q, s)-entropy entanglement of assistance follows a polygamy relation. This polygamy relation also holds in multi-particle systems. Furthermore, a generalized monogamy relation is provided for unified (q, s)-entropy entanglement in the multi-qubit system.

Investigating Friction as a Main Source of Entropy Generation in the Expansion of Confined Gas in a Piston-and-Cylinder Device

ERIC Educational Resources Information Center

Kang, Dun-Yen; Liou, Kai-Hsin; Chang, Wei-Lun

2015-01-01

The expansion or compression of gas confined in a piston-and-cylinder device is a classic working example used for illustrating the First and Second Laws of Thermodynamics. The balance of energy and entropy enables the estimation of a number of thermodynamic properties. The entropy generation (also called entropy production) resulting from this…

A Graphical Proof of the Positive Entropy Change in Heat Transfer between Two Objects

ERIC Educational Resources Information Center

Kiatgamolchai, Somchai

2015-01-01

It is well known that heat transfer between two objects results in a positive change in the total entropy of the two-object system. The second law of thermodynamics states that the entropy change of a naturally irreversible process is positive. In other words, if the entropy change of any process is positive, it can be inferred that such a process…

Entropy Analyses of Four Familiar Processes.

ERIC Educational Resources Information Center

Craig, Norman C.

1988-01-01

Presents entropy analysis of four processes: a chemical reaction, a heat engine, the dissolution of a solid, and osmosis. Discusses entropy, the second law of thermodynamics, and the Gibbs free energy function. (MVL)

Dynamic Approximate Entropy Electroanatomic Maps Detect Rotors in a Simulated Atrial Fibrillation Model

PubMed Central

Ugarte, Juan P.; Orozco-Duque, Andrés; Tobón, Catalina; Kremen, Vaclav; Novak, Daniel; Saiz, Javier; Oesterlein, Tobias; Schmitt, Clauss; Luik, Armin; Bustamante, John

2014-01-01

There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping. PMID:25489858

Characterizing Brain Structures and Remodeling after TBI Based on Information Content, Diffusion Entropy

PubMed Central

Fozouni, Niloufar; Chopp, Michael; Nejad-Davarani, Siamak P.; Zhang, Zheng Gang; Lehman, Norman L.; Gu, Steven; Ueno, Yuji; Lu, Mei; Ding, Guangliang; Li, Lian; Hu, Jiani; Bagher-Ebadian, Hassan; Hearshen, David; Jiang, Quan

2013-01-01

Background To overcome the limitations of conventional diffusion tensor magnetic resonance imaging resulting from the assumption of a Gaussian diffusion model for characterizing voxels containing multiple axonal orientations, Shannon's entropy was employed to evaluate white matter structure in human brain and in brain remodeling after traumatic brain injury (TBI) in a rat. Methods Thirteen healthy subjects were investigated using a Q-ball based DTI data sampling scheme. FA and entropy values were measured in white matter bundles, white matter fiber crossing areas, different gray matter (GM) regions and cerebrospinal fluid (CSF). Axonal densities' from the same regions of interest (ROIs) were evaluated in Bielschowsky and Luxol fast blue stained autopsy (n = 30) brain sections by light microscopy. As a case demonstration, a Wistar rat subjected to TBI and treated with bone marrow stromal cells (MSC) 1 week after TBI was employed to illustrate the superior ability of entropy over FA in detecting reorganized crossing axonal bundles as confirmed by histological analysis with Bielschowsky and Luxol fast blue staining. Results Unlike FA, entropy was less affected by axonal orientation and more affected by axonal density. A significant agreement (r = 0.91) was detected between entropy values from in vivo human brain and histologically measured axonal density from post mortum from the same brain structures. The MSC treated TBI rat demonstrated that the entropy approach is superior to FA in detecting axonal remodeling after injury. Compared with FA, entropy detected new axonal remodeling regions with crossing axons, confirmed with immunohistological staining. Conclusions Entropy measurement is more effective in distinguishing axonal remodeling after injury, when compared with FA. Entropy is also more sensitive to axonal density than axonal orientation, and thus may provide a more accurate reflection of axonal changes that occur in neurological injury and disease. PMID:24143186

Characterizing brain structures and remodeling after TBI based on information content, diffusion entropy.

PubMed

Fozouni, Niloufar; Chopp, Michael; Nejad-Davarani, Siamak P; Zhang, Zheng Gang; Lehman, Norman L; Gu, Steven; Ueno, Yuji; Lu, Mei; Ding, Guangliang; Li, Lian; Hu, Jiani; Bagher-Ebadian, Hassan; Hearshen, David; Jiang, Quan

2013-01-01

To overcome the limitations of conventional diffusion tensor magnetic resonance imaging resulting from the assumption of a Gaussian diffusion model for characterizing voxels containing multiple axonal orientations, Shannon's entropy was employed to evaluate white matter structure in human brain and in brain remodeling after traumatic brain injury (TBI) in a rat. Thirteen healthy subjects were investigated using a Q-ball based DTI data sampling scheme. FA and entropy values were measured in white matter bundles, white matter fiber crossing areas, different gray matter (GM) regions and cerebrospinal fluid (CSF). Axonal densities' from the same regions of interest (ROIs) were evaluated in Bielschowsky and Luxol fast blue stained autopsy (n = 30) brain sections by light microscopy. As a case demonstration, a Wistar rat subjected to TBI and treated with bone marrow stromal cells (MSC) 1 week after TBI was employed to illustrate the superior ability of entropy over FA in detecting reorganized crossing axonal bundles as confirmed by histological analysis with Bielschowsky and Luxol fast blue staining. Unlike FA, entropy was less affected by axonal orientation and more affected by axonal density. A significant agreement (r = 0.91) was detected between entropy values from in vivo human brain and histologically measured axonal density from post mortum from the same brain structures. The MSC treated TBI rat demonstrated that the entropy approach is superior to FA in detecting axonal remodeling after injury. Compared with FA, entropy detected new axonal remodeling regions with crossing axons, confirmed with immunohistological staining. Entropy measurement is more effective in distinguishing axonal remodeling after injury, when compared with FA. Entropy is also more sensitive to axonal density than axonal orientation, and thus may provide a more accurate reflection of axonal changes that occur in neurological injury and disease.

Spectral Entropy Can Predict Changes of Working Memory Performance Reduced by Short-Time Training in the Delayed-Match-to-Sample Task

PubMed Central

Tian, Yin; Zhang, Huiling; Xu, Wei; Zhang, Haiyong; Yang, Li; Zheng, Shuxing; Shi, Yupan

2017-01-01

Spectral entropy, which was generated by applying the Shannon entropy concept to the power distribution of the Fourier-transformed electroencephalograph (EEG), was utilized to measure the uniformity of power spectral density underlying EEG when subjects performed the working memory tasks twice, i.e., before and after training. According to Signed Residual Time (SRT) scores based on response speed and accuracy trade-off, 20 subjects were divided into two groups, namely high-performance and low-performance groups, to undertake working memory (WM) tasks. We found that spectral entropy derived from the retention period of WM on channel FC4 exhibited a high correlation with SRT scores. To this end, spectral entropy was used in support vector machine classifier with linear kernel to differentiate these two groups. Receiver operating characteristics analysis and leave-one out cross-validation (LOOCV) demonstrated that the averaged classification accuracy (CA) was 90.0 and 92.5% for intra-session and inter-session, respectively, indicating that spectral entropy could be used to distinguish these two different WM performance groups successfully. Furthermore, the support vector regression prediction model with radial basis function kernel and the root-mean-square error of prediction revealed that spectral entropy could be utilized to predict SRT scores on individual WM performance. After testing the changes in SRT scores and spectral entropy for each subject by short-time training, we found that 16 in 20 subjects’ SRT scores were clearly promoted after training and 15 in 20 subjects’ SRT scores showed consistent changes with spectral entropy before and after training. The findings revealed that spectral entropy could be a promising indicator to predict individual’s WM changes by training and further provide a novel application about WM for brain–computer interfaces. PMID:28912701

Renyi Entropies in Multiparticle Production

NASA Astrophysics Data System (ADS)

Bialas, A.; Czyz, W.

2000-12-01

Renyi entropies are calculated for some multiparticle systems. Arguments are presented that measurements of Renyi entropies as functions of the average number of particles produced in high energy collisions carry important information on the produced system.

Transfer Entropy as a Log-Likelihood Ratio

NASA Astrophysics Data System (ADS)

Barnett, Lionel; Bossomaier, Terry

2012-09-01

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology, and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic χ2 distribution is established for the transfer entropy estimator. The result generalizes the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense.

Transfer entropy as a log-likelihood ratio.

PubMed

Barnett, Lionel; Bossomaier, Terry

2012-09-28

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology, and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic χ2 distribution is established for the transfer entropy estimator. The result generalizes the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense.

The limit behavior of the evolution of the Tsallis entropy in self-gravitating systems

NASA Astrophysics Data System (ADS)

Zheng, Yahui; Du, Jiulin; Liang, Faku

2017-06-01

In this letter, we study the limit behavior of the evolution of the Tsallis entropy in self-gravitating systems. The study is carried out under two different situations, drawing the same conclusion. No matter in the energy transfer process or in the mass transfer process inside the system, when the nonextensive parameter q is more than unity, the total entropy is bounded; on the contrary, when this parameter is less than unity, the total entropy is unbounded. There are proofs in both theory and observation that the q is always more than unity. So the Tsallis entropy in self-gravitating systems generally exhibits a bounded property. This indicates the existence of a global maximum of the Tsallis entropy. It is possible for self-gravitating systems to evolve to thermodynamically stable states.

Entropy generation across Earth's collisionless bow shock.

PubMed

Parks, G K; Lee, E; McCarthy, M; Goldstein, M; Fu, S Y; Cao, J B; Canu, P; Lin, N; Wilber, M; Dandouras, I; Réme, H; Fazakerley, A

2012-02-10

Earth's bow shock is a collisionless shock wave but entropy has never been directly measured across it. The plasma experiments on Cluster and Double Star measure 3D plasma distributions upstream and downstream of the bow shock allowing calculation of Boltzmann's entropy function H and his famous H theorem, dH/dt≤0. The collisionless Boltzmann (Vlasov) equation predicts that the total entropy does not change if the distribution function across the shock becomes nonthermal, but it allows changes in the entropy density. Here, we present the first direct measurements of entropy density changes across Earth's bow shock and show that the results generally support the model of the Vlasov analysis. These observations are a starting point for a more sophisticated analysis that includes 3D computer modeling of collisionless shocks with input from observed particles, waves, and turbulences.

Effect of Entropy Generation on Wear Mechanics and System Reliability

NASA Astrophysics Data System (ADS)

Gidwani, Akshay; James, Siddanth; Jagtap, Sagar; Karthikeyan, Ram; Vincent, S.

2018-04-01

Wear is an irreversible phenomenon. Processes such as mutual sliding and rolling between materials involve entropy generation. These processes are monotonic with respect to time. The concept of entropy generation is further quantified using Degradation Entropy Generation theorem formulated by Michael D. Bryant. The sliding-wear model can be extrapolated to different instances in order to further provide a potential analysis of machine prognostics as well as system and process reliability for various processes besides even mere mechanical processes. In other words, using the concept of ‘entropy generation’ and wear, one can quantify the reliability of a system with respect to time using a thermodynamic variable, which is the basis of this paper. Thus in the present investigation, a unique attempt has been made to establish correlation between entropy-wear-reliability which can be useful technique in preventive maintenance.

Comparison of transfer entropy methods for financial time series

NASA Astrophysics Data System (ADS)

He, Jiayi; Shang, Pengjian

2017-09-01

There is a certain relationship between the global financial markets, which creates an interactive network of global finance. Transfer entropy, a measurement for information transfer, offered a good way to analyse the relationship. In this paper, we analysed the relationship between 9 stock indices from the U.S., Europe and China (from 1995 to 2015) by using transfer entropy (TE), effective transfer entropy (ETE), Rényi transfer entropy (RTE) and effective Rényi transfer entropy (ERTE). We compared the four methods in the sense of the effectiveness for identification of the relationship between stock markets. In this paper, two kinds of information flows are given. One reveals that the U.S. took the leading position when in terms of lagged-current cases, but when it comes to the same date, China is the most influential. And ERTE could provide superior results.

Effect of electron count and chemical complexity in the Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor

DOE Office of Scientific and Technical Information (OSTI.GOV)

von Rohr, Fabian; Winiarski, Michał J.; Tao, Jing

High-entropy alloys are made from random mixtures of principal elements on simple lattices, stabilized by a high mixing entropy. The recently discovered body-centered cubic (BCC) Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor appears to display properties of both simple crystalline intermetallics and amorphous materials; e.g., it has a well-defined superconducting transition along with an exceptional robustness against disorder. Here we show that the valence electron count dependence of the superconducting transition temperature in the high-entropy alloy falls between those of analogous simple solid solutions and amorphous materials and test the effect of alloy complexity on the superconductivity. We propose high-entropy alloys as excellentmore » intermediate systems for studying superconductivity as it evolves between crystalline and amorphous materials.« less

Entropy production in a photovoltaic cell

NASA Astrophysics Data System (ADS)

Ansari, Mohammad H.

2017-05-01

We evaluate entropy production in a photovoltaic cell that is modeled by four electronic levels resonantly coupled to thermally populated field modes at different temperatures. We use a formalism recently proposed, the so-called multiple parallel worlds, to consistently address the nonlinearity of entropy in terms of density matrix. Our result shows that entropy production is the difference between two flows: a semiclassical flow that linearly depends on occupational probabilities, and another flow that depends nonlinearly on quantum coherence and has no semiclassical analog. We show that entropy production in the cells depends on environmentally induced decoherence time and energy detuning. We characterize regimes where reversal flow of information takes place from a cold to hot bath. Interestingly, we identify a lower bound on entropy production, which sets limitations on the statistics of dissipated heat in the cells.

Effect of electron count and chemical complexity in the Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor

PubMed Central

von Rohr, Fabian; Winiarski, Michał J.; Tao, Jing; Klimczuk, Tomasz; Cava, Robert Joseph

2016-01-01

High-entropy alloys are made from random mixtures of principal elements on simple lattices, stabilized by a high mixing entropy. The recently discovered body-centered cubic (BCC) Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor appears to display properties of both simple crystalline intermetallics and amorphous materials; e.g., it has a well-defined superconducting transition along with an exceptional robustness against disorder. Here we show that the valence electron count dependence of the superconducting transition temperature in the high-entropy alloy falls between those of analogous simple solid solutions and amorphous materials and test the effect of alloy complexity on the superconductivity. We propose high-entropy alloys as excellent intermediate systems for studying superconductivity as it evolves between crystalline and amorphous materials. PMID:27803330

Effect of electron count and chemical complexity in the Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor

DOE PAGES

von Rohr, Fabian; Winiarski, Michał J.; Tao, Jing; ...

2016-11-01

High-entropy alloys are made from random mixtures of principal elements on simple lattices, stabilized by a high mixing entropy. The recently discovered body-centered cubic (BCC) Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor appears to display properties of both simple crystalline intermetallics and amorphous materials; e.g., it has a well-defined superconducting transition along with an exceptional robustness against disorder. Here we show that the valence electron count dependence of the superconducting transition temperature in the high-entropy alloy falls between those of analogous simple solid solutions and amorphous materials and test the effect of alloy complexity on the superconductivity. We propose high-entropy alloys as excellentmore » intermediate systems for studying superconductivity as it evolves between crystalline and amorphous materials.« less

Enthalpy-entropy compensation: the role of solvation.

PubMed

Dragan, Anatoliy I; Read, Christopher M; Crane-Robinson, Colyn

2017-05-01

Structural modifications to interacting systems frequently lead to changes in both the enthalpy (heat) and entropy of the process that compensate each other, so that the Gibbs free energy is little changed: a major barrier to the development of lead compounds in drug discovery. The conventional explanation for such enthalpy-entropy compensation (EEC) is that tighter contacts lead to a more negative enthalpy but increased molecular constraints, i.e., a compensating conformational entropy reduction. Changes in solvation can also contribute to EEC but this contribution is infrequently discussed. We review long-established and recent cases of EEC and conclude that the large fluctuations in enthalpy and entropy observed are too great to be a result of only conformational changes and must result, to a considerable degree, from variations in the amounts of water immobilized or released on forming complexes. Two systems exhibiting EEC show a correlation between calorimetric entropies and local mobilities, interpreted to mean conformational control of the binding entropy/free energy. However, a substantial contribution from solvation gives the same effect, as a consequence of a structural link between the amount of bound water and the protein flexibility. Only by assuming substantial changes in solvation-an intrinsically compensatory process-can a more complete understanding of EEC be obtained. Faced with such large, and compensating, changes in the enthalpies and entropies of binding, the best approach to engineering elevated affinities must be through the addition of ionic links, as they generate increased entropy without affecting the enthalpy.

Relative entropy equals bulk relative entropy

DOE PAGES

Jafferis, Daniel L.; Lewkowycz, Aitor; Maldacena, Juan; ...

2016-06-01

We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.

Entropy bound of local quantum field theory with generalized uncertainty principle

NASA Astrophysics Data System (ADS)

Kim, Yong-Wan; Lee, Hyung Won; Myung, Yun Soo

2009-03-01

We study the entropy bound for local quantum field theory (LQFT) with generalized uncertainty principle. The generalized uncertainty principle provides naturally a UV cutoff to the LQFT as gravity effects. Imposing the non-gravitational collapse condition as the UV-IR relation, we find that the maximal entropy of a bosonic field is limited by the entropy bound A 3 / 4 rather than A with A the boundary area.

Quelques applications de la decomposition de l'entropie en psychologie et pedagogie (Some Applications of the Resolution of Entropy in Psychology and Pedagogy)

ERIC Educational Resources Information Center

Gillet, Louis

1971-01-01

Psychological and educational measurement is carried out according to the type of model used and data collected. The H entropy which shows the dispersion of the data can be divided into intragroup and intergroup entropy. Choice of colors, sociometrical choice, and the communications are three situations where this resolution can be applied. (MF)

The Rényi entropy H2 as a rigorous, measurable lower bound for the entropy of the interaction region in multi-particle production processes

NASA Astrophysics Data System (ADS)

Bialas, A.; Czyz, W.; Zalewski, K.

2006-10-01

A model-independent lower bound on the entropy S of the multi-particle system produced in high energy collisions, provided by the measurable Rényi entropy H2, is shown to be very effective. Estimates show that the ratio H2/S remains close to one half for all realistic values of the parameters.

Archaeon and archaeal virus diversity classification via sequence entropy and fractal dimension

NASA Astrophysics Data System (ADS)

Tremberger, George, Jr.; Gallardo, Victor; Espinoza, Carola; Holden, Todd; Gadura, N.; Cheung, E.; Schneider, P.; Lieberman, D.; Cheung, T.

2010-09-01

Archaea are important potential candidates in astrobiology as their metabolism includes solar, inorganic and organic energy sources. Archaeal viruses would also be expected to be present in a sustainable archaeal exobiological community. Genetic sequence Shannon entropy and fractal dimension can be used to establish a two-dimensional measure for classification and phylogenetic study of these organisms. A sequence fractal dimension can be calculated from a numerical series consisting of the atomic numbers of each nucleotide. Archaeal 16S and 23S ribosomal RNA sequences were studied. Outliers in the 16S rRNA fractal dimension and entropy plot were found to be halophilic archaea. Positive correlation (R-square ~ 0.75, N = 18) was observed between fractal dimension and entropy across the studied species. The 16S ribosomal RNA sequence entropy correlates with the 23S ribosomal RNA sequence entropy across species with R-square 0.93, N = 18. Entropy values correspond positively with branch lengths of a published phylogeny. The studied archaeal virus sequences have high fractal dimensions of 2.02 or more. A comparison of selected extremophile sequences with archaeal sequences from the Humboldt Marine Ecosystem database (Wood-Hull Oceanography Institute, MIT) suggests the presence of continuous sequence expression as inferred from distributions of entropy and fractal dimension, consistent with the diversity expected in an exobiological archaeal community.

Small-window parametric imaging based on information entropy for ultrasound tissue characterization

PubMed Central

Tsui, Po-Hsiang; Chen, Chin-Kuo; Kuo, Wen-Hung; Chang, King-Jen; Fang, Jui; Ma, Hsiang-Yang; Chou, Dean

2017-01-01

Constructing ultrasound statistical parametric images by using a sliding window is a widely adopted strategy for characterizing tissues. Deficiency in spatial resolution, the appearance of boundary artifacts, and the prerequisite data distribution limit the practicability of statistical parametric imaging. In this study, small-window entropy parametric imaging was proposed to overcome the above problems. Simulations and measurements of phantoms were executed to acquire backscattered radiofrequency (RF) signals, which were processed to explore the feasibility of small-window entropy imaging in detecting scatterer properties. To validate the ability of entropy imaging in tissue characterization, measurements of benign and malignant breast tumors were conducted (n = 63) to compare performances of conventional statistical parametric (based on Nakagami distribution) and entropy imaging by the receiver operating characteristic (ROC) curve analysis. The simulation and phantom results revealed that entropy images constructed using a small sliding window (side length = 1 pulse length) adequately describe changes in scatterer properties. The area under the ROC for using small-window entropy imaging to classify tumors was 0.89, which was higher than 0.79 obtained using statistical parametric imaging. In particular, boundary artifacts were largely suppressed in the proposed imaging technique. Entropy enables using a small window for implementing ultrasound parametric imaging. PMID:28106118

The cancer Warburg effect may be a testable example of the minimum entropy production rate principle

NASA Astrophysics Data System (ADS)

Marín, Dolores; Sabater, Bartolomé

2017-04-01

Cancer cells consume more glucose by glycolytic fermentation to lactate than by respiration, a characteristic known as the Warburg effect. In contrast with the 36 moles of ATP produced by respiration, fermentation produces two moles of ATP per mole of glucose consumed, which poses a puzzle with regard to the function of the Warburg effect. The production of free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) per mole linearly varies with the fraction (x) of glucose consumed by fermentation that is frequently estimated around 0.9. Hence, calculation shows that, in respect to pure respiration, the predominant fermentative metabolism decreases around 10% the production of entropy per mole of glucose consumed in cancer cells. We hypothesize that increased fermentation could allow cancer cells to accomplish the Prigogine theorem of the trend to minimize the rate of production of entropy. According to the theorem, open cellular systems near the steady state could evolve to minimize the rates of entropy production that may be reached by modified replicating cells producing entropy at a low rate. Remarkably, at CO2 concentrations above 930 ppm, glucose respiration produces less entropy than fermentation, which suggests experimental tests to validate the hypothesis of minimization of the rate of entropy production through the Warburg effect.

Dual-threshold segmentation using Arimoto entropy based on chaotic bee colony optimization

NASA Astrophysics Data System (ADS)

Li, Li

2018-03-01

In order to extract target from complex background more quickly and accurately, and to further improve the detection effect of defects, a method of dual-threshold segmentation using Arimoto entropy based on chaotic bee colony optimization was proposed. Firstly, the method of single-threshold selection based on Arimoto entropy was extended to dual-threshold selection in order to separate the target from the background more accurately. Then intermediate variables in formulae of Arimoto entropy dual-threshold selection was calculated by recursion to eliminate redundant computation effectively and to reduce the amount of calculation. Finally, the local search phase of artificial bee colony algorithm was improved by chaotic sequence based on tent mapping. The fast search for two optimal thresholds was achieved using the improved bee colony optimization algorithm, thus the search could be accelerated obviously. A large number of experimental results show that, compared with the existing segmentation methods such as multi-threshold segmentation method using maximum Shannon entropy, two-dimensional Shannon entropy segmentation method, two-dimensional Tsallis gray entropy segmentation method and multi-threshold segmentation method using reciprocal gray entropy, the proposed method can segment target more quickly and accurately with superior segmentation effect. It proves to be an instant and effective method for image segmentation.

Refined generalized multiscale entropy analysis for physiological signals

NASA Astrophysics Data System (ADS)

Liu, Yunxiao; Lin, Youfang; Wang, Jing; Shang, Pengjian

2018-01-01

Multiscale entropy analysis has become a prevalent complexity measurement and been successfully applied in various fields. However, it only takes into account the information of mean values (first moment) in coarse-graining procedure. Then generalized multiscale entropy (MSEn) considering higher moments to coarse-grain a time series was proposed and MSEσ2 has been implemented. However, the MSEσ2 sometimes may yield an imprecise estimation of entropy or undefined entropy, and reduce statistical reliability of sample entropy estimation as scale factor increases. For this purpose, we developed the refined model, RMSEσ2, to improve MSEσ2. Simulations on both white noise and 1 / f noise show that RMSEσ2 provides higher entropy reliability and reduces the occurrence of undefined entropy, especially suitable for short time series. Besides, we discuss the effect on RMSEσ2 analysis from outliers, data loss and other concepts in signal processing. We apply the proposed model to evaluate the complexity of heartbeat interval time series derived from healthy young and elderly subjects, patients with congestive heart failure and patients with atrial fibrillation respectively, compared to several popular complexity metrics. The results demonstrate that RMSEσ2 measured complexity (a) decreases with aging and diseases, and (b) gives significant discrimination between different physiological/pathological states, which may facilitate clinical application.

Uncertainty relations with quantum memory for the Wehrl entropy

NASA Astrophysics Data System (ADS)

De Palma, Giacomo

2018-03-01

We prove two new fundamental uncertainty relations with quantum memory for the Wehrl entropy. The first relation applies to the bipartite memory scenario. It determines the minimum conditional Wehrl entropy among all the quantum states with a given conditional von Neumann entropy and proves that this minimum is asymptotically achieved by a suitable sequence of quantum Gaussian states. The second relation applies to the tripartite memory scenario. It determines the minimum of the sum of the Wehrl entropy of a quantum state conditioned on the first memory quantum system with the Wehrl entropy of the same state conditioned on the second memory quantum system and proves that also this minimum is asymptotically achieved by a suitable sequence of quantum Gaussian states. The Wehrl entropy of a quantum state is the Shannon differential entropy of the outcome of a heterodyne measurement performed on the state. The heterodyne measurement is one of the main measurements in quantum optics and lies at the basis of one of the most promising protocols for quantum key distribution. These fundamental entropic uncertainty relations will be a valuable tool in quantum information and will, for example, find application in security proofs of quantum key distribution protocols in the asymptotic regime and in entanglement witnessing in quantum optics.

The cancer Warburg effect may be a testable example of the minimum entropy production rate principle.

PubMed

Marín, Dolores; Sabater, Bartolomé

2017-04-28

Cancer cells consume more glucose by glycolytic fermentation to lactate than by respiration, a characteristic known as the Warburg effect. In contrast with the 36 moles of ATP produced by respiration, fermentation produces two moles of ATP per mole of glucose consumed, which poses a puzzle with regard to the function of the Warburg effect. The production of free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) per mole linearly varies with the fraction (x) of glucose consumed by fermentation that is frequently estimated around 0.9. Hence, calculation shows that, in respect to pure respiration, the predominant fermentative metabolism decreases around 10% the production of entropy per mole of glucose consumed in cancer cells. We hypothesize that increased fermentation could allow cancer cells to accomplish the Prigogine theorem of the trend to minimize the rate of production of entropy. According to the theorem, open cellular systems near the steady state could evolve to minimize the rates of entropy production that may be reached by modified replicating cells producing entropy at a low rate. Remarkably, at CO 2 concentrations above 930 ppm, glucose respiration produces less entropy than fermentation, which suggests experimental tests to validate the hypothesis of minimization of the rate of entropy production through the Warburg effect.

Small-window parametric imaging based on information entropy for ultrasound tissue characterization

NASA Astrophysics Data System (ADS)

Tsui, Po-Hsiang; Chen, Chin-Kuo; Kuo, Wen-Hung; Chang, King-Jen; Fang, Jui; Ma, Hsiang-Yang; Chou, Dean

2017-01-01

Constructing ultrasound statistical parametric images by using a sliding window is a widely adopted strategy for characterizing tissues. Deficiency in spatial resolution, the appearance of boundary artifacts, and the prerequisite data distribution limit the practicability of statistical parametric imaging. In this study, small-window entropy parametric imaging was proposed to overcome the above problems. Simulations and measurements of phantoms were executed to acquire backscattered radiofrequency (RF) signals, which were processed to explore the feasibility of small-window entropy imaging in detecting scatterer properties. To validate the ability of entropy imaging in tissue characterization, measurements of benign and malignant breast tumors were conducted (n = 63) to compare performances of conventional statistical parametric (based on Nakagami distribution) and entropy imaging by the receiver operating characteristic (ROC) curve analysis. The simulation and phantom results revealed that entropy images constructed using a small sliding window (side length = 1 pulse length) adequately describe changes in scatterer properties. The area under the ROC for using small-window entropy imaging to classify tumors was 0.89, which was higher than 0.79 obtained using statistical parametric imaging. In particular, boundary artifacts were largely suppressed in the proposed imaging technique. Entropy enables using a small window for implementing ultrasound parametric imaging.

Structure of the entanglement entropy of (3+1)-dimensional gapped phases of matter

NASA Astrophysics Data System (ADS)

Zheng, Yunqin; He, Huan; Bradlyn, Barry; Cano, Jennifer; Neupert, Titus; Bernevig, B. Andrei

2018-05-01

We study the entanglement entropy of gapped phases of matter in three spatial dimensions. We focus in particular on size-independent contributions to the entropy across entanglement surfaces of arbitrary topologies. We show that for low energy fixed-point theories, the constant part of the entanglement entropy across any surface can be reduced to a linear combination of the entropies across a sphere and a torus. We first derive our results using strong sub-additivity inequalities along with assumptions about the entanglement entropy of fixed-point models, and identify the topological contribution by considering the renormalization group flow; in this way we give an explicit definition of topological entanglement entropy Stopo in (3+1)D, which sharpens previous results. We illustrate our results using several concrete examples and independent calculations, and show adding "twist" terms to the Lagrangian can change Stopo in (3+1)D. For the generalized Walker-Wang models, we find that the ground state degeneracy on a 3-torus is given by exp(-3 Stopo[T2] ) in terms of the topological entanglement entropy across a 2-torus. We conjecture that a similar relationship holds for Abelian theories in (d +1 ) dimensional spacetime, with the ground state degeneracy on the d -torus given by exp(-d Stopo[Td -1] ) .

Entropy generation in magnetohydrodynamic radiative flow due to rotating disk in presence of viscous dissipation and Joule heating

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Qayyum, Sumaira; Khan, Muhammad Ijaz; Alsaedi, Ahmed

2018-01-01

Simultaneous effects of viscous dissipation and Joule heating in flow by rotating disk of variable thickness are examined. Radiative flow saturating porous space is considered. Much attention is given to entropy generation outcome. Developed nonlinear ordinary differential systems are computed for the convergent series solutions. Specifically, the results of velocity, temperature, entropy generation, Bejan number, coefficient of skin friction, and local Nusselt number are discussed. Clearly the entropy generation rate depends on velocity and temperature distributions. Moreover the entropy generation rate is a decreasing function of Hartmann number, Eckert number, and Reynolds number, while they gave opposite behavior for Bejan numbers.

Characterizations of matrix and operator-valued Φ-entropies, and operator Efron-Stein inequalities.

PubMed

Cheng, Hao-Chung; Hsieh, Min-Hsiu

2016-03-01

We derive new characterizations of the matrix Φ-entropy functionals introduced in Chen & Tropp (Chen, Tropp 2014 Electron. J. Prob. 19 , 1-30. (doi:10.1214/ejp.v19-2964)). These characterizations help us to better understand the properties of matrix Φ-entropies, and are a powerful tool for establishing matrix concentration inequalities for random matrices. Then, we propose an operator-valued generalization of matrix Φ-entropy functionals, and prove the subadditivity under Löwner partial ordering. Our results demonstrate that the subadditivity of operator-valued Φ-entropies is equivalent to the convexity. As an application, we derive the operator Efron-Stein inequality.

Natural entropy production in an inflationary model for a polarized vacuum

NASA Astrophysics Data System (ADS)

Berman, Marcelo Samuel; Som, Murari M.

2007-08-01

Though entropy production is forbidden in standard FRW Cosmology, Berman and Som presented a simple inflationary model where entropy production by bulk viscosity, during standard inflation without ad hoc pressure terms can be accommodated with Robertson Walker’s metric, so the requirement that the early Universe be anisotropic is not essential in order to have entropy growth during inflationary phase, as we show. Entropy also grows due to shear viscosity, for the anisotropic case. The intrinsically inflationary metric that we propose can be thought of as defining a polarized vacuum, and leads directly to the desired effects without the need of introducing extra pressure terms.

Entropy-based link prediction in weighted networks

NASA Astrophysics Data System (ADS)

Xu, Zhongqi; Pu, Cunlai; Ramiz Sharafat, Rajput; Li, Lunbo; Yang, Jian

2017-01-01

Information entropy has been proved to be an effective tool to quantify the structural importance of complex networks. In the previous work (Xu et al, 2016 \\cite{xu2016}), we measure the contribution of a path in link prediction with information entropy. In this paper, we further quantify the contribution of a path with both path entropy and path weight, and propose a weighted prediction index based on the contributions of paths, namely Weighted Path Entropy (WPE), to improve the prediction accuracy in weighted networks. Empirical experiments on six weighted real-world networks show that WPE achieves higher prediction accuracy than three typical weighted indices.

On q-non-extensive statistics with non-Tsallisian entropy

NASA Astrophysics Data System (ADS)

Jizba, Petr; Korbel, Jan

2016-02-01

We combine an axiomatics of Rényi with the q-deformed version of Khinchin axioms to obtain a measure of information (i.e., entropy) which accounts both for systems with embedded self-similarity and non-extensivity. We show that the entropy thus obtained is uniquely solved in terms of a one-parameter family of information measures. The ensuing maximal-entropy distribution is phrased in terms of a special function known as the Lambert W-function. We analyze the corresponding "high" and "low-temperature" asymptotics and reveal a non-trivial structure of the parameter space. Salient issues such as concavity and Schur concavity of the new entropy are also discussed.

Entropy of measurement and erasure: Szilard's membrane model revisited

NASA Astrophysics Data System (ADS)

Leff, Harvey S.; Rex, Andrew F.

1994-11-01

It is widely believed that measurement is accompanied by irreversible entropy increase. This conventional wisdom is based in part on Szilard's 1929 study of entropy decrease in a thermodynamic system by intelligent intervention (i.e., a Maxwell's demon) and Brillouin's association of entropy with information. Bennett subsequently argued that information acquisition is not necessarily irreversible, but information erasure must be dissipative (Landauer's principle). Inspired by the ensuing debate, we revisit the membrane model introduced by Szilard and find that it can illustrate and clarify (1) reversible measurement, (2) information storage, (3) decoupling of the memory from the system being measured, and (4) entropy increase associated with memory erasure and resetting.

Subgrid-scale Condensation Modeling for Entropy-based Large Eddy Simulations of Clouds

NASA Astrophysics Data System (ADS)

Kaul, C. M.; Schneider, T.; Pressel, K. G.; Tan, Z.

2015-12-01

An entropy- and total water-based formulation of LES thermodynamics, such as that used by the recently developed code PyCLES, is advantageous from physical and numerical perspectives. However, existing closures for subgrid-scale thermodynamic fluctuations assume more traditional choices for prognostic thermodynamic variables, such as liquid potential temperature, and are not directly applicable to entropy-based modeling. Since entropy and total water are generally nonlinearly related to diagnosed quantities like temperature and condensate amounts, neglecting their small-scale variability can lead to bias in simulation results. Here we present the development of a subgrid-scale condensation model suitable for use with entropy-based thermodynamic formulations.

A Study of Turkish Chemistry Undergraduates' Understandings of Entropy

ERIC Educational Resources Information Center

Sozbilir, Mustafa; Bennett, Judith M.

2007-01-01

Entropy is that fundamental concept of chemical thermodynamics, which explains the natural tendency of matter and energy in the Universe. The analysis presents the description of entropy, as understood by the Turkish chemistry undergraduates.

Contour entropy: a new determinant of perceiving ground or a hole.

PubMed

Gillam, Barbara J; Grove, Philip M

2011-06-01

Figure-ground perception is typically described as seeing one surface occluding another. Figure properties, not ground properties, are considered the significant factors. In scenes, however, a near surface will often occlude multiple contours and surfaces, often at different depths, producing alignments that are improbable except under conditions of occlusion. We thus hypothesized that unrelated (high entropy) lines would tend to appear as ground in a figure-ground paradigm more often than similarly aligned ordered (low entropy) lines. We further hypothesized that for lines spanning a closed area, high line entropy should increase the hole-like appearance of that area. These predictions were confirmed in three experiments. The probability that patterned rectangles were seen as ground when alternated with blank rectangles increased with pattern entropy. A single rectangular shape appeared more hole-like when the entropy of the enclosed contours increased. Furthermore, these same contours, with the outline shape removed, gave rise to bounding illusory contours whose strength increased with contour entropy. We conclude that figure-ground and hole perception can be determined by properties of ground in the absence of any figural shape, or surround, factors.

Entropy density of an adiabatic relativistic Bose-Einstein condensate star

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khaidir, Ahmad Firdaus; Kassim, Hasan Abu; Yusof, Norhasliza

Inspired by recent works, we investigate how the thermodynamics parameters (entropy, temperature, number density, energy density, etc) of Bose-Einstein Condensate star scale with the structure of the star. Below the critical temperature in which the condensation starts to occur, we study how the entropy behaves with varying temperature till it reaches its own stability against gravitational collapse and singularity. Compared to photon gases (pressure is described by radiation) where the chemical potential, μ is zero, entropy of photon gases obeys the Stefan-Boltzmann Law for a small values of T while forming a spiral structure for a large values of Tmore » due to general relativity. The entropy density of Bose-Einstein Condensate is obtained following the similar sequence but limited under critical temperature condition. We adopt the scalar field equation of state in Thomas-Fermi limit to study the characteristics of relativistic Bose-Einstein condensate under varying temperature and entropy. Finally, we obtain the entropy density proportional to (σT{sup 3}-3T) which obeys the Stefan-Boltzmann Law in ultra-relativistic condition.« less

AdS and dS Entropy from String Junctions or The Function of Junction Conjunctions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Silverstein, Eva M

Flux compactifications of string theory exhibiting the possibility of discretely tuning the cosmological constant to small values have been constructed. The highly tuned vacua in this discretuum have curvature radii which scale as large powers of the flux quantum numbers, exponential in the number of cycles in the compactification. By the arguments of Susskind/Witten (in the AdS case) and Gibbons/Hawking (in the dS case), we expect correspondingly large entropies associated with these vacua. If they are to provide a dual description of these vacua on their Coulomb branch, branes traded for the flux need to account for this entropy atmore » the appropriate energy scale. In this note, we argue that simple string junctions and webs ending on the branes can account for this large entropy, obtaining a rough estimate for junction entropy that agrees with the existing rough estimates for the spacing of the discretuum. In particular, the brane entropy can account for the (A)dS entropy far away from string scale correspondence limits.« less

All the entropies on the light-cone

NASA Astrophysics Data System (ADS)

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2018-05-01

We determine the explicit universal form of the entanglement and Renyi entropies, for regions with arbitrary boundary on a null plane or the light-cone. All the entropies are shown to saturate the strong subadditive inequality. This Renyi Markov property implies that the vacuum behaves like a product state. For the null plane, our analysis applies to general quantum field theories, and we show that the entropies do not depend on the region. For the light-cone, our approach is restricted to conformal field theories. In this case, the construction of the entropies is related to dilaton effective actions in two less dimensions. In particular, the universal logarithmic term in the entanglement entropy arises from a Wess-Zumino anomaly action. We also consider these properties in theories with holographic duals, for which we construct the minimal area surfaces for arbitrary shapes on the light-cone. We recover the Markov property and the universal form of the entropy, and argue that these properties continue to hold upon including stringy and quantum corrections. We end with some remarks on the recently proved entropic a-theorem in four spacetime dimensions.

Irreversibility and entropy production in transport phenomena, III—Principle of minimum integrated entropy production including nonlinear responses

NASA Astrophysics Data System (ADS)

Suzuki, Masuo

2013-01-01

A new variational principle of steady states is found by introducing an integrated type of energy dissipation (or entropy production) instead of instantaneous energy dissipation. This new principle is valid both in linear and nonlinear transport phenomena. Prigogine’s dream has now been realized by this new general principle of minimum “integrated” entropy production (or energy dissipation). This new principle does not contradict with the Onsager-Prigogine principle of minimum instantaneous entropy production in the linear regime, but it is conceptually different from the latter which does not hold in the nonlinear regime. Applications of this theory to electric conduction, heat conduction, particle diffusion and chemical reactions are presented. The irreversibility (or positive entropy production) and long time tail problem in Kubo’s formula are also discussed in the Introduction and last section. This constitutes the complementary explanation of our theory of entropy production given in the previous papers (M. Suzuki, Physica A 390 (2011) 1904 and M. Suzuki, Physica A 391 (2012) 1074) and has given the motivation of the present investigation of variational principle.

Unification of field theory and maximum entropy methods for learning probability densities

NASA Astrophysics Data System (ADS)

Kinney, Justin B.

2015-09-01

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.

Thermodynamic constraints on a varying cosmological-constant-like term from the holographic equipartition law with a power-law corrected entropy

NASA Astrophysics Data System (ADS)

Komatsu, Nobuyoshi

2017-11-01

A power-law corrected entropy based on a quantum entanglement is considered to be a viable black-hole entropy. In this study, as an alternative to Bekenstein-Hawking entropy, a power-law corrected entropy is applied to Padmanabhan's holographic equipartition law to thermodynamically examine an extra driving term in the cosmological equations for a flat Friedmann-Robertson-Walker universe at late times. Deviations from the Bekenstein-Hawking entropy generate an extra driving term (proportional to the α th power of the Hubble parameter, where α is a dimensionless constant for the power-law correction) in the acceleration equation, which can be derived from the holographic equipartition law. Interestingly, the value of the extra driving term in the present model is constrained by the second law of thermodynamics. From the thermodynamic constraint, the order of the driving term is found to be consistent with the order of the cosmological constant measured by observations. In addition, the driving term tends to be constantlike when α is small, i.e., when the deviation from the Bekenstein-Hawking entropy is small.

Rényi continuous entropy of DNA sequences.

PubMed

Vinga, Susana; Almeida, Jonas S

2004-12-07

Entropy measures of DNA sequences estimate their randomness or, inversely, their repeatability. L-block Shannon discrete entropy accounts for the empirical distribution of all length-L words and has convergence problems for finite sequences. A new entropy measure that extends Shannon's formalism is proposed. Renyi's quadratic entropy calculated with Parzen window density estimation method applied to CGR/USM continuous maps of DNA sequences constitute a novel technique to evaluate sequence global randomness without some of the former method drawbacks. The asymptotic behaviour of this new measure was analytically deduced and the calculation of entropies for several synthetic and experimental biological sequences was performed. The results obtained were compared with the distributions of the null model of randomness obtained by simulation. The biological sequences have shown a different p-value according to the kernel resolution of Parzen's method, which might indicate an unknown level of organization of their patterns. This new technique can be very useful in the study of DNA sequence complexity and provide additional tools for DNA entropy estimation. The main MATLAB applications developed and additional material are available at the webpage . Specialized functions can be obtained from the authors.

Entanglement entropy in critical phenomena and analog models of quantum gravity

NASA Astrophysics Data System (ADS)

Fursaev, Dmitri V.

2006-06-01

A general geometrical structure of the entanglement entropy for spatial partition of a relativistic QFT system is established by using methods of the effective gravity action and the spectral geometry. A special attention is payed to the subleading terms in the entropy in different dimensions and to behavior in different states. It is conjectured, on the base of relation between the entropy and the action, that in a fundamental theory the ground state entanglement entropy per unit area equals 1/(4GN), where GN is the Newton constant in the low-energy gravity sector of the theory. The conjecture opens a new avenue in analogue gravity models. For instance, in higher-dimensional condensed matter systems, which near a critical point are described by relativistic QFT’s, the entanglement entropy density defines an effective gravitational coupling. By studying the properties of this constant one can get new insights in quantum gravity phenomena, such as the universality of the low-energy physics, the renormalization group behavior of GN, the statistical meaning of the Bekenstein-Hawking entropy.

Entropy in bimolecular simulations: A comprehensive review of atomic fluctuations-based methods.

PubMed

Kassem, Summer; Ahmed, Marawan; El-Sheikh, Salah; Barakat, Khaled H

2015-11-01

Entropy of binding constitutes a major, and in many cases a detrimental, component of the binding affinity in biomolecular interactions. While the enthalpic part of the binding free energy is easier to calculate, estimating the entropy of binding is further more complicated. A precise evaluation of entropy requires a comprehensive exploration of the complete phase space of the interacting entities. As this task is extremely hard to accomplish in the context of conventional molecular simulations, calculating entropy has involved many approximations. Most of these golden standard methods focused on developing a reliable estimation of the conformational part of the entropy. Here, we review these methods with a particular emphasis on the different techniques that extract entropy from atomic fluctuations. The theoretical formalisms behind each method is explained highlighting its strengths as well as its limitations, followed by a description of a number of case studies for each method. We hope that this brief, yet comprehensive, review provides a useful tool to understand these methods and realize the practical issues that may arise in such calculations. Copyright © 2015 Elsevier Inc. All rights reserved.

Using Link Disconnection Entropy Disorder to Detect Fast Moving Nodes in MANETs.

PubMed

Alvarez, Carlos F; Palafox, Luis E; Aguilar, Leocundo; Sanchez, Mauricio A; Martinez, Luis G

2016-01-01

Mobile ad-hoc networks (MANETs) are dynamic by nature; this dynamism comes from node mobility, traffic congestion, and other transmission conditions. Metrics to evaluate the effects of those conditions shine a light on node's behavior in an ad-hoc network, helping to identify the node or nodes with better conditions of connection. In this paper, we propose a relative index to evaluate a single node reliability, based on the link disconnection entropy disorder using neighboring nodes as reference. Link disconnection entropy disorder is best used to identify fast moving nodes or nodes with unstable communications, this without the need of specialized sensors such as GPS. Several scenarios were studied to verify the index, measuring the effects of Speed and traffic density on the link disconnection entropy disorder. Packet delivery ratio is associated to the metric detecting a strong relationship, enabling the use of the link disconnection entropy disorder to evaluate the stability of a node to communicate with other nodes. To expand the utilization of the link entropy disorder, we identified nodes with higher speeds in network simulations just by using the link entropy disorder.

Two faces of entropy and information in biological systems.

PubMed

Mitrokhin, Yuriy

2014-10-21

The article attempts to overcome the well-known paradox of contradictions between the emerging biological organization and entropy production in biological systems. It is assumed that quality, speculative correlation between entropy and antientropy processes taking place both in the past and today in the metabolic and genetic cellular systems may be perfectly authorized for adequate description of the evolution of biological organization. So far as thermodynamic entropy itself cannot compensate for the high degree of organization which exists in the cell, we discuss the mode of conjunction of positive entropy events (mutations) in the genetic systems of the past generations and the formation of organized structures of current cells. We argue that only the information which is generated in the conditions of the information entropy production (mutations and other genome reorganization) in genetic systems of the past generations provides the physical conjunction of entropy and antientropy processes separated from each other in time generations. It is readily apparent from the requirements of the Second law of thermodynamics. Copyright © 2014 Elsevier Ltd. All rights reserved.

Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes

NASA Astrophysics Data System (ADS)

Liu, Yong; Shu, Chi-Wang; Zhang, Mengping

2018-02-01

We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi-discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by Godunov [32], the entropy stable DG framework with suitable quadrature rules [15], the entropy conservative flux in [14] inside each cell and the entropy dissipative approximate Godunov type numerical flux at cell interfaces to make the scheme entropy stable. The main difficulty in the generalization of the results in [15] is the appearance of the non-conservative "source terms" added in the modified MHD model introduced by Godunov [32], which do not exist in the general hyperbolic system studied in [15]. Special care must be taken to discretize these "source terms" adequately so that the resulting DG scheme satisfies entropy stability. Total variation diminishing / bounded (TVD/TVB) limiters and bound-preserving limiters are applied to control spurious oscillations. We demonstrate the accuracy and robustness of this new scheme on standard MHD examples.

Unification of field theory and maximum entropy methods for learning probability densities.

PubMed

Kinney, Justin B

2015-09-01

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship between them has remained unclear. Here I unify these two methods by showing that every maximum entropy density estimate can be recovered in the infinite smoothness limit of an appropriate Bayesian field theory. I also show that Bayesian field theory estimation can be performed without imposing any boundary conditions on candidate densities, and that the infinite smoothness limit of these theories recovers the most common types of maximum entropy estimates. Bayesian field theory thus provides a natural test of the maximum entropy null hypothesis and, furthermore, returns an alternative (lower entropy) density estimate when the maximum entropy hypothesis is falsified. The computations necessary for this approach can be performed rapidly for one-dimensional data, and software for doing this is provided.

Entropy stable discontinuous interfaces coupling for the three-dimensional compressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-06-01

Non-linear entropy stability and a summation-by-parts (SBP) framework are used to derive entropy stable interior interface coupling for the semi-discretized three-dimensional (3D) compressible Navier-Stokes equations. A complete semi-discrete entropy estimate for the interior domain is achieved combining a discontinuous entropy conservative operator of any order [1,2] with an entropy stable coupling condition for the inviscid terms, and a local discontinuous Galerkin (LDG) approach with an interior penalty (IP) procedure for the viscous terms. The viscous penalty contributions scale with the inverse of the Reynolds number (Re) so that for Re → ∞ their contributions vanish and only the entropy stable inviscid interface penalty term is recovered. This paper extends the interface couplings presented [1,2] and provides a simple and automatic way to compute the magnitude of the viscous IP term. The approach presented herein is compatible with any diagonal norm summation-by-parts (SBP) spatial operator, including finite element, finite volume, finite difference schemes and the class of high-order accurate methods which include the large family of discontinuous Galerkin discretizations and flux reconstruction schemes.

Cleavage Entropy as Quantitative Measure of Protease Specificity

PubMed Central

Fuchs, Julian E.; von Grafenstein, Susanne; Huber, Roland G.; Margreiter, Michael A.; Spitzer, Gudrun M.; Wallnoefer, Hannes G.; Liedl, Klaus R.

2013-01-01

A purely information theory-guided approach to quantitatively characterize protease specificity is established. We calculate an entropy value for each protease subpocket based on sequences of cleaved substrates extracted from the MEROPS database. We compare our results with known subpocket specificity profiles for individual proteases and protease groups (e.g. serine proteases, metallo proteases) and reflect them quantitatively. Summation of subpocket-wise cleavage entropy contributions yields a measure for overall protease substrate specificity. This total cleavage entropy allows ranking of different proteases with respect to their specificity, separating unspecific digestive enzymes showing high total cleavage entropy from specific proteases involved in signaling cascades. The development of a quantitative cleavage entropy score allows an unbiased comparison of subpocket-wise and overall protease specificity. Thus, it enables assessment of relative importance of physicochemical and structural descriptors in protease recognition. We present an exemplary application of cleavage entropy in tracing substrate specificity in protease evolution. This highlights the wide range of substrate promiscuity within homologue proteases and hence the heavy impact of a limited number of mutations on individual substrate specificity. PMID:23637583

Clarifying the link between von Neumann and thermodynamic entropies

NASA Astrophysics Data System (ADS)

Deville, Alain; Deville, Yannick

2013-01-01

The state of a quantum system being described by a density operator ρ, quantum statistical mechanics calls the quantity - kTr( ρln ρ), introduced by von Neumann, its von Neumann or statistical entropy. A 1999 Shenker's paper initiated a debate about its link with the entropy of phenomenological thermodynamics. Referring to Gibbs's and von Neumann's founding texts, we replace von Neumann's 1932 contribution in its historical context, after Gibbs's 1902 treatise and before the creation of the information entropy concept, which places boundaries into the debate. Reexamining von Neumann's reasoning, we stress that the part of his reasoning implied in the debate mainly uses thermodynamics, not quantum mechanics, and identify two implicit postulates. We thoroughly examine Shenker's and ensuing papers, insisting upon the presence of open thermodynamical subsystems, imposing us the use of the chemical potential concept. We briefly mention Landau's approach to the quantum entropy. On the whole, it is shown that von Neumann's viewpoint is right, and why Shenker's claim that von Neumann entropy "is not the quantum-mechanical correlate of thermodynamic entropy" can't be retained.

Lower and upper bounds for entanglement of Rényi-α entropy.

PubMed

Song, Wei; Chen, Lin; Cao, Zhuo-Liang

2016-12-23

Entanglement Rényi-α entropy is an entanglement measure. It reduces to the standard entanglement of formation when α tends to 1. We derive analytical lower and upper bounds for the entanglement Rényi-α entropy of arbitrary dimensional bipartite quantum systems. We also demonstrate the application our bound for some concrete examples. Moreover, we establish the relation between entanglement Rényi-α entropy and some other entanglement measures.

Renyi Entropies of a Black Hole

NASA Astrophysics Data System (ADS)

Bialas, A.; Czyz, W.

2008-08-01

The Renyi entropies, Hl, of Hawking radiation contained in a thin shell surrounding the black hole are evaluated. When the width of the shell is adjusted to the energy content corresponding to the mass defect, the Bekenstein-Hawking formula for the Shannon (S=H1) entropy of a black hole is reproduced. This result does not depend on the distance of the shell from the horizon. The Renyi entropies of higher order, however, are sensitive to it.

Entanglement entropy and entanglement spectrum of the Kitaev model.

PubMed

Yao, Hong; Qi, Xiao-Liang

2010-08-20

In this letter, we obtain an exact formula for the entanglement entropy of the ground state and all excited states of the Kitaev model. Remarkably, the entanglement entropy can be expressed in a simple separable form S = SG+SF, with SF the entanglement entropy of a free Majorana fermion system and SG that of a Z2 gauge field. The Z2 gauge field part contributes to the universal "topological entanglement entropy" of the ground state while the fermion part is responsible for the nonlocal entanglement carried by the Z2 vortices (visons) in the non-Abelian phase. Our result also enables the calculation of the entire entanglement spectrum and the more general Renyi entropy of the Kitaev model. Based on our results we propose a new quantity to characterize topologically ordered states--the capacity of entanglement, which can distinguish the st ates with and without topologically protected gapless entanglement spectrum.