NASA Astrophysics Data System (ADS)
Goradia, Shantilal
2015-10-01
We modify Newtonian gravity to probabilistic quantum mechanical gravity to derive strong coupling. If this approach is valid, we should be able to extend it to the physical body (life) as follows. Using Boltzmann equation, we get the entropy of the universe (137) as if its reciprocal, the fine structure constant (ALPHA), is the hidden candidate representing the negative entropy of the universe which is indicative of the binary information as its basis (http://www.arXiv.org/pdf/physics0210040v5). Since ALPHA relates to cosmology, it must relate to molecular biology too, with the binary system as the fundamental source of information for the nucleotides of the DNA as implicit in the book by the author: ``Quantum Consciousness - The Road to Reality.'' We debate claims of anthropic principle based on the negligible variation of ALPHA and throw light on thermodynamics. We question constancy of G in multiple ways.
Photosynthesis and negative entropy production.
Jennings, Robert C; Engelmann, Enrico; Garlaschi, Flavio; Casazza, Anna Paola; Zucchelli, Giuseppe
2005-09-30
The widely held view that the maximum efficiency of a photosynthetic pigment system is given by the Carnot cycle expression (1-T/Tr) for energy transfer from a hot bath (radiation at temperature Tr) to a cold bath (pigment system at temperature T) is critically examined and demonstrated to be inaccurate when the entropy changes associated with the microscopic process of photon absorption and photochemistry at the level of single photosystems are considered. This is because entropy losses due to excited state generation and relaxation are extremely small (DeltaS < T/Tr) and are essentially associated with the absorption-fluorescence Stokes shift. Total entropy changes associated with primary photochemistry for single photosystems are shown to depend critically on the thermodynamic efficiency of the process. This principle is applied to the case of primary photochemistry of the isolated core of higher plant photosystem I and photosystem II, which are demonstrated to have maximal thermodynamic efficiencies of xi > 0.98 and xi > 0.92 respectively, and which, in principle, function with negative entropy production. It is demonstrated that for the case of xi > (1-T/Tr) entropy production is always negative and only becomes positive when xi < (1-T/Tr). PMID:16139784
Negative temperatures and the definition of entropy
NASA Astrophysics Data System (ADS)
Swendsen, Robert H.; Wang, Jian-Sheng
2016-07-01
The concept of negative temperature has recently received renewed interest in the context of debates about the correct definition of the thermodynamic entropy in statistical mechanics. Several researchers have identified the thermodynamic entropy exclusively with the "volume entropy" suggested by Gibbs, and have further concluded that by this definition, negative temperatures violate the principles of thermodynamics. We disagree with these conclusions. We demonstrate that volume entropy is inconsistent with the postulates of thermodynamics for systems with non-monotonic energy densities, while a definition of entropy based on the probability distributions of macroscopic variables does satisfy the postulates of thermodynamics. Our results confirm that negative temperature is a valid extension of thermodynamics.
Entropy analysis of systems exhibiting negative probabilities
NASA Astrophysics Data System (ADS)
Tenreiro Machado, J. A.
2016-07-01
This paper addresses the concept of negative probability and its impact upon entropy. An analogy between the probability generating functions, in the scope of quasiprobability distributions, and the Grünwald-Letnikov definition of fractional derivatives, is explored. Two distinct cases producing negative probabilities are formulated and their distinct meaning clarified. Numerical calculations using the Shannon entropy characterize further the characteristics of the two limit cases.
Negative entropy of mixing for vanadium-platinum solutions.
Delaire, O; Swan-Wood, T; Fultz, B
2004-10-29
The phonon densities of states for pure vanadium and the solid solutions V-6.25% Ni, Pd, Pt were determined from inelastic neutron scattering measurements. The solute atoms caused a large stiffening of the phonons, resulting in large, negative vibrational entropies of mixing. For V-6.25%Pt, the negative vibrational entropy of mixing exceeds the conventional positive chemical entropy of mixing. This negative total entropy of mixing should extend to lower concentrations of Pt, and the effect on the bcc solvus line is discussed. The experimental data were inverted to obtain interatomic force constants by using a Born-von Kármán model with an iterative optimization algorithm. The stiffening of bonds responsible for the decrease of entropy was found to occur mainly in first-nearest-neighbor solute-host bonds, and correlates in part with the solute metallic radius. PMID:15525182
Negative Entropy of Mixing for Vanadium-Platinum Solutions
NASA Astrophysics Data System (ADS)
Delaire, O.; Swan–Wood, T.; Fultz, B.
2004-10-01
The phonon densities of states for pure vanadium and the solid solutions V-6.25% Ni, Pd, Pt were determined from inelastic neutron scattering measurements. The solute atoms caused a large stiffening of the phonons, resulting in large, negative vibrational entropies of mixing. For V-6.25%Pt, the negative vibrational entropy of mixing exceeds the conventional positive chemical entropy of mixing. This negative total entropy of mixing should extend to lower concentrations of Pt, and the effect on the bcc solvus line is discussed. The experimental data were inverted to obtain interatomic force constants by using a Born von Kármán model with an iterative optimization algorithm. The stiffening of bonds responsible for the decrease of entropy was found to occur mainly in first-nearest-neighbor solute-host bonds, and correlates in part with the solute metallic radius.
Connectivity in the human brain dissociates entropy and complexity of auditory inputs.
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. PMID:25536493
The Contrast Theory of Negative Input.
ERIC Educational Resources Information Center
Saxton, Matthew
1997-01-01
Presents an alternative definition of negative evidence, based on the idea that the unique discourse structure created in the juxtaposition of child error and adult correct form can reveal the child in contrast or conflict between the two forms. Findings reveal that children reproduced the correct irregular model more often and persisted with…
Entropy versus APE production: On the buoyancy power input in the oceans energy cycle
NASA Astrophysics Data System (ADS)
Tailleux, R.
2010-11-01
This letter argues that the current controversy about whether Wbuoyancy, the power input due to the surface buoyancy fluxes, is large or small in the oceans stems from two distinct and incompatible views on how Wbuoyancy relates to the volume-integrated work of expansion/contraction B. The current prevailing view is that Wbuoyancy should be identified with the net value of B, which current theories estimate to be small. The alternative view, defended here, is that only the positive part of B, i.e., the one converting internal energy into mechanical energy, should enter the definition of Wbuoyancy, since the negative part of B is associated with the non-viscous dissipation of mechanical energy. Two indirect methods suggest that by contrast, the positive part of B is potentially large.
Entropies of negative incomes, Pareto-distributed loss, and financial crises.
Gao, Jianbo; Hu, Jing; Mao, Xiang; Zhou, Mi; Gurbaxani, Brian; Lin, Johnny
2011-01-01
Health monitoring of world economy is an important issue, especially in a time of profound economic difficulty world-wide. The most important aspect of health monitoring is to accurately predict economic downturns. To gain insights into how economic crises develop, we present two metrics, positive and negative income entropy and distribution analysis, to analyze the collective "spatial" and temporal dynamics of companies in nine sectors of the world economy over a 19 year period from 1990-2008. These metrics provide accurate predictive skill with a very low false-positive rate in predicting downturns. The new metrics also provide evidence of phase transition-like behavior prior to the onset of recessions. Such a transition occurs when negative pretax incomes prior to or during economic recessions transition from a thin-tailed exponential distribution to the higher entropy Pareto distribution, and develop even heavier tails than those of the positive pretax incomes. These features propagate from the crisis initiating sector of the economy to other sectors. PMID:22007270
NASA Astrophysics Data System (ADS)
Karakaya, Gulsah; Taormina, Riccardo; Galelli, Stefano; Damla Ahipasaoglu, Selin
2015-04-01
Input Variable Selection (IVS) is an essential step in hydrological modelling problems, since it allows determining the optimal subset of input variables from a large set of candidates to characterize a preselected output. Interestingly, most of the existing IVS algorithms select a single subset, or, at most, one subset of input variables for each cardinality level, thus overlooking the fact that, for a given cardinality, there can be several subsets with similar information content. In this study, we develop a novel IVS approach specifically conceived to account for this issue. The approach is based on the formulation of a four-objective optimization problem that aims at minimizing the number of selected variables and maximizing the prediction accuracy of a data-driven model, while optimizing two entropy-based measures of relevance and redundancy. The redundancy measure ensures that the cross-dependence between the variables in a subset is minimized, while the relevance measure guarantees that the information content of each subset is maximized. In addition to the capability of selecting equally informative subsets, the approach is characterized by two other properties, namely 1) the capability of handling nonlinear interactions between the candidate input variables and preselected output, and 2) computational efficiency. These properties are guaranteed by the adoption of Extreme Learning Machine and Borg MOEA as data-driven model and heuristic optimization procedure, respectively. The approach is demonstrated on a long-term streamflow prediction problem, with the input dataset including both hydro-meteorological variables and climate indices representing dominant modes of climate variability. Results show that the availability of several equally informative subsets allows 1) determining the relative importance of each candidate input, thus supporting the understanding of the underlying physical processes, and 2) finding a better trade-off between multiple
Dordek, Yedidyah; Soudry, Daniel; Meir, Ron; Derdikman, Dori
2016-01-01
Many recent models study the downstream projection from grid cells to place cells, while recent data have pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input from the place cells. We propose a single-layer neural network with feedforward weights connecting place-like input cells to grid cell outputs. Place-to-grid weights are learned via a generalized Hebbian rule. The architecture of this network highly resembles neural networks used to perform Principal Component Analysis (PCA). Both numerical results and analytic considerations indicate that if the components of the feedforward neural network are non-negative, the output converges to a hexagonal lattice. Without the non-negativity constraint, the output converges to a square lattice. Consistent with experiments, grid spacing ratio between the first two consecutive modules is −1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA. DOI: http://dx.doi.org/10.7554/eLife.10094.001 PMID:26952211
NASA Astrophysics Data System (ADS)
Wen, Xueda; Matsuura, Shunji; Ryu, Shinsei
2016-06-01
We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1)-dimensional topologically ordered phases. Our approach is complementary to, e.g., the existing methods using replica trick and Witten's method of surgery, and applies to a generic spatial manifold of genus g , which can be bipartitioned in an arbitrary way. The effects of fusion and braiding of Wilson lines can be also straightforwardly studied within our framework. By considering a generic superposition of states with different Wilson line configurations, through an interference effect, we can detect, by the entanglement entropy, the topological data of Chern-Simons theories, e.g., the R symbols, monodromy, and topological spins of quasiparticles. Furthermore, by using our method, we calculate other entanglement/correlation measures such as the mutual information and the entanglement negativity. In particular, it is found that the entanglement negativity of two adjacent noncontractible regions on a torus provides a simple way to distinguish Abelian and non-Abelian topological orders.
Jaeken, Laurent; Vasilievich Matveev, Vladimir
2012-01-01
Observations of coherent cellular behavior cannot be integrated into widely accepted membrane (pump) theory (MT) and its steady state energetics because of the thermal noise of assumed ordinary cell water and freely soluble cytoplasmic K+. However, Ling disproved MT and proposed an alternative based on coherence, showing that rest (R) and action (A) are two different phases of protoplasm with different energy levels. The R-state is a coherent metastable low-entropy state as water and K+ are bound to unfolded proteins. The A-state is the higher-entropy state because water and K+ are free. The R-to-A phase transition is regarded as a mechanism to release energy for biological work, replacing the classical concept of high-energy bonds. Subsequent inactivation during the endergonic A-to-R phase transition needs an input of metabolic energy to restore the low entropy R-state. Matveev’s native aggregation hypothesis allows to integrate the energetic details of globular proteins into this view. PMID:23264833
Lubkin, E.
1987-05-01
It is only by neglecting self-adsorption (a treatment referred to as pure-energy, PE) that one gets textbook thermodynamics of a surface, based upon the tension L as a function of temperature T, and one finds negative specific heat for hot water. Any lower critical point and PE provides the other exciting negatives: nicotine-and-water is an example. In order to include adsorption, T must be known in terms of T and chemical potentials as independent variables; this forces measurement of the tension of curved menisci. Will the minus signs remain.
Sharma, Animesh N; Aoun, Paul; Wigham, Jean R; Weist, Suanne M; Veldhuis, Johannes D
2014-05-01
How sex steroids modulate glucocorticoid feedback on the hypothalamic-pituitary-corticotrope (HPC) unit is controversial in humans. We postulated that testosterone (T) in men and estradiol (E2) in women govern unstressed cortisol-mediated negative feedback on ACTH secretion. To test this hypothesis, 24 men and 24 women age 58 ± 2.4 yr were pretreated with leuprolide and either sex steroid (E2 in women, T in men) or placebo addback. Placebo or ketoconazole (KTCZ) was administered overnight to inhibit adrenal steroidogenesis during overnight 14-h intravenous infusions of saline or cortisol in a continuous versus pulsatile manner to test for feedback differences. ACTH was measured every 10 min during the last 8 h of the infusions. The main outcome measures were mean ACTH concentrations, pulsatile ACTH secretion, and ACTH approximate entropy (ApEn). ACTH concentrations were lower in women than men (P < 0.01), and in women in the E2+ compared with E2- group under both continuous (P = 0.01) and pulsatile (P = 0.006) cortisol feedback, despite higher cortisol binding globulin and lower free cortisol levels in women than men (P < 0.01). In the combined groups, under both modes of cortisol addback, ACTH concentrations, pulsatile ACTH secretion, and ACTH secretory-burst mass correlated negatively and univariately with E2 levels (each P < 0.005). E2 also suppressed ACTH ApEn (process randomness) during continuous cortisol feedback (P = 0.004). T had no univariate effect but was a positive correlate of ACTH when assessed jointly with E2 (negative) under cortisol pulses. In conclusion, sex steroids modulate selective gender-related hypothalamic-pituitary adrenal-axis adaptations to cortisol feedback in unstressed humans. PMID:24573184
Park, Sang-Min; Shin, Sung-Young; Cho, Kwang-Hyun
2016-01-01
Revealing the hidden mechanism of how cells sense and react to environmental signals has been a central question in cell biology. We focused on the rate of increase of stimulation, or temporal gradient, known to cause different responses of cells. We have investigated all possible three-node enzymatic networks and identified a network motif that robustly generates a transient or sustained response by acute or gradual stimulation, respectively. We also found that a regulated double-negative feedback within the motif is essential for the temporal gradient-sensitive switching. Our analysis highlights the essential structure and mechanism enabling cells to properly respond to dynamic environmental changes. PMID:27584002
Minimum output entropy of bosonic channels: A conjecture
Giovannetti, Vittorio; Guha, Saikat; Maccone, Lorenzo; Shapiro, Jeffrey H.; Lloyd, Seth
2004-09-01
The von Neumann entropy at the output of a bosonic channel with thermal noise is analyzed. Coherent-state inputs are conjectured to minimize this output entropy. Physical and mathematical evidence in support of the conjecture is provided. A stronger conjecture - that output states resulting from coherent-state inputs majorize the output states from other inputs - is also discussed.
Chechenova, Maria B.; Maes, Sara; Cripps, Richard M.
2015-01-01
Most animals express multiple isoforms of structural muscle proteins to produce tissues with different physiological properties. In Drosophila, the adult muscles include tubular-type muscles and the fibrillar indirect flight muscles. Regulatory processes specifying tubular muscle fate remain incompletely understood, therefore we chose to analyze the transcriptional regulation of TpnC41C, a Troponin C gene expressed in the tubular jump muscles, but not in the fibrillar flight muscles. We identified a 300-bp promoter fragment of TpnC41C sufficient for the fiber-specific reporter expression. Through an analysis of this regulatory element, we identified two sites necessary for the activation of the enhancer. Mutations in each of these sites resulted in 70% reduction of enhancer activity. One site was characterized as a binding site for Myocyte Enhancer Factor-2. In addition, we identified a repressive element that prevents activation of the enhancer in other muscle fiber types. Mutation of this site increased jump muscle-specific expression of the reporter, but more importantly reporter expression expanded into the indirect flight muscles. Our findings demonstrate that expression of the TpnC41C gene in jump muscles requires integration of multiple positive and negative transcriptional inputs. Identification of the transcriptional regulators binding the cis-elements that we identified will reveal the regulatory pathways controlling muscle fiber differentiation. PMID:26641463
The entropy in supernova explosions
Colgate, S.A.
1990-12-06
The explosion of a supernova forms because of the collapse to a neutron star. In addition an explosion requires that a region of relatively high entropy be in contact with the neutron star and persisting for a relatively protracted period of time. The high entropy region ensures that the maximum temperature in contact with the neutron star and in hydrostatic equilibrium is less than some maximum. This temperature must be low enough such that neutrino emission cooling is small, otherwise the equilibrium atmosphere will collapse adding a large accretion mass to the neutron star. A so-called normal explosion shock that must reverse the accretion flow corresponding to a typical stellar collapse must have sufficient strength or pressure to reverse this flow and eject the matter with 10{sup 51} ergs for a typical type II supernova. Surprisingly the matter behind such a shock wave has a relatively low entropy low enough such that neutrino cooling would be orders of magnitude faster than the expansion rate. The resulting accretion low would be inside the Bondi radius and result in free-fall accretion inside the expanding rarefaction wave. The accreted mass or reimplosion mass unless stopped by a high entropy bubble could than exceed that of bound neutron star models. In addition the explosion shock would be overtaken by the rarefaction wave and either disappear or at least weaken. Hence, a hot, high entropy bubble is required to support an equilibrium atmosphere in contact with a relatively cold neutron star. Subsequently during the expansion of the high entropy bubble that drives or pushes on the shocked matter, mixing of the matter of the high entropy bubble and lower entropy shock-ejected matter is ensured. The mixing is driven by the negative entropy gradient between the high entropy bubble accelerating the shocked matter and the lower entropy of the matter behind the shock.
Entropy, materials, and posterity
Cloud, P.
1977-01-01
Materials and energy are the interdependent feedstocks of economic systems, and thermodynamics is their moderator. It costs energy to transform the dispersed minerals of Earth's crust into ordered materials and structures. And it costs materials to collect and focus the energy to perform work - be it from solar, fossil fuel, nuclear, or other sources. The greater the dispersal of minerals sought, the more energy is required to collect them into ordered states. But available energy can be used once only. And the ordered materials of industrial economies become disordered with time. They may be partially reordered and recycled, but only at further costs in energy. Available energy everywhere degrades to bound states and order to disorder - for though entropy may be juggled it always increases. Yet industry is utterly dependent on low entropy states of matter and energy, while decreasing grades of ore require ever higher inputs of energy to convert them to metals, with ever increasing growth both of entropy and environmental hazard. Except as we may prize a thing for its intrinsic qualities - beauty, leisure, love, or gold - low-entropy is the only thing of real value. It is worth whatever the market will bear, and it becomes more valuable as entropy increases. It would be foolish of suppliers to sell it more cheaply or in larger amounts than their own enjoyment of life requires, whatever form it may take. For this reason, and because of physical constraints on the availability of all low-entropy states, the recent energy crises is only the first of a sequence of crises to be expected in energy and materials as long as current trends continue. The apportioning of low-entropy states in a modern industrial society is achieved more or less according to the theory of competitive markets. But the rational powers of this theory suffer as the world grows increasingly polarized into rich, over-industrialized nations with diminishing resource bases and poor, supplier nations
Saturating the holographic entropy bound
Bousso, Raphael; Freivogel, Ben; Leichenauer, Stefan
2010-10-15
The covariant entropy bound states that the entropy, S, of matter on a light sheet cannot exceed a quarter of its initial area, A, in Planck units. The gravitational entropy of black holes saturates this inequality. The entropy of matter systems, however, falls short of saturating the bound in known examples. This puzzling gap has led to speculation that a much stronger bound, S < or approx. A{sup 3/4}, may hold true. In this note, we exhibit light sheets whose entropy exceeds A{sup 3/4} by arbitrarily large factors. In open Friedmann-Robertson-Walker universes, such light sheets contain the entropy visible in the sky; in the limit of early curvature domination, the covariant bound can be saturated but not violated. As a corollary, we find that the maximum observable matter and radiation entropy in universes with positive (negative) cosmological constant is of order {Lambda}{sup -1} ({Lambda}{sup -2}), and not |{Lambda}|{sup -3/4} as had hitherto been believed. Our results strengthen the evidence for the covariant entropy bound, while showing that the stronger bound S < or approx. A{sup 3/4} is not universally valid. We conjecture that the stronger bound does hold for static, weakly gravitating systems.
Upper entropy axioms and lower entropy axioms
NASA Astrophysics Data System (ADS)
Guo, Jin-Li; Suo, Qi
2015-04-01
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, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics.
Upper entropy axioms and lower entropy axioms
Guo, Jin-Li 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, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics.
Thermodynamic law from the entanglement entropy bound
NASA Astrophysics Data System (ADS)
Park, Chanyong
2016-04-01
From black hole thermodynamics, the Bekenstein bound has been proposed as a universal thermal entropy bound. It has been further generalized to an entanglement entropy bound which is valid even in a quantum system. In a quantumly entangled system, the non-negativity of the relative entropy leads to the entanglement entropy bound. When the entanglement entropy bound is saturated, a quantum system satisfies the thermodynamicslike law with an appropriately defined entanglement temperature. We show that the saturation of the entanglement entropy bound accounts for a universal feature of the entanglement temperature proportional to the inverse of the system size. In addition, we show that the deformed modular Hamiltonian under a global quench also satisfies the generalized entanglement entropy boundary after introducing a new quantity called the entanglement chemical potential.
In defense of negative temperature
NASA Astrophysics Data System (ADS)
Poulter, J.
2016-03-01
This pedagogical comment highlights three misconceptions concerning the usefulness of the concept of negative temperature, being derived from the usual, often termed Boltzmann, definition of entropy. First, both the Boltzmann and Gibbs entropies must obey the same thermodynamic consistency relation. Second, the Boltzmann entropy does obey the second law of thermodynamics. Third, there exists an integrating factor of the heat differential with both definitions of entropy.
Descending entropy in expanding the universe
NASA Astrophysics Data System (ADS)
Portnov, Yuriy A.
2015-11-01
Inter-relation between 1-form of nonmetricity and change of entropy in the course of time is considered in the study. It is shown that change of entropy in expanding universe will be always negative. The obtained result contravenes the second law of thermodynamics, however it explains available ordered macrostructures in the universe.
The Maximum Entropy Principle for Generalized Entropies
NASA Astrophysics Data System (ADS)
Tsukada, Makoto
2008-03-01
It is well known that Gibbs states and the Gaussian distribution are characterized by the maximum entropy principle. In this paper we discuss probability distributions which maximize generalized entropies including Rényi's and Tsal-lis's.
Entropy power inequalities for qudits
NASA Astrophysics Data System (ADS)
Audenaert, Koenraad; Datta, Nilanjana; Ozols, Maris
2016-05-01
Shannon's entropy power inequality (EPI) can be viewed as a statement of concavity of an entropic function of a continuous random variable under a scaled addition rule: f ( √{ a } X + √{ 1 - a } Y ) ≥ a f ( X ) + ( 1 - a ) f ( Y ) ∀ a ∈ [ 0 , 1 ] . Here, X and Y are continuous random variables and the function f is either the differential entropy or the entropy power. König and Smith [IEEE Trans. Inf. Theory 60(3), 1536-1548 (2014)] and De Palma, Mari, and Giovannetti [Nat. Photonics 8(12), 958-964 (2014)] obtained quantum analogues of these inequalities for continuous-variable quantum systems, where X and Y are replaced by bosonic fields and the addition rule is the action of a beam splitter with transmissivity a on those fields. In this paper, we similarly establish a class of EPI analogues for d-level quantum systems (i.e., qudits). The underlying addition rule for which these inequalities hold is given by a quantum channel that depends on the parameter a ∈ [0, 1] and acts like a finite-dimensional analogue of a beam splitter with transmissivity a, converting a two-qudit product state into a single qudit state. We refer to this channel as a partial swap channel because of the particular way its output interpolates between the states of the two qudits in the input as a is changed from zero to one. We obtain analogues of Shannon's EPI, not only for the von Neumann entropy and the entropy power for the output of such channels, but also for a much larger class of functions. This class includes the Rényi entropies and the subentropy. We also prove a qudit analogue of the entropy photon number inequality (EPnI). Finally, for the subclass of partial swap channels for which one of the qudit states in the input is fixed, our EPIs and EPnI yield lower bounds on the minimum output entropy and upper bounds on the Holevo capacity.
NASA Astrophysics Data System (ADS)
de Souza, R. A.; de Avellar, M. G. B.; Horvath, J. E.
2015-11-01
An appraisal of the behavior of stellar entropy along stellar evolution is made. It is shown that the entropy per baryon of a star of a fixed baryon number decreases monotonically with increasing compactness of the star. The same entropy per baryon increases only whenever an irreversible collapse of the star happens. The recent proposals for a gravitational entropy related to curvature may justify the huge increase of the entropy in the ultimate collapse to a black hole.
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.
Generalized entropy production phenomena: a master-equation approach.
Casas, G A; Nobre, F D; Curado, E M F
2014-01-01
The time rate of generalized entropic forms, defined in terms of discrete probabilities following a master equation, is investigated. Both contributions, namely entropy production and flux, are obtained, extending works carried previously for the Boltzmann-Gibbs entropy to a wide class of entropic forms. Particularly, it is shown that the entropy-production contribution is always non-negative for such entropies. Some illustrative examples for known generalized entropic forms in the literature are also worked out. Since generalized entropies have been lately associated with several complex systems in nature, the present analysis should be applicable to irreversible processes in these systems. PMID:24580179
Structural complexity and configurational entropy of crystals.
Krivovichev, Sergey V
2016-04-01
Using a statistical approach, it is demonstrated that the complexity of a crystal structure measured as the Shannon information per atom [Krivovichev (2012). Acta Cryst. A68, 393-398] represents a negative contribution to the configurational entropy of a crystalline solid. This conclusion is in full accordance with the general agreement that information and entropy are reciprocal variables. It also agrees well with the understanding that complex structures possess lower entropies relative to their simpler counterparts. The obtained equation is consistent with the Landauer principle and points out that the information encoded in a crystal structure has a physical nature. PMID:27048729
Generalized entanglement entropy
NASA Astrophysics Data System (ADS)
Taylor, Marika
2016-07-01
We discuss two measures of entanglement in quantum field theory and their holographic realizations. For field theories admitting a global symmetry, we introduce a global symmetry entanglement entropy, associated with the partitioning of the symmetry group. This quantity is proposed to be related to the generalized holographic entanglement entropy defined via the partitioning of the internal space of the bulk geometry. Thesecond measure of quantum field theory entanglement is the field space entanglement entropy, obtained by integrating out a subset of the quantum fields. We argue that field space entanglement entropy cannot be precisely realised geometrically in a holographic dual. However, for holographic geometries with interior decoupling regions, the differential entropy provides a close analogue to the field space entanglement entropy. We derive generic descriptions of such inner throat regions in terms of gravity coupled to massive scalars and show how the differential entropy in the throat captures features of the field space entanglement entropy.
Entropy descriptors and Entropy Stabilized Oxides
NASA Astrophysics Data System (ADS)
Curtarolo, Stefano
In this presentation we will discuss the development of entropy descriptors for the AFLOWLIB.org ab-initio repository and the path leading to the synthesis of the novel entropy stabilized oxides. [Nat. Comm. 6:8485 (2015)]. Research sponsored by DOD-ONR N000141310635 and N000141512863.
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)
RNA Thermodynamic Structural Entropy
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
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.
On variational definition of quantum entropy
Belavkin, Roman V.
2015-01-13
Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ-measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure ν from the probability measure P; 3) as the supremum of Shannon’s mutual information taken over all channels such that P is the output probability, in which case it is dual of some transportation problem. In classical (i.e. commutative) probability, all three definitions lead to the same quantity, providing only different interpretations of entropy. In non-commutative (i.e. quantum) probability, however, these definitions are not equivalent. In particular, the third definition, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy. It was proposed originally by V. Belavkin and Ohya [1] and called the proper quantum entropy, because it allows one to define quantum conditional entropy that is always non-negative. Here we extend these ideas to define also quantum counterpart of proper cross-entropy and cross-information. We also show inequality for the values of classical and quantum information.
Applications of quantum entropy to statistics
Silver, R.N.; Martz, H.F.
1994-07-01
This paper develops two generalizations of the maximum entropy (ME) principle. First, Shannon classical entropy is replaced by von Neumann quantum entropy to yield a broader class of information divergences (or penalty functions) for statistics applications. Negative relative quantum entropy enforces convexity, positivity, non-local extensivity and prior correlations such as smoothness. This enables the extension of ME methods from their traditional domain of ill-posed in-verse problems to new applications such as non-parametric density estimation. Second, given a choice of information divergence, a combination of ME and Bayes rule is used to assign both prior and posterior probabilities. Hyperparameters are interpreted as Lagrange multipliers enforcing constraints. Conservation principles are proposed to act statistical regularization and other hyperparameters, such as conservation of information and smoothness. ME provides an alternative to heirarchical Bayes methods.
Relative entropy equals bulk relative entropy
NASA Astrophysics Data System (ADS)
Jafferis, Daniel L.; Lewkowycz, Aitor; Maldacena, Juan; Suh, S. Josephine
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.
Configurational Entropy Revisited
NASA Astrophysics Data System (ADS)
Lambert, Frank L.
2007-09-01
Entropy change is categorized in some prominent general chemistry textbooks as being either positional (configurational) or thermal. In those texts, the accompanying emphasis on the dispersal of matter—independent of energy considerations and thus in discord with kinetic molecular theory—is most troubling. This article shows that the variants of entropy can be treated from a unified viewpoint and argues that to decrease students' confusion about the nature of entropy change these variants of entropy should be merged. Molecular energy dispersal in space is implicit but unfortunately tacit in the cell models of statistical mechanics that develop the configurational entropy change in gas expansion, fluids mixing, or the addition of a non-volatile solute to a solvent. Two factors are necessary for entropy change in chemistry. An increase in thermodynamic entropy is enabled in a process by the motional energy of molecules (that, in chemical reactions, can arise from the energy released from a bond energy change). However, entropy increase is only actualized if the process results in a larger number of arrangements for the system's energy, that is, a final state that involves the most probable distribution for that energy under the new constraints. Positional entropy should be eliminated from general chemistry instruction and, especially benefiting "concrete minded" students, it should be replaced by emphasis on the motional energy of molecules as enabling entropy change.
Maximum entropy and drug absorption.
Charter, M K; Gull, S F
1991-10-01
The application of maximum entropy to the calculation of drug absorption rates was introduced in an earlier paper. Here it is developed further, and the whole procedure is presented as a problem in scientific inference to be solved using Bayes' theorem. Blood samples do not need to be taken at equally spaced intervals, and no smoothing, interpolation, extrapolation, or other preprocessing of the data is necessary. The resulting input rate estimates are smooth and physiologically realistic, even with noisy data, and their accuracy is quantified. Derived quantities such as the proportion of the dose absorbed, and the mean and median absorption times, are also obtained, together with their error estimates. There are no arbitrarily valued parameters in the analysis, and no specific functional form, such as an exponential or polynomial, is assumed for the input rate functions. PMID:1783989
Theory of entropy production in quantum many-body systems
NASA Astrophysics Data System (ADS)
Solano-Carrillo, E.; Millis, A. J.
2016-06-01
We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second, and third laws of thermodynamics. For weakly coupled subsystems of an isolated system, an expression for the long-time limit of the expectation value of the rate of change of the thermodynamically measurable part of the entropy operator is derived and interpreted in terms of entropy production and entropy transport terms. The interpretation is justified by comparison to the known expression for the entropy production in an aged classical Markovian system with Gaussian fluctuations and by a calculation of the current-induced entropy production in a conductor with electron-phonon scattering.
NASA Astrophysics Data System (ADS)
Santos, A. P.; Silva, R.; Alcaniz, J. S.; Anselmo, D. H. A. L.
2011-08-01
A deduction of generalized quantum entropies within the Tsallis and Kaniadakis frameworks is derived using a generalization of the ordinary multinomial coefficient. This generalization is based on the respective deformed multiplication and division. We show that the two above entropies are consistent with ones arbitrarily assumed at other contexts.
Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael
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
ERIC Educational Resources Information Center
Marder, Daniel
The Second Law of Thermodynamics demonstrates the idea of entropy, the tendency of ordered energy to free itself and thus break apart the system that contains it and dissipate that system into chaos. When applied to communications theory, entropy increases not only with noise but with the density of information--particles of possible meaning…
Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael
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 phase 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.
NASA Astrophysics Data System (ADS)
Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael
2015-09-01
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 phase 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.
Charged topological entanglement entropy
NASA Astrophysics Data System (ADS)
Matsuura, Shunji; Wen, Xueda; Hung, Ling-Yan; Ryu, Shinsei
2016-05-01
A charged entanglement entropy is a new measure which probes quantum entanglement between different charge sectors. We study symmetry-protected topological (SPT) phases in (2+1)-dimensional space-time by using this charged entanglement entropy. SPT phases are short-range entangled states without topological order and hence cannot be detected by the topological entanglement entropy. We demonstrate that the universal part of the charged entanglement entropy is nonzero for nontrivial SPT phases and therefore it is a useful measure to detect short-range entangled topological phases. We also discuss that the classification of SPT phases based on the charged topological entanglement entropy is related to that of the braiding statistics of quasiparticles.
Continuity of the entropy of macroscopic quantum systems.
Swendsen, Robert H
2015-11-01
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper, I analyze and calculate the thermodynamic entropy for large but finite quantum mechanical systems. A special feature of this analysis is that the thermodynamic energy of a quantum system is shown to be a continuous variable, rather than being associated with discrete energy eigenvalues. Calculations of the entropy as a function of energy can be carried out with a Legendre transform of thermodynamic potentials obtained from a canonical ensemble. The resultant expressions for the entropy are able to describe equilibrium between quantum systems having incommensurate energy-level spacings. This definition of entropy preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics. It demonstrates the consistency of the concept of negative temperature with the principles of thermodynamics. PMID:26651650
Repositioning Recitation Input in College English Teaching
ERIC Educational Resources Information Center
Xu, Qing
2009-01-01
This paper tries to discuss how recitation input helps overcome the negative influences on the basis of second language acquisition theory and confirms the important role that recitation input plays in improving college students' oral and written English.
NASA Astrophysics Data System (ADS)
Jia, Husen; Liggins, John R.; Chow, Wah Soon
2014-02-01
According to the Second Law of Thermodynamics, an overall increase of entropy contributes to the driving force for any physicochemical process, but entropy has seldom been investigated in biological systems. Here, for the first time, we apply Isothermal Titration Calorimetry (ITC) to investigate the Mg2+-induced spontaneous stacking of photosynthetic membranes isolated from spinach leaves. After subtracting a large endothermic interaction of MgCl2 with membranes, unrelated to stacking, we demonstrate that the enthalpy change (heat change at constant pressure) is zero or marginally positive or negative. This first direct experimental evidence strongly suggests that an entropy increase significantly drives membrane stacking in this ordered biological structure. Possible mechanisms for the entropy increase include: (i) the attraction between discrete oppositely-charged areas, releasing counterions; (ii) the release of loosely-bound water molecules from the inter-membrane gap; (iii) the increased orientational freedom of previously-aligned water dipoles; and (iv) the lateral rearrangement of membrane components.
The vibrational and configurational entropy of α-brass☆
Benisek, Artur; Dachs, Edgar; Salihović, Miralem; Paunovic, Aleksandar; Maier, Maria E.
2014-01-01
The heat capacities of two samples of a fcc Cu–Zn alloy with the composition CuZn15 and CuZn34 were measured from T = 5 K to 573 K using relaxation and differential scanning calorimetry. Below ∼90 K, they are characterised by negative excess heat capacities deviating from ideal mixing by up to −0.20 and −0.44 J · mol−1 · K−1 for CuZn15 and CuZn34, respectively. The excess heat capacities produce excess vibrational entropies, which are less negative compared to the excess entropy available from the literature. Since the literature entropy data contain both, the configurational and the vibrational part of the entropy, the difference is attributed to the excess configurational entropy. The thermodynamics of different short-range ordered samples was also investigated. The extent of the short-range order had no influence on the heat capacity below T = 300 K. Above T = 300 K, where the ordering changed during the measurement, the heat capacity depended strongly on the thermal history of the samples. From these data, the heat and entropy of ordering was calculated. The results on the vibrational entropy of this study were also used to test a relationship for estimating the excess vibrational entropy of mixing. PMID:24926103
Conditional entropy of ordinal patterns
NASA Astrophysics Data System (ADS)
Unakafov, Anton M.; Keller, Karsten
2014-02-01
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given ordinal pattern. We observe that this quantity provides a good estimation of the Kolmogorov-Sinai entropy in many cases. In particular, the conditional entropy of ordinal patterns of a finite order coincides with the Kolmogorov-Sinai entropy for periodic dynamics and for Markov shifts over a binary alphabet. Finally, the conditional entropy of ordinal patterns is computationally simple and thus can be well applied to real-world data.
ERIC Educational Resources Information Center
Kyle, Benjamin G.
1988-01-01
Illustrates qualitative and metaphoric applications of entropy in the areas of cosmology, the birth and death of the universe and time; life and evolution; literature and art; and social science. (RT)
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1997-01-01
The entropy associated with absolute equilibrium ensemble theories of ideal, homogeneous, fluid and magneto-fluid turbulence is discussed and the three-dimensional fluid case is examined in detail. A sigma-function is defined, whose minimum value with respect to global parameters is the entropy. A comparison is made between the use of global functions sigma and phase functions H (associated with the development of various H-theorems of ideal turbulence). It is shown that the two approaches are complimentary though conceptually different: H-theorems show that an isolated system tends to equilibrium while sigma-functions allow the demonstration that entropy never decreases when two previously isolated systems are combined. This provides a more complete picture of entropy in the statistical mechanics of ideal fluids.
Local entropy generation analysis
Drost, M.K.; White, M.D.
1991-02-01
Second law analysis techniques have been widely used to evaluate the sources of irreversibility in components and systems of components but the evaluation of local sources of irreversibility in thermal processes has received little attention. While analytical procedures for evaluating local entropy generation have been developed, applications have been limited to fluid flows with analytical solutions for the velocity and temperature fields. The analysis of local entropy generation can be used to evaluate more complicated flows by including entropy generation calculations in a computational fluid dynamics (CFD) code. The research documented in this report consists of incorporating local entropy generation calculations in an existing CFD code and then using the code to evaluate the distribution of thermodynamic losses in two applications: an impinging jet and a magnetic heat pump. 22 refs., 13 figs., 9 tabs.
Staniek, Matthäus; Lehnertz, Klaus
2008-04-18
We propose to estimate transfer entropy using a technique of symbolization. We demonstrate numerically that symbolic transfer entropy is a robust and computationally fast method to quantify the dominating direction of information flow between time series from structurally identical and nonidentical coupled systems. Analyzing multiday, multichannel electroencephalographic recordings from 15 epilepsy patients our approach allowed us to reliably identify the hemisphere containing the epileptic focus without observing actual seizure activity. PMID:18518155
NASA Astrophysics Data System (ADS)
Staniek, Matthäus; Lehnertz, Klaus
2008-04-01
We propose to estimate transfer entropy using a technique of symbolization. We demonstrate numerically that symbolic transfer entropy is a robust and computationally fast method to quantify the dominating direction of information flow between time series from structurally identical and nonidentical coupled systems. Analyzing multiday, multichannel electroencephalographic recordings from 15 epilepsy patients our approach allowed us to reliably identify the hemisphere containing the epileptic focus without observing actual seizure activity.
Dorogovtsev, Andrei A
2010-06-29
For sets in a Hilbert space the concept of quadratic entropy is introduced. It is shown that this entropy is finite for the range of a stochastic flow of Brownian particles on R. This implies, in particular, the fact that the total time of the free travel in the Arratia flow of all particles that started from a bounded interval is finite. Bibliography: 10 titles.
NASA Astrophysics Data System (ADS)
Bousso, Raphael
2016-07-01
We show that known entropy bounds constrain the information carried off by radiation to null infinity. We consider distant, planar null hypersurfaces in asymptotically flat spacetime. Their focusing and area loss can be computed perturbatively on a Minkowski background, yielding entropy bounds in terms of the energy flux of the outgoing radiation. In the asymptotic limit, we obtain boundary versions of the quantum null energy condition, of the generalized Second Law, and of the quantum Bousso bound.
Anomalies and entanglement entropy
NASA Astrophysics Data System (ADS)
Nishioka, Tatsuma; Yarom, Amos
2016-03-01
We initiate a systematic study of entanglement and Rényi entropies in the presence of gauge and gravitational anomalies in even-dimensional quantum field theories. We argue that the mixed and gravitational anomalies are sensitive to boosts and obtain a closed form expression for their behavior under such transformations. Explicit constructions exhibiting the dependence of entanglement entropy on boosts is provided for theories on spacetimes with non-trivial magnetic fluxes and (or) non-vanishing Pontryagin classes.
Connectivity in the human brain dissociates entropy and complexity of auditory inputs☆
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
Entropy, matter, and cosmology.
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. PMID:16593747
Lemos, Jose P. S.; Zaslavskii, Oleg B.
2010-03-15
We trace the origin of the black hole entropy S, replacing a black hole by a quasiblack hole. Let the boundary of a static body approach its own gravitational radius, in such a way that a quasihorizon forms. We show that if the body is thermal with the temperature taking the Hawking value at the quasihorizon limit, it follows, in the nonextremal case, from the first law of thermodynamics that the entropy approaches the Bekenstein-Hawking value S=A/4. In this setup, the key role is played by the surface stresses on the quasihorizon and one finds that the entropy comes from the quasihorizon surface. Any distribution of matter inside the surface leads to the same universal value for the entropy in the quasihorizon limit. This can be of some help in the understanding of black hole entropy. Other similarities between black holes and quasiblack holes such as the mass formulas for both objects had been found previously. We also discuss the entropy for extremal quasiblack holes, a more subtle issue.
Entropy, matter, and cosmology
Prigogine, I.; Géhéniau, J.
1986-01-01
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. PMID:16593747
The continuity of the output entropy of positive maps
Shirokov, Maxim E
2011-10-31
Global and local continuity conditions for the output von Neumann entropy for positive maps between Banach spaces of trace-class operators in separable Hilbert spaces are obtained. Special attention is paid to completely positive maps: infinite dimensional quantum channels and operations. It is shown that as a result of some specific properties of the von Neumann entropy (as a function on the set of density operators) several results on the output entropy of positive maps can be obtained, which cannot be derived from the general properties of entropy type functions. In particular, it is proved that global continuity of the output entropy of a positive map follows from its finiteness. A characterization of positive linear maps preserving continuity of the entropy (in the following sense: continuity of the entropy on an arbitrary subset of input operators implies continuity of the output entropy on this subset) is obtained. A connection between the local continuity properties of two completely positive complementary maps is considered. Bibliography: 21 titles.
Entanglement entropy and variational methods: Interacting scalar fields
NASA Astrophysics Data System (ADS)
Cotler, Jordan S.; Mueller, Mark T.
2016-02-01
We develop a variational approximation to the entanglement entropy for scalar ϕ4 theory in 1 + 1, 2 + 1, and 3 + 1 dimensions, and then examine the entanglement entropy as a function of the coupling. We find that in 1 + 1 and 2 + 1 dimensions, the entanglement entropy of ϕ4 theory as a function of coupling is monotonically decreasing and convex. While ϕ4 theory with positive bare coupling in 3 + 1 dimensions is thought to lead to a trivial free theory, we analyze a version of ϕ4 with infinitesimal negative bare coupling, an asymptotically free theory known as precariousϕ4 theory, and explore the monotonicity and convexity of its entanglement entropy as a function of coupling. Within the variational approximation, the stability of precarious ϕ4 theory is related to the sign of the first and second derivatives of the entanglement entropy with respect to the coupling.
NASA Astrophysics Data System (ADS)
Dupuis, Frédéric; Wilde, Mark M.
2016-03-01
This paper introduces "swiveled Rényi entropies" as an alternative to the Rényi entropic quantities put forward in Berta et al. (Phys Rev A 91(2):022333, 2015). What distinguishes the swiveled Rényi entropies from the prior proposal of Berta et al. is that there is an extra degree of freedom: an optimization over unitary rotations with respect to particular fixed bases (swivels). A consequence of this extra degree of freedom is that the swiveled Rényi entropies are ordered, which is an important property of the Rényi family of entropies. The swiveled Rényi entropies are, however, generally discontinuous at α =1 and do not converge to the von Neumann entropy-based measures in the limit as α rightarrow 1, instead bounding them from above and below. Particular variants reduce to known Rényi entropies, such as the Rényi relative entropy or the sandwiched Rényi relative entropy, but also lead to ordered Rényi conditional mutual information and ordered Rényi generalizations of a relative entropy difference. Refinements of entropy inequalities such as monotonicity of quantum relative entropy and strong subadditivity follow as a consequence of the aforementioned properties of the swiveled Rényi entropies. Due to the lack of convergence at α =1, it is unclear whether the swiveled Rényi entropies would be useful in one-shot information theory, so that the present contribution represents partial progress toward this goal.
Entanglement entropy on fractals
NASA Astrophysics Data System (ADS)
Faraji Astaneh, Amin
2016-03-01
We use the heat kernel method to calculate the entanglement entropy for a given entangling region on a fractal. The leading divergent term of the entropy is obtained as a function of the fractal dimension as well as the walk dimension. The power of the UV cutoff parameter is (generally) a fractional number, which, indeed, is a certain combination of these two indices. This exponent is known as the spectral dimension. We show that there is a novel log-periodic oscillatory behavior in the expression of entropy which has root in the complex dimension of the fractal. We finally indicate that the holographic calculation in a certain hyperscaling-violating bulk geometry yields the same leading term for the entanglement entropy, if one identifies the effective dimension of the hyperscaling-violating theory with the spectral dimension of the fractal. We provide additional support by comparing the behavior of the thermal entropy in terms of the temperature, computed for two geometries, the fractal geometry and the hyperscaling-violating background.
NASA Astrophysics Data System (ADS)
Farokhi, Saeed; Taghavi, Ray; Keshmiri, Shawn
2015-11-01
Stealth technology is developed for military aircraft to minimize their signatures. The primary attention was focused on radar signature, followed by the thermal and noise signatures of the vehicle. For radar evasion, advanced configuration designs, extensive use of carbon composites and radar-absorbing material, are developed. On thermal signature, mainly in the infra-red (IR) bandwidth, the solution was found in blended rectangular nozzles of high aspect ratio that are shielded from ground detectors. For noise, quiet and calm jets are integrated into vehicles with low-turbulence configuration design. However, these technologies are totally incapable of detecting new generation of revolutionary aircraft. These shall use all electric, distributed, propulsion system that are thermally transparent. In addition, composite skin and non-emitting sensors onboard the aircraft will lead to low signature. However, based on the second-law of thermodynamics, there is no air vehicle that can escape from leaving an entropy trail. Entropy is thus the only inevitable signature of any system, that once measured, can detect the source. By characterizing the entropy field based on its statistical properties, the source may be recognized, akin to face recognition technology. Direct measurement of entropy is cumbersome, however as a derived property, it can be easily measured. The measurement accuracy depends on the probe design and the sensors onboard. One novel air data sensor suite is introduced with promising potential to capture the entropy trail.
Causality & holographic entanglement entropy
NASA Astrophysics Data System (ADS)
Headrick, Matthew; Hubeny, Veronika E.; Lawrence, Albion; Rangamani, Mukund
2014-12-01
We identify conditions for the entanglement entropy as a function of spatial region to be compatible with causality in an arbitrary relativistic quantum field theory. We then prove that the covariant holographic entanglement entropy prescription (which relates entanglement entropy of a given spatial region on the boundary to the area of a certain extremal surface in the bulk) obeys these conditions, as long as the bulk obeys the null energy condition. While necessary for the validity of the prescription, this consistency requirement is quite nontrivial from the bulk standpoint, and therefore provides important additional evidence for the prescription. In the process, we introduce a codimension-zero bulk region, named the entanglement wedge, naturally associated with the given boundary spatial region. We propose that the entanglement wedge is the most natural bulk region corresponding to the boundary reduced density matrix.
Holographic entropy production
NASA Astrophysics Data System (ADS)
Tian, Yu; Wu, Xiao-Ning; Zhang, Hongbao
2014-10-01
The suspicion that gravity is holographic has been supported mainly by a variety of specific examples from string theory. In this paper, we propose that such a holography can actually be observed in the context of Einstein's gravity and at least a class of generalized gravitational theories, based on a definite holographic principle where neither is the bulk space-time required to be asymptotically AdS nor the boundary to be located at conformal infinity, echoing Wilson's formulation of quantum field theory. After showing the general equilibrium thermodynamics from the corresponding holographic dictionary, in particular, we provide a rather general proof of the equality between the entropy production on the boundary and the increase of black hole entropy in the bulk, which can be regarded as strong support to this holographic principle. The entropy production in the familiar holographic superconductors/superfluids is investigated as an important example, where the role played by the holographic renormalization is explained.
Casimir entropy for magnetodielectrics
NASA Astrophysics Data System (ADS)
Klimchitskaya, G. L.; Korikov, C. C.
2015-06-01
We find the analytic expressions for the Casimir free energy, entropy and pressure at low temperature in the configuration of two parallel plates made of magnetodielectic material. The cases of constant and frequency-dependent dielectic permittivity and magnetic permeability of the plates are considered. Special attention is paid to the account of dc conductivity. It is shown that in the case of finite static dielectric permittivity and magnetic permeability the Nernst heat theorem for the Casimir entropy is satisfied. If the dc conductivity is taken into account, the Casimir entropy goes to a positive nonzero limit depending on the parameters of a system when the temperature vanishes, i.e. the Nernst theorem is violated. The experimental situation is also discussed.
Generalized gravitational entropy
NASA Astrophysics Data System (ADS)
Lewkowycz, Aitor; Maldacena, Juan
2013-08-01
We consider classical Euclidean gravity solutions with a boundary. The boundary contains a non-contractible circle. These solutions can be interpreted as computing the trace of a density matrix in the full quantum gravity theory, in the classical approximation. When the circle is contractible in the bulk, we argue that the entropy of this density matrix is given by the area of a minimal surface. This is a generalization of the usual black hole entropy formula to euclidean solutions without a Killing vector. A particular example of this set up appears in the computation of the entanglement entropy of a subregion of a field theory with a gravity dual. In this context, the minimal area prescription was proposed by Ryu and Takayanagi. Our arguments explain their conjecture.
EEG entropy measures in anesthesia
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
Entropy squeezing for qubit – field system under decoherence effect
Abdel-Khalek, S; Berrada, K; A-S F Obada; Wahiddin, M R
2014-03-28
We study in detail the dynamics of field entropy squeezing (FES) for a qubit – field system whose dynamics is described by the phase-damped model. The results of calculations show that the initial state and decoherence play a crucial role in the evolution of FES. During the temporal evolution of the system under decoherence effect, an interesting monotonic relation between FES, Wehrl entropy (WE) and negativity is observed. (laser applications and other topics in quantum electronics)
Valence bond entanglement entropy.
Alet, Fabien; Capponi, Sylvain; Laflorencie, Nicolas; Mambrini, Matthieu
2007-09-14
We introduce for SU(2) quantum spin systems the valence bond entanglement entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a valence bond solid state and multiplicative logarithmic corrections for the Néel phase. PMID:17930468
NASA Astrophysics Data System (ADS)
Liu, Hang; Meng, Xin-he
2016-08-01
In this paper, we investigate the angular momentum independence of the entropy sum and product for AdS rotating black holes based on the first law of thermodynamics and a mathematical lemma related to Vandermonde determinant. The advantage of this method is that the explicit forms of the spacetime metric, black hole mass and charge are not needed but the Hawking temperature and entropy formula on the horizons are necessary for static black holes, while our calculations require the expressions of metric and angular velocity formula. We find that the entropy sum is always independent of angular momentum for all dimensions and the angular momentum-independence of entropy product only holds for the dimensions d > 4 with at least one rotation parameter ai = 0, while the mass-free of entropy sum and entropy product for rotating black holes only stand for higher dimensions (d > 4) and for all dimensions, respectively. On the other hand, we find that the introduction of a negative cosmological constant does not affect the angular momentum-free of entropy sum and product but the criterion for angular momentum-independence of entropy product will be affected.
NASA Astrophysics Data System (ADS)
Amblard, Pierre-Olivier; Vignat, Christophe
2006-06-01
The aim of the paper is to study the link between non-additivity of some entropies and their boundedness. We propose an axiomatic construction of the entropy relying on the fact that entropy belongs to a group isomorphic to the usual additive group. This allows to show that the entropies that are additive with respect to the addition of the group for independent random variables are nonlinear transforms of the Rényi entropies, including the particular case of the Shannon entropy. As a particular example, we study as a group a bounded interval in which the addition is a generalization of the addition of velocities in special relativity. We show that Tsallis-Havrda-Charvat entropy is included in the family of entropies we define. Finally, a link is made between the approach developed in the paper and the theory of deformed logarithms.
Gradient-based manipulation of nonparametric entropy estimates.
Schraudolph, Nicol N
2004-07-01
This paper derives a family of differential learning rules that optimize the Shannon entropy at the output of an adaptive system via kernel density estimation. In contrast to parametric formulations of entropy, this nonparametric approach assumes no particular functional form of the output density. We address problems associated with quantized data and finite sample size, and implement efficient maximum likelihood techniques for optimizing the regularizer. We also develop a normalized entropy estimate that is invariant with respect to affine transformations, facilitating optimization of the shape, rather than the scale, of the output density. Kernel density estimates are smooth and differentiable; this makes the derived entropy estimates amenable to manipulation by gradient descent. The resulting weight updates are surprisingly simple and efficient learning rules that operate on pairs of input samples. They can be tuned for data-limited or memory-limited situations, or modified to give a fully online implementation. PMID:15461076
Shannon information entropy in position space for two-electron atomic systems
NASA Astrophysics Data System (ADS)
Lin, Chien-Hao; Ho, Yew Kam
2015-07-01
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited states in helium-like systems. In this work, we adopt another entropic measure, Shannon entropy, to probe the nature of correlation effects. Besides the results of the Shannon entropy in coordinate space for the singlet ground states of helium-like systems including positronium negative ion, hydrogen negative ion, helium atom, and lithium positive ion, we also show results for systems with nucleus charge around the ionization threshold.
NASA Astrophysics Data System (ADS)
Hansen, Frank
2016-06-01
Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.
Entropy Effects in Chelation Reactions.
ERIC Educational Resources Information Center
Chung, Chung-Sun
1984-01-01
The entropy change for a reaction in aqueous solution can be evaluated as a combination of entropy factors. Valuable insight or understanding can be obtained from a detailed examination of these factors. Several entropy effects of inorganic chemical reactions are discussed as examples. (Author/JN)
NASA Astrophysics Data System (ADS)
Styer, Daniel F.
2008-11-01
Quantitative estimates of the entropy involved in biological evolution demonstrate that there is no conflict between evolution and the second law of thermodynamics. The calculations are elementary and could be used to enliven the thermodynamics portion of a high school or introductory college physics course.
Rescaling Temperature and Entropy
ERIC Educational Resources Information Center
Olmsted, John, III
2010-01-01
Temperature and entropy traditionally are expressed in units of kelvin and joule/kelvin. These units obscure some important aspects of the natures of these thermodynamic quantities. Defining a rescaled temperature using the Boltzmann constant, T' = k[subscript B]T, expresses temperature in energy units, thereby emphasizing the close relationship…
NASA Astrophysics Data System (ADS)
Pougaza, Doriano-Boris; Mohammad-Djafari, Ali
2011-03-01
New families of copulas are obtained in a two-step process: first considering the inverse problem which consists of finding a joint distribution from its given marginals as the constrained maximization of some entropies (Shannon, Rényi, Burg, Tsallis-Havrda-Charvát), and then using Sklar's theorem, to define the corresponding copula.
NASA Astrophysics Data System (ADS)
Sato, Humitaka
2010-06-01
Charles Darwin's calculation of a life of Earth had ignited Kelvin's insight on a life of Sun, which had eventually inherited to the physical study of stellar structure and energy source. Nuclear energy had secured a longevity of the universe and the goal of the cosmic evolution has been secured by the entropy of black holes.
NASA Astrophysics Data System (ADS)
Zucker, M. H.
This paper is a critical analysis and reassessment of entropic functioning as it applies to the question of whether the ultimate fate of the universe will be determined in the future to be "open" (expanding forever to expire in a big chill), "closed" (collapsing to a big crunch), or "flat" (balanced forever between the two). The second law of thermodynamics declares that entropy can only increase and that this principle extends, inevitably, to the universe as a whole. This paper takes the position that this extension is an unwarranted projection based neither on experience nonfact - an extrapolation that ignores the powerful effect of a gravitational force acting within a closed system. Since it was originally presented by Clausius, the thermodynamic concept of entropy has been redefined in terms of "order" and "disorder" - order being equated with a low degree of entropy and disorder with a high degree. This revised terminology more subjective than precise, has generated considerable confusion in cosmology in several critical instances. For example - the chaotic fireball of the big bang, interpreted by Stephen Hawking as a state of disorder (high entropy), is infinitely hot and, thermally, represents zero entropy (order). Hawking, apparently focusing on the disorderly "chaotic" aspect, equated it with a high degree of entropy - overlooking the fact that the universe is a thermodynamic system and that the key factor in evaluating the big-bang phenomenon is the infinitely high temperature at the early universe, which can only be equated with zero entropy. This analysis resolves this confusion and reestablishes entropy as a cosmological function integrally linked to temperature. The paper goes on to show that, while all subsystems contained within the universe require external sources of energization to have their temperatures raised, this requirement does not apply to the universe as a whole. The universe is the only system that, by itself can raise its own
Entropy of Li intercalation in Lix CoO2
NASA Astrophysics Data System (ADS)
Reynier, Yvan; Graetz, Jason; Swan-Wood, Tabitha; Rez, Peter; Yazami, Rachid; Fultz, Brent
2004-11-01
The entropy of lithiation of LixCoO2 for 0.5
Entropy Production in Convective Hydrothermal Systems
NASA Astrophysics Data System (ADS)
Boersing, Nele; Wellmann, Florian; Niederau, Jan
2016-04-01
Rayleigh number and moderate aspect ratio, entropy production even enables to predict a preferred convection mode for a model with homogeneous parameter distribution. As a general rule, the thermodynamic measure of entropy production can be used to analyze uncertainties accompanied by modelling convective hydrothermal systems. Without considering any probability distributions of input data, this synthetic study shows that a higher entropy production implies a lower ability to uniquely predict the convection pattern. This in turn means that the uncertainty in estimating subsurface temperatures is higher.
Diffusive mixing and Tsallis entropy
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.
Renyi entropy as a statistical entropy for complex systems
NASA Astrophysics Data System (ADS)
Bashkirov, A. G.
2006-11-01
To describe a complex system, we propose using the Renyi entropy depending on the parameter q (0 < q ≤ 1) and passing into the Gibbs-Shannon entropy at q = 1. The maximum principle for the Renyi entropy yields a Renyi distribution that passes into the Gibbs canonical distribution at q = 1. The thermodynamic entropy of the complex system is defined as the Renyi entropy for the Renyi distribution. In contrast to the usual entropy based on the Gibbs-Shannon entropy, the Renyi entropy increases as the distribution deviates from the Gibbs distribution (the deviation is estimated by the parameter η = 1 - q) and reaches its maximum at the maximum possible value ηmax. As this occurs, the Renyi distribution becomes a power-law distribution. The parameter η can be regarded as an order parameter. At η = 0, the derivative of the thermodynamic entropy with respect to η exhibits a jump, which indicates a kind of phase transition into a more ordered state. The evolution of the system toward further order in this phase state is accompanied by an entropy gain. This means that in accordance with the second law of thermodynamics, a natural evolution in the direction of self-organization is preferable.
Do `negative' temperatures exist?
NASA Astrophysics Data System (ADS)
Lavenda, B. H.
1999-06-01
A modification of the second law is required for a system with a bounded density of states and not the introduction of a `negative' temperature scale. The ascending and descending branches of the entropy versus energy curve describe particle and hole states, having thermal equations of state that are given by the Fermi and logistic distributions, respectively. Conservation of energy requires isentropic states to be isothermal. The effect of adiabatically reversing the field is entirely mechanical because the only difference between the two states is their energies. The laws of large and small numbers, leading to the normal and Poisson approximations, characterize statistically the states of infinite and zero temperatures, respectively. Since the heat capacity also vanishes in the state of maximum disorder, the third law can be generalized in systems with a bounded density of states: the entropy tends to a constant as the temperature tends to either zero or infinity.
Weinberg, A.M.
1982-10-01
Utopians who use entropy to warn of a vast deterioration of energy and mineral resources seek a self-fulfilling prophesy when they work to deny society access to new energy sources, particularly nuclear power. While theoretically correct, entropy is not the relevant factor for the rest of this century. The more extreme entropists call for a return to an eotechnic society based on decentralized, renewable energy technologies, which rests on the assumptions of a loss in Gibbs Free Energy, a mineral depletion that will lead to OPEC-like manipulation, and a current technology that is destroying the environment. The author challenges these assumptions and calls for an exorcism of public fears over reactor accidents. He foresees a resurgence in public confidence in nuclear power by 1990 that will resolve Western dependence on foreign oil. (DCK)
NASA Astrophysics Data System (ADS)
Rost, Christina M.; Sachet, Edward; Borman, Trent; Moballegh, Ali; Dickey, Elizabeth C.; Hou, Dong; Jones, Jacob L.; Curtarolo, Stefano; Maria, Jon-Paul
2015-09-01
Configurational disorder can be compositionally engineered into mixed oxide by populating a single sublattice with many distinct cations. The formulations promote novel and entropy-stabilized forms of crystalline matter where metal cations are incorporated in new ways. Here, through rigorous experiments, a simple thermodynamic model, and a five-component oxide formulation, we demonstrate beyond reasonable doubt that entropy predominates the thermodynamic landscape, and drives a reversible solid-state transformation between a multiphase and single-phase state. In the latter, cation distributions are proven to be random and homogeneous. The findings validate the hypothesis that deliberate configurational disorder provides an orthogonal strategy to imagine and discover new phases of crystalline matter and untapped opportunities for property engineering.
Rost, Christina M.; Sachet, Edward; Borman, Trent; Moballegh, Ali; Dickey, Elizabeth C.; Hou, Dong; Jones, Jacob L.; Curtarolo, Stefano; Maria, Jon-Paul
2015-01-01
Configurational disorder can be compositionally engineered into mixed oxide by populating a single sublattice with many distinct cations. The formulations promote novel and entropy-stabilized forms of crystalline matter where metal cations are incorporated in new ways. Here, through rigorous experiments, a simple thermodynamic model, and a five-component oxide formulation, we demonstrate beyond reasonable doubt that entropy predominates the thermodynamic landscape, and drives a reversible solid-state transformation between a multiphase and single-phase state. In the latter, cation distributions are proven to be random and homogeneous. The findings validate the hypothesis that deliberate configurational disorder provides an orthogonal strategy to imagine and discover new phases of crystalline matter and untapped opportunities for property engineering. PMID:26415623
Maximal entanglement versus entropy for mixed quantum states
Wei, T.-C.; Goldbart, Paul M.; Kwiat, Paul G.; Nemoto, Kae; Munro, William J.; Verstraete, Frank
2003-02-01
Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the corresponding maximally entangled mixed states is determined primarily analytically. As measures of entanglement, we consider entanglement of formation, relative entropy of entanglement, and negativity; as measures of mixedness, we consider linear and von Neumann entropies. We show that the forms of the maximally entangled mixed states can vary with the combination of (entanglement and mixedness) measures chosen. Moreover, for certain combinations, the forms of the maximally entangled mixed states can change discontinuously at a specific value of the entropy. Along the way, we determine the states that, for a given value of entropy, achieve maximal violation of Bell's inequality.
Entropy production and Fluctuation Relation in turbulent thermal convection
NASA Astrophysics Data System (ADS)
Zonta, Francesco; Chibbaro, Sergio
2016-06-01
We report on a numerical experiment performed to analyze fluctuations of the entropy production in turbulent thermal convection, a physical configuration taken here as a prototype of an out-of-equilibrium dissipative system. We estimate the entropy production from instantaneous measurements of the local temperature and velocity fields sampled along the trajectory of a large number of pointwise Lagrangian tracers. The entropy production is characterized by large fluctuations and becomes often negative. This represents a sort of “finite-time” violation of the second principle of thermodynamics, since the direction of the energy flux is opposite to that prescribed by the external gradient. We clearly show that the entropy production normalized by a suitable small-scale energy verifies the Fluctuation Relation (FR), even though the system is time-irreversible.
NASA Astrophysics Data System (ADS)
Smirnov, Sergey
2015-11-01
In thermodynamics a macroscopic state of a system results from a number of its microscopic states. This number is given by the exponent of the system's entropy exp(S ) . In noninteracting systems with discrete energy spectra, such as large scale quantum dots, S as a function of the temperature has usually a plateau shape with integer values of exp(S ) on these plateaus. Plateaus with noninteger values of exp(S ) are fundamentally forbidden and would be thermodynamically infeasible. Here we investigate the entropy of a noninteracting quantum dot coupled via tunneling to normal metals with continuum spectra as well as to topological superconductors. We show that the entropy may have noninteger plateaus if the topological superconductors support weakly overlapping Majorana bound states. This brings a fundamental change in the thermodynamics of the quantum dot whose specific heat cV acquires low-temperature Majorana peaks which should be absent according to the conventional thermodynamics. We also provide a fundamental thermodynamic understanding of the transport properties, such as the linear conductance. In general our results show that the thermodynamics of systems coupled to Majorana modes represents a fundamental physical interest with diverse applications depending on versatility of possible coupling mechanisms.
NASA Astrophysics Data System (ADS)
Lucia, Umberto
2015-02-01
Is there a link between the macroscopic description of the irreversibility and microscopic behaviour of the systems? Transfer of the exergy, i.e., consumption of free energy will keep the system away from a stable equilibrium. So entropy generation results from the redistribution of energy, momentum, mass and charge. Moreover, irreversible consumption of free energy was underlined to create time's arrow. This concept represents the essence of the thermodynamic approach to irreversibility. The analysis developed in this paper points out that the principle of maximum of entropy generation and the least action can be recognized as the only single law. Quanta are exchanged between a system and its surroundings. Each quantum carries energy. The natural behaviour of the open systems is ascribed to the decrease of free energy in the least time, which can be related to the extremum entropy generation theorem. Irreversibility is the result of the interaction between systems and their environment with the consequence time symmetry breaking. The fundamental result of this paper is to introduce a link between the global analysis of irreversibility and Noether's results.
NASA Astrophysics Data System (ADS)
Caticha, Ariel
2007-11-01
What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds. This problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), which is designed for updating from arbitrary priors given information in the form of arbitrary constraints, includes as special cases both MaxEnt (which allows arbitrary constraints) and Bayes' rule (which allows arbitrary priors). Thus, ME unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme that allows us to handle problems that lie beyond the reach of either of the two methods separately. I conclude with a couple of simple illustrative examples.
NASA Astrophysics Data System (ADS)
Anninos, Dionysios; Samani, Joshua; Shaghoulian, Edgar
2014-02-01
We study the applicability of the covariant holographic entanglement entropy proposal to asymptotically warped AdS3 spacetimes with an SL(2, ℝ) × U(1) isometry. We begin by applying the proposal to locally AdS3 backgrounds which are written as an ℝ1 fibration over AdS2. We then perturb away from this geometry by considering a warping parameter a = 1 + δ to get an asymptotically warped AdS3 spacetime and compute the dual entanglement entropy perturbatively in δ. We find that for large separation in the fiber coordinate, the entanglement entropy can be computed to all orders in δ and takes the universal form appropriate for two-dimensional CFTs. The warping-dependent central charge thus identified exactly agrees with previous calculations in the literature. Performing the same perturbative calculations for the warped BTZ black hole again gives universal two-dimensional CFT answers, with the left-moving and right-moving temperatures appearing appropriately in the result.
On the entropy of a hidden Markov process⋆
Jacquet, Philippe; Seroussi, Gadiel; Szpankowski, Wojciech
2008-01-01
We study the entropy rate of a hidden Markov process (HMP) defined by observing the output of a binary symmetric channel whose input is a first-order binary Markov process. Despite the simplicity of the models involved, the characterization of this entropy is a long standing open problem. By presenting the probability of a sequence under the model as a product of random matrices, one can see that the entropy rate sought is equal to a top Lyapunov exponent of the product. This offers an explanation for the elusiveness of explicit expressions for the HMP entropy rate, as Lyapunov exponents are notoriously difficult to compute. Consequently, we focus on asymptotic estimates, and apply the same product of random matrices to derive an explicit expression for a Taylor approximation of the entropy rate with respect to the parameter of the binary symmetric channel. The accuracy of the approximation is validated against empirical simulation results. We also extend our results to higher-order Markov processes and to Rényi entropies of any order. PMID:19169438
Gravitational entropy of local cosmic voids
NASA Astrophysics Data System (ADS)
Sussman, Roberto A.; Larena, Julien
2015-08-01
We undertake a non-perturbative study of the evolution of the ‘gravitational entropy’ proposed by Clifton, Ellis and Tavakol (CET) on local expanding cosmic CDM voids of ˜50-100 Mpc size described as spherical under-dense regions with negative spatial curvature, whose dynamics is determined by Lemaître-Tolman-Bondi (LTB) dust models asymptotic to three different types of FLRW background: ΛCDM, Einstein-de Sitter and ‘open’ FLRW with Λ =0 and negative spatial curvature. By assuming generic nearly spatially flat and linear initial conditions at the last scattering time, we examine analytically and numerically the CET entropy evolution into a fully nonlinear regime in our present cosmic time and beyond. Both analytic and numerical analysis reveal that the late time CET entropy growth is determined by the amplitude of initial fluctuations of spatial curvature at the last scattering time. This entropy growth decays to zero in the late asymptotic time range for all voids, but at a faster rate in voids with ΛCDM and open FLRW backgrounds. However, only for voids in a ΛCDM background is this suppression sufficiently rapid for the CET entropy itself to reach a terminal equilibrium (or ‘saturation’) value. The CET gravitational temperature vanishes asymptotically if Λ =0 and becomes asymptotically proportional to Λ for voids in a ΛCDM background. In the linear regime of the LTB evolution our results coincide, qualitatively and quantitatively, with previous results based on linear perturbation theory.
Entropy meters and the entropy of non-extensive systems
Lieb, Elliott H.; Yngvason, Jakob
2014-01-01
In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states, we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This leaves open the question of defining the entropy of macroscopic, but unscalable systems, such as gravitating bodies or systems where surface effects are important. We show here how the problem can be overcome, in principle, with the aid of an ‘entropy meter’. An entropy meter can also be used to determine entropy functions for non-equilibrium states and mesoscopic systems. PMID:25002830
Entropy generation method to quantify thermal comfort
NASA Technical Reports Server (NTRS)
Boregowda, S. C.; Tiwari, S. N.; Chaturvedi, S. K.
2001-01-01
The present paper presents a thermodynamic approach to assess the quality of human-thermal environment interaction and quantify thermal comfort. The approach involves development of entropy generation term by applying second law of thermodynamics to the combined human-environment system. The entropy generation term combines both human thermal physiological responses and thermal environmental variables to provide an objective measure of thermal comfort. The original concepts and definitions form the basis for establishing the mathematical relationship between thermal comfort and entropy generation term. As a result of logic and deterministic approach, an Objective Thermal Comfort Index (OTCI) is defined and established as a function of entropy generation. In order to verify the entropy-based thermal comfort model, human thermal physiological responses due to changes in ambient conditions are simulated using a well established and validated human thermal model developed at the Institute of Environmental Research of Kansas State University (KSU). The finite element based KSU human thermal computer model is being utilized as a "Computational Environmental Chamber" to conduct series of simulations to examine the human thermal responses to different environmental conditions. The output from the simulation, which include human thermal responses and input data consisting of environmental conditions are fed into the thermal comfort model. Continuous monitoring of thermal comfort in comfortable and extreme environmental conditions is demonstrated. The Objective Thermal Comfort values obtained from the entropy-based model are validated against regression based Predicted Mean Vote (PMV) values. Using the corresponding air temperatures and vapor pressures that were used in the computer simulation in the regression equation generates the PMV values. The preliminary results indicate that the OTCI and PMV values correlate well under ideal conditions. However, an experimental study
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
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.
Self-organization and entropy reduction in a living cell
Davies, Paul C.W.; Rieper, Elisabeth; Tuszynski, Jack A.
2012-01-01
In this paper we discuss the entropy and information aspects of a living cell. Particular attention is paid to the information gain on assembling and maintaining a living state. Numerical estimates of the information and entropy reduction are given and discussed in the context of the cell’s metabolic activity. We discuss a solution to an apparent paradox that there is less information content in DNA than in the proteins that are assembled based on the genetic code encrypted in DNA. When energy input required for protein synthesis is accounted for, the paradox is clearly resolved. Finally, differences between biological information and instruction are discussed. PMID:23159919
Entanglement entropy on fuzzy spaces
Dou, Djamel; Ydri, Badis
2006-08-15
We study the entanglement entropy of a scalar field in 2+1 spacetime where space is modeled by a fuzzy sphere and a fuzzy disc. In both models we evaluate numerically the resulting entropies and find that they are proportional to the number of boundary degrees of freedom. In the Moyal plane limit of the fuzzy disc the entanglement entropy per unite area (length) diverges if the ignored region is of infinite size. The divergence is (interpreted) of IR-UV mixing origin. In general we expect the entanglement entropy per unite area to be finite on a noncommutative space if the ignored region is of finite size.
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.
Order and correlation contributions to the entropy of hydrophobic solvation.
Liu, Maoyuan; Besford, Quinn Alexander; Mulvaney, Thomas; Gray-Weale, Angus
2015-03-21
The entropy of hydrophobic solvation has been explained as the result of ordered solvation structures, of hydrogen bonds, of the small size of the water molecule, of dispersion forces, and of solvent density fluctuations. We report a new approach to the calculation of the entropy of hydrophobic solvation, along with tests of and comparisons to several other methods. The methods are assessed in the light of the available thermodynamic and spectroscopic information on the effects of temperature on hydrophobic solvation. Five model hydrophobes in SPC/E water give benchmark solvation entropies via Widom's test-particle insertion method, and other methods and models are tested against these particle-insertion results. Entropies associated with distributions of tetrahedral order, of electric field, and of solvent dipole orientations are examined. We find these contributions are small compared to the benchmark particle-insertion entropy. Competitive with or better than other theories in accuracy, but with no free parameters, is the new estimate of the entropy contributed by correlations between dipole moments. Dipole correlations account for most of the hydrophobic solvation entropy for all models studied and capture the distinctive temperature dependence seen in thermodynamic and spectroscopic experiments. Entropies based on pair and many-body correlations in number density approach the correct magnitudes but fail to describe temperature and size dependences, respectively. Hydrogen-bond definitions and free energies that best reproduce entropies from simulations are reported, but it is difficult to choose one hydrogen bond model that fits a variety of experiments. The use of information theory, scaled-particle theory, and related methods is discussed briefly. Our results provide a test of the Frank-Evans hypothesis that the negative solvation entropy is due to structured water near the solute, complement the spectroscopic detection of that solvation structure by
Order and correlation contributions to the entropy of hydrophobic solvation
NASA Astrophysics Data System (ADS)
Liu, Maoyuan; Besford, Quinn Alexander; Mulvaney, Thomas; Gray-Weale, Angus
2015-03-01
The entropy of hydrophobic solvation has been explained as the result of ordered solvation structures, of hydrogen bonds, of the small size of the water molecule, of dispersion forces, and of solvent density fluctuations. We report a new approach to the calculation of the entropy of hydrophobic solvation, along with tests of and comparisons to several other methods. The methods are assessed in the light of the available thermodynamic and spectroscopic information on the effects of temperature on hydrophobic solvation. Five model hydrophobes in SPC/E water give benchmark solvation entropies via Widom's test-particle insertion method, and other methods and models are tested against these particle-insertion results. Entropies associated with distributions of tetrahedral order, of electric field, and of solvent dipole orientations are examined. We find these contributions are small compared to the benchmark particle-insertion entropy. Competitive with or better than other theories in accuracy, but with no free parameters, is the new estimate of the entropy contributed by correlations between dipole moments. Dipole correlations account for most of the hydrophobic solvation entropy for all models studied and capture the distinctive temperature dependence seen in thermodynamic and spectroscopic experiments. Entropies based on pair and many-body correlations in number density approach the correct magnitudes but fail to describe temperature and size dependences, respectively. Hydrogen-bond definitions and free energies that best reproduce entropies from simulations are reported, but it is difficult to choose one hydrogen bond model that fits a variety of experiments. The use of information theory, scaled-particle theory, and related methods is discussed briefly. Our results provide a test of the Frank-Evans hypothesis that the negative solvation entropy is due to structured water near the solute, complement the spectroscopic detection of that solvation structure by
Order and correlation contributions to the entropy of hydrophobic solvation
Liu, Maoyuan; Besford, Quinn Alexander; Mulvaney, Thomas; Gray-Weale, Angus
2015-03-21
The entropy of hydrophobic solvation has been explained as the result of ordered solvation structures, of hydrogen bonds, of the small size of the water molecule, of dispersion forces, and of solvent density fluctuations. We report a new approach to the calculation of the entropy of hydrophobic solvation, along with tests of and comparisons to several other methods. The methods are assessed in the light of the available thermodynamic and spectroscopic information on the effects of temperature on hydrophobic solvation. Five model hydrophobes in SPC/E water give benchmark solvation entropies via Widom’s test-particle insertion method, and other methods and models are tested against these particle-insertion results. Entropies associated with distributions of tetrahedral order, of electric field, and of solvent dipole orientations are examined. We find these contributions are small compared to the benchmark particle-insertion entropy. Competitive with or better than other theories in accuracy, but with no free parameters, is the new estimate of the entropy contributed by correlations between dipole moments. Dipole correlations account for most of the hydrophobic solvation entropy for all models studied and capture the distinctive temperature dependence seen in thermodynamic and spectroscopic experiments. Entropies based on pair and many-body correlations in number density approach the correct magnitudes but fail to describe temperature and size dependences, respectively. Hydrogen-bond definitions and free energies that best reproduce entropies from simulations are reported, but it is difficult to choose one hydrogen bond model that fits a variety of experiments. The use of information theory, scaled-particle theory, and related methods is discussed briefly. Our results provide a test of the Frank-Evans hypothesis that the negative solvation entropy is due to structured water near the solute, complement the spectroscopic detection of that solvation structure by
Note on entropies for quantum dynamical systems.
Watanabe, Noboru
2016-05-28
Quantum entropy and channel are fundamental concepts for quantum information theory progressed recently in various directions. We will review the fundamental aspects of mean entropy and mean mutual entropy and calculate them for open system dynamics. PMID:27091165
Thermal Expansion Anomaly Regulated by Entropy
Liu, Zi-Kui; Wang, Yi; Shang, ShunLi
2014-01-01
Thermal expansion, defined as the temperature dependence of volume under constant pressure, is a common phenomenon in nature and originates from anharmonic lattice dynamics. However, it has been poorly understood how thermal expansion can show anomalies such as colossal positive, zero, or negative thermal expansion (CPTE, ZTE, or NTE), especially in quantitative terms. Here we show that changes in configurational entropy due to metastable micro(scopic)states can lead to quantitative prediction of these anomalies. We integrate the Maxwell relation, statistic mechanics, and first-principles calculations to demonstrate that when the entropy is increased by pressure, NTE occurs such as in Invar alloy (Fe3Pt, for example), silicon, ice, and water, and when the entropy is decreased dramatically by pressure, CPTE is expected such as in anti-Invar cerium, ice and water. Our findings provide a theoretic framework to understand and predict a broad range of anomalies in nature in addition to thermal expansion, which may include gigantic electrocaloric and electromechanical responses, anomalously reduced thermal conductivity, and spin distributions. PMID:25391631
Waterlike structural and excess entropy anomalies in liquid beryllium fluoride.
Agarwal, Manish; Chakravarty, Charusita
2007-11-22
The relationship between structural order metrics and the excess entropy is studied using the transferable rigid ion model (TRIM) of beryllium fluoride melt, which is known to display waterlike thermodynamic anomalies. The order map for liquid BeF2, plotted between translational and tetrahedral order metrics, shows a structurally anomalous regime, similar to that seen in water and silica melt, corresponding to a band of state points for which average tetrahedral (q(tet)) and translational (tau) order are strongly correlated. The tetrahedral order parameter distributions further substantiate the analogous structural properties of BeF2, SiO2, and H2O. A region of excess entropy anomaly can be defined within which the pair correlation contribution to the excess entropy (S2) shows an anomalous rise with isothermal compression. Within this region of anomalous entropy behavior, q(tet) and S2 display a strong negative correlation, indicating the connection between the thermodynamic and the structural anomalies. The existence of this region of excess entropy anomaly must play an important role in determining the existence of diffusional and mobility anomalies, given the excess entropy scaling of transport properties observed in many liquids. PMID:17963376
Trajectory versus probability density entropy.
Bologna, M; Grigolini, P; Karagiorgis, M; Rosa, A
2001-07-01
We show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable. We adopt the definition of density entropy as a functional of a distribution density whose time evolution is determined by a transport equation, conceived as the only prescription to use for the calculation. Although the transport equation is built up for the purpose of affording a picture equivalent to that stemming from trajectory dynamics, no direct use of trajectory time evolution is allowed, once the transport equation is defined. With this definition in mind we prove that the detection of a time regime of increase of the density entropy with a rate identical to the KS entropy is possible only in a limited number of cases. The proposals made by some authors to establish a connection between the two entropies in general, violate our definition of density entropy and imply the concept of trajectory, which is foreign to that of density entropy. PMID:11461383
Trajectory versus probability density entropy
NASA Astrophysics Data System (ADS)
Bologna, Mauro; Grigolini, Paolo; Karagiorgis, Markos; Rosa, Angelo
2001-07-01
We show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable. We adopt the definition of density entropy as a functional of a distribution density whose time evolution is determined by a transport equation, conceived as the only prescription to use for the calculation. Although the transport equation is built up for the purpose of affording a picture equivalent to that stemming from trajectory dynamics, no direct use of trajectory time evolution is allowed, once the transport equation is defined. With this definition in mind we prove that the detection of a time regime of increase of the density entropy with a rate identical to the KS entropy is possible only in a limited number of cases. The proposals made by some authors to establish a connection between the two entropies in general, violate our definition of density entropy and imply the concept of trajectory, which is foreign to that of density entropy.
Approximate entropy of network parameters.
West, James; Lacasa, Lucas; Severini, Simone; Teschendorff, Andrew
2012-04-01
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches. PMID:22680542
Approximate entropy of network parameters
NASA Astrophysics Data System (ADS)
West, James; Lacasa, Lucas; Severini, Simone; Teschendorff, Andrew
2012-04-01
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.
Entropy, Its Language, and Interpretation
NASA Astrophysics Data System (ADS)
Leff, Harvey S.
2007-12-01
The language of entropy is examined for consistency with its mathematics and physics, and for its efficacy as a guide to what entropy means. Do common descriptors such as disorder, missing information, and multiplicity help or hinder understanding? Can the language of entropy be helpful in cases where entropy is not well defined? We argue in favor of the descriptor spreading, which entails space, time, and energy in a fundamental way. This includes spreading of energy spatially during processes and temporal spreading over accessible microstates states in thermodynamic equilibrium. Various examples illustrate the value of the spreading metaphor. To provide further support for this metaphor’s utility, it is shown how a set of reasonable spreading properties can be used to derive the entropy function. A main conclusion is that it is appropriate to view entropy’s symbol S as shorthand for spreading.
NASA Astrophysics Data System (ADS)
Winter, Andreas
2016-03-01
We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: first, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible form that depends only on the system dimension and the trace distance of the states. Almost the same proof can be used to derive similar continuity bounds for the relative entropy distance from a convex set of states or positive operators. As applications, we give new proofs, with tighter bounds, of the asymptotic continuity of the relative entropy of entanglement, E R , and its regularization {E_R^{∞}} , as well as of the entanglement of formation, E F . Using a novel "quantum coupling" of density operators, which may be of independent interest, we extend the latter to an asymptotic continuity bound for the regularized entanglement of formation, aka entanglement cost, {E_C=E_F^{∞}} . Second, we derive analogous continuity bounds for the von Neumann entropy and conditional entropy in infinite dimensional systems under an energy constraint, most importantly systems of multiple quantum harmonic oscillators. While without an energy bound the entropy is discontinuous, it is well-known to be continuous on states of bounded energy. However, a quantitative statement to that effect seems not to have been known. Here, under some regularity assumptions on the Hamiltonian, we find that, quite intuitively, the Gibbs entropy at the given energy roughly takes the role of the Hilbert space dimension in the finite-dimensional Fannes inequality.
Multiple sensitivity profiles to diversity and transition structure in non-stationary input.
Tobia, Michael J; Iacovella, Vittorio; Hasson, Uri
2012-04-01
Recent formalizations suggest that the human brain codes for the degree of order in the environment and utilizes this knowledge to optimize perception and performance in the immediate future. However, the neural bases of how the brain spontaneously codes for order are poorly understood. It has been shown that activity in lateral temporal cortex and the hippocampus is linearly correlated with the order of short visual series under tasks requiring attention to the input and when series order is invariant over time. Here, we examined if sensitivity to order is manifested in both linear and non-linear BOLD response profiles, quantified the degree to which order-sensitive regions operate as a functional network, and evaluated these questions using a paradigm in which performance of the ongoing task could be completed without any attention to the stimulus whose order was manipulated. Participants listened to a 10-minute sequence of tones characterized by non-stationary order, and fMRI identified cortical regions sensitive to time-varying statistical features of this input. Activity in perisylvian regions was negatively correlated with input diversity, quantified via Shannon's Entropy. Activity in ventral premotor, lateral temporal, and insular regions was correlated linearly, parabolically, or via a step-function with the strength of transition constraints in the series, quantified via Markov Entropy. Granger-causality analysis revealed that order-sensitive regions form a functional network, with regions showing non-linear responses to order associated with more afferent connectivity than those showing linear responses. These findings identify networks that spontaneously code and respond to diverse aspects of order via multiple response profiles, and that play a central role in generating and gating predictive neural activity. PMID:22285219
Topological entanglement entropy.
Kitaev, Alexei; Preskill, John
2006-03-24
We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity. We show that - gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium. PMID:16605802
Revisiting sample entropy analysis
NASA Astrophysics Data System (ADS)
Govindan, R. B.; Wilson, J. D.; Eswaran, H.; Lowery, C. L.; Preißl, H.
2007-03-01
We modify the definition of sample entropy (SaEn) by incorporating a time delay between the components of the block (from which the densities are estimated) and show that the modified method characterizes the complexity of the system better than the original version. We apply the modified SaEn to the standard deterministic systems and stochastic processes (uncorrelated and long range correlated (LRC) processes) and show that the underlying complexity of the system is better quantified by the modified method. We extend this analysis to the RR intervals of the normal and congestive heart failure (CHF) subjects (available via www.physionet.org) and show that there is a good degree of separation between the two groups.
FULL PARTICLE ELECTROMAGNETIC SIMULATIONS OF ENTROPY GENERATION ACROSS A COLLISIONLESS SHOCK
Yang, Zhongwei; Liu, Ying D.; Wang, Rui; Hu, Huidong; Parks, George K.; Wu, Pin; Huang, Can; Shi, Run
2014-09-20
Experimental data from Cluster have shown that entropy density can be generated across Earth's bow shock. These new observations are a starting point for a more sophisticated analysis that includes computer modeling of a collisionless shock using observed shock parameters as input. In this Letter, we present the first comparison between observations and particle-in-cell simulations of such entropy generation across a collisionless shock. The ion heating at the shock is dominated by the phase mixing of reflected and directly transmitted ions, which are separated from the incident ions. The electron heating is a nearly thermal process due to the conservation of their angular momentum. For both species, we calculate the entropy density across the shock, and obtain good consistency between observations and simulations on entropy generation across the shock. We also find that the entropy generation rate is reduced as the shock Mach number decreases.
Thermodynamical property of entanglement entropy for excited states.
Bhattacharya, Jyotirmoy; Nozaki, Masahiro; Takayanagi, Tadashi; Ugajin, Tomonori
2013-03-01
We argue that the entanglement entropy for a very small subsystem obeys a property which is analogous to the first law of thermodynamics when we excite the system. In relativistic setups, its effective temperature is proportional to the inverse of the subsystem size. This provides a universal relationship between the energy and the amount of quantum information. We derive the results using holography and confirm them in two-dimensional field theories. We will also comment on an example with negative specific heat and suggest a connection between the second law of thermodynamics and the strong subadditivity of entanglement entropy. PMID:23496702
Ho, Szu-Han; Chen, Ching-En; Tseng, Tseung-Yuen; Chang, Ting-Chang Lu, Ying-Hsin; Tsai, Jyun-Yu; Liu, Kuan-Ju; Cheng, Osbert; Huang, Cheng-Tung; Lu, Ching-Sen
2014-03-17
This letter investigates abnormal negative threshold voltage shifts under positive bias stress in input/output (I/O) TiN/HfO{sub 2} n-channel metal-oxide-semiconductor field-effect transistors using fast I-V measurement. This phenomenon is attributed to a reversible charge/discharge effect in pre-existing bulk traps. Moreover, in standard performance devices, threshold-voltage (V{sub t}) shifts positively during fast I-V double sweep measurement. However, in I/O devices, V{sub t} shifts negatively since electrons escape from bulk traps to metal gate rather than channel electrons injecting to bulk traps. Consequently, decreasing pre-existing bulk traps in I/O devices, which can be achieved by adopting Hf{sub x}Zr{sub 1−x}O{sub 2} as gate oxide, can reduce the charge/discharge effect.
Entanglement entropy converges to classical entropy around periodic orbits
NASA Astrophysics Data System (ADS)
Asplund, Curtis T.; Berenstein, David
2016-03-01
We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert-space factors, to investigate the dependence of the entanglement entropy on the choice of coarse graining. We find that for almost all choices the asymptotic growth rate is the same.
Entropy distance: New quantum phenomena
Weis, Stephan; Knauf, Andreas
2012-10-15
We study a curve of Gibbsian families of complex 3 Multiplication-Sign 3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance, and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology, and information geometry. This research is motivated by a theory of infomax principles, where we contribute by computing first order optimality conditions of the entropy distance.
Gravitational entropy and global structure
NASA Astrophysics Data System (ADS)
Hawking, S. W.; Hunter, C. J.
1999-02-01
The underlying reason for the existence of gravitational entropy is traced to the impossibility of foliating topologically non-trivial Euclidean spacetimes with a time function to give a unitary Hamiltonian evolution. In d dimensions the entropy can be expressed in terms of the d-2 obstructions to foliation, bolts and Misner strings, by a universal formula. We illustrate with a number of examples including spaces with nut charge. In these cases, the entropy is not just a quarter the area of the bolt, as it is for black holes.
Neuronal Entropy Depends on the Level of Alertness in the Parkinsonian Globus Pallidus in vivo
Andres, Daniela Sabrina; Cerquetti, Daniel; Merello, Marcelo; Stoop, Ruedi
2014-01-01
A new working hypothesis of Parkinson’s disease (PD) proposes to focus on the central role of entropy increase in the basal ganglia (BG) in movement disorders. The conditions necessary for entropy increase in vivo are, however, still not fully described. We recorded the activity of single globus pallidus pars interna neurons during the transition from deep anesthesia to full alertness in relaxed, head-restrained, control, and parkinsonian (6-hydroxydopamine-lesioned group-lesioned) rats. We found that during awakening from anesthesia, the variation of neuronal entropy was significantly higher in the parkinsonian than in the control group. This implies in our view that in PD the entropy of the output neurons of the BG varies dynamically with the input to the network, which is determined by the level of alertness. Therefore, entropy needs to be interpreted as a dynamic, emergent property that characterizes the global state of the BG neuronal network, rather than a static property of parkinsonian neurons themselves. Within the framework of the “entropy hypothesis,” this implies the presence of a pathological feedback loop in the parkinsonian BG, where increasing the network input results in a further increase of neuronal entropy and a worsening of akinesia. PMID:25009529
Holographic entropy increases in quadratic curvature gravity
NASA Astrophysics Data System (ADS)
Bhattacharjee, Srijit; Sarkar, Sudipta; Wall, Aron C.
2015-09-01
Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is nonstationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We explicitly calculate the entropy increase for Vaidya-like solutions in Ricci-tensor gravity to show that (unlike the Wald entropy) the holographic entropy obeys a second law.
Entropy exchange and entanglement in the Jaynes-Cummings model
NASA Astrophysics Data System (ADS)
Boukobza, E.; Tannor, D. J.
2005-06-01
The Jaynes-Cummings model (JCM) is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight [Ann. Phys. 186, 381 (1988)] of the JCM by considering mixed states of both the light and matter. We present examples of qualitatively different entropic correlations. In particular, we explore the regime of entropy exchange between light and matter, i.e., where the rate of change of the two are anticorrelated. This behavior contrasts with the case of pure light-matter states in which the rate of change of the two entropies are positively correlated and in fact identical. We give an analytical derivation of the anticorrelation phenomenon and discuss the regime of its validity. Finally, we show a strong correlation between the region of the Bloch sphere characterized by entropy exchange and that characterized by minimal entanglement as measured by the negative eigenvalues of the partially transposed density matrix.
Quantum jumps and entropy production
Breuer, Heinz-Peter
2003-09-01
The irreversible motion of an open quantum system can be represented through an ensemble of state vectors following a stochastic dynamics with piecewise deterministic paths. It is shown that this representation leads to a natural definition of the rate of quantum entropy production. The entropy production rate is expressed in terms of the von Neumann entropy and of the numbers of quantum jumps corresponding to the various decay channels of the open system. The proof of the positivity and of the convexity of the entropy production rate is given. Monte Carlo simulations of the stochastic dynamics of a driven qubit and of a {lambda} configuration involving a dark state are performed in order to illustrate the general theory.
Entropy of quantum states: Ambiguities
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; de Queiroz, A. R.; Vaidya, S.
2013-10-01
The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H -theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.
Scaling behaviour of entropy estimates
NASA Astrophysics Data System (ADS)
Schürmann, Thomas
2002-02-01
Entropy estimation of information sources is highly non-trivial for symbol sequences with strong long-range correlations. The rabbit sequence, related to the symbolic dynamics of the nonlinear circle map at the critical point as well as the logistic map at the Feigenbaum point, is known to produce long memory tails. For both dynamical systems the scaling behaviour of the block entropy of order n has been shown to increase ∝log n. In contrast to such probabilistic concepts, we investigate the scaling behaviour of certain non-probabilistic entropy estimation schemes suggested by Lempel and Ziv (LZ) in the context of algorithmic complexity and data compression. These are applied in a sequential manner with the scaling variable being the length N of the sequence. We determine the scaling law for the LZ entropy estimate applied to the case of the critical circle map and the logistic map at the Feigenbaum point in a binary partition.
An adaptable binary entropy coder
NASA Technical Reports Server (NTRS)
Kiely, A.; Klimesh, M.
2001-01-01
We present a novel entropy coding technique which is based on recursive interleaving of variable-to-variable length binary source codes. We discuss code design and performance estimation methods, as well as practical encoding and decoding algorithms.
Boundary effects in entanglement entropy
NASA Astrophysics Data System (ADS)
Berthiere, Clément; Solodukhin, Sergey N.
2016-09-01
We present a number of explicit calculations of Renyi and entanglement entropies in situations where the entangling surface intersects the boundary of d-dimensional Minkowski spacetime. When the boundary is a single plane we compute the contribution to the entropy due to this intersection, first in the case of the Neumann and Dirichlet boundary conditions, and then in the case of a generic Robin type boundary condition. The flow in the boundary coupling between the Neumann and Dirichlet phases is analyzed in arbitrary dimension d and is shown to be monotonic, the peculiarity of d = 3 case is noted. We argue that the translational symmetry along the entangling surface is broken due the presence of the boundary which reveals that the entanglement is not homogeneous. In order to characterize this quantitatively, we introduce a density of entanglement entropy and compute it explicitly. This quantity clearly indicates that the entanglement is maximal near the boundary. We then consider the situation where the boundary is composed of two parallel planes at a finite separation and compute the entanglement entropy as well as its density in this case. The complete contribution to entanglement entropy due to the boundaries is shown not to depend on the distance between the planes and is simply twice the entropy in the case of single plane boundary. Additionally, we find how the area law, the part in the entropy proportional to the area of entire entangling surface, depends on the size of the separation between the two boundaries. The latter is shown to appear in the UV finite part of the entropy.
State Ensembles and Quantum Entropy
NASA Astrophysics Data System (ADS)
Kak, Subhash
2016-06-01
This paper considers quantum communication involving an ensemble of states. Apart from the von Neumann entropy, it considers other measures one of which may be useful in obtaining information about an unknown pure state and another that may be useful in quantum games. It is shown that under certain conditions in a two-party quantum game, the receiver of the states can increase the entropy by adding another pure state.
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
Configurational entropy in thermoset polymers.
Jensen, Martin; Jakobsen, Johnny
2015-04-30
The configurational entropy describes the atomic structure in a material and controls several material properties. Often the configurational entropy is determined through dielectric or calorimetric measurements where the difference between the entropies of the crystalline state and the amorphous state is determined. Many amorphous materials such as thermoset polymers have a high crystallization barrier, greatly limiting the applicability of the existing methods for determining the configurational entropy. In this work, a novel differential scanning calorimetry (DSC) method, based on measurement of the glass transition temperature at different heating rates, for determination of the configurational entropy is introduced. The theory behind the method has a universal character for amorphous materials, as it solely involves measurement of the glass transition temperature. The temperature dependency of the configurational entropy is determined for epoxy resins and PMMA (poly(methyl methacrylate)) to demonstrate the versatility of the method. On the basis of the findings of the introduced method, the influence of the degree of cross-linking and the chemical structure of the network is discussed. PMID:25844504
Holographic holes and differential entropy
NASA Astrophysics Data System (ADS)
Headrick, Matthew; Myers, Robert C.; Wien, Jason
2014-10-01
Recently it has been shown that the Bekenstein-Hawking entropy formula evaluated on certain closed surfaces in the bulk of a holographic spacetime has an interpretation as the differential entropy of a particular family of intervals (or strips) in the boundary theory [1, 2]. We first extend this construction to bulk surfaces which vary in time. We then give a general proof of the equality between the gravitational entropy and the differential entropy. This proof applies to a broad class of holographic backgrounds possessing a generalized planar symmetry and to certain classes of higher-curvature theories of gravity. To apply this theorem, one can begin with a bulk surface and determine the appropriate family of boundary intervals by considering extremal surfaces tangent to the given surface in the bulk. Alternatively, one can begin with a family of boundary intervals; as we show, the differential entropy then equals the gravitational entropy of a bulk surface that emerges from the intersection of the neighboring entanglement wedges, in a continuum limit.
NASA Technical Reports Server (NTRS)
Cheeseman, Peter; Stutz, John
2005-01-01
A long standing mystery in using Maximum Entropy (MaxEnt) is how to deal with constraints whose values are uncertain. This situation arises when constraint values are estimated from data, because of finite sample sizes. One approach to this problem, advocated by E.T. Jaynes [1], is to ignore this uncertainty, and treat the empirically observed values as exact. We refer to this as the classic MaxEnt approach. Classic MaxEnt gives point probabilities (subject to the given constraints), rather than probability densities. We develop an alternative approach that assumes that the uncertain constraint values are represented by a probability density {e.g: a Gaussian), and this uncertainty yields a MaxEnt posterior probability density. That is, the classic MaxEnt point probabilities are regarded as a multidimensional function of the given constraint values, and uncertainty on these values is transmitted through the MaxEnt function to give uncertainty over the MaXEnt probabilities. We illustrate this approach by explicitly calculating the generalized MaxEnt density for a simple but common case, then show how this can be extended numerically to the general case. This paper expands the generalized MaxEnt concept introduced in a previous paper [3].
ERIC Educational Resources Information Center
Berliss-Vincent, Jane; Whitford, Gigi
2002-01-01
This article presents both the factors involved in successful speech input use and the potential barriers that may suggest that other access technologies could be more appropriate for a given individual. Speech input options that are available are reviewed and strategies for optimizing use of speech recognition technology are discussed. (Contains…
NASA Technical Reports Server (NTRS)
Johnson-Throop, Kathy A.; Vowell, C. W.; Smith, Byron; Darcy, Jeannette
2006-01-01
This viewgraph presentation reviews the inputs to the MDS Medical Information Communique (MIC) catalog. The purpose of the group is to provide input for updating the MDS MIC Catalog and to request that MMOP assign Action Item to other working groups and FSs to support the MITWG Process for developing MIC-DDs.
High input impedance amplifier
NASA Technical Reports Server (NTRS)
Kleinberg, Leonard L.
1995-01-01
High input impedance amplifiers are provided which reduce the input impedance solely to a capacitive reactance, or, in a somewhat more complex design, provide an extremely high essentially infinite, capacitive reactance. In one embodiment, where the input impedance is reduced in essence, to solely a capacitive reactance, an operational amplifier in a follower configuration is driven at its non-inverting input and a resistor with a predetermined magnitude is connected between the inverting and non-inverting inputs. A second embodiment eliminates the capacitance from the input by adding a second stage to the first embodiment. The second stage is a second operational amplifier in a non-inverting gain-stage configuration where the output of the first follower stage drives the non-inverting input of the second stage and the output of the second stage is fed back to the non-inverting input of the first stage through a capacitor of a predetermined magnitude. These amplifiers, while generally useful, are very useful as sensor buffer amplifiers that may eliminate significant sources of error.
Relative Entropy and Squashed Entanglement
NASA Astrophysics Data System (ADS)
Li, Ke; Winter, Andreas
2014-02-01
We are interested in the properties and relations of entanglement measures. Especially, we focus on the squashed entanglement and relative entropy of entanglement, as well as their analogues and variants. Our first result is a monogamy-like inequality involving the relative entropy of entanglement and its one-way LOCC variant. The proof is accomplished by exploring the properties of relative entropy in the context of hypothesis testing via one-way LOCC operations, and by making use of an argument resembling that by Piani on the faithfulness of regularized relative entropy of entanglement. Following this, we obtain a commensurate and faithful lower bound for squashed entanglement, in the form of one-way LOCC relative entropy of entanglement. This gives a strengthening to the strong subadditivity of von Neumann entropy. Our result improves the trace-distance-type bound derived in Brandão et al. (Commun Math Phys, 306:805-830, 2011), where faithfulness of squashed entanglement was first proved. Applying Pinsker's inequality, we are able to recover the trace-distance-type bound, even with slightly better constant factor. However, the main improvement is that our new lower bound can be much larger than the old one and it is almost a genuine entanglement measure. We evaluate exactly the relative entropy of entanglement under various restricted measurement classes, for maximally entangled states. Then, by proving asymptotic continuity, we extend the exact evaluation to their regularized versions for all pure states. Finally, we consider comparisons and separations between some important entanglement measures and obtain several new results on these, too.
Relative entropies in conformal field theory.
Lashkari, Nima
2014-08-01
Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance. PMID:25126908
NASA Astrophysics Data System (ADS)
Hammond, Richard T.
2015-03-01
Some physical aspects of negative mass are examined. Several unusual properties, such as the ability of negative mass to penetrate any armor, are analysed. Other surprising effects include the bizarre system of negative mass chasing positive mass, naked singularities and the violation of cosmic censorship, wormholes, and quantum mechanical results as well. In addition, a brief look into the implications for strings is given.
Some new measures of entropy, useful tools in biocomputing.
Garrido, Angel
2010-01-01
The basic problem rooted in Information Theory (IT) foundations (Shannon, Bell Syst Tech J 27:379-423 and 623-656, 1948; Volkenstein, Entropy and Information. Series: Progress in Mathematical Physics, 2009) is to reconstruct, as closely as possible, the input signal after observing the received output signal.The Shannon information measure is the only possible one in this context, but it must be clear that it is only valid within the more restricted scope of coding problems that C. E. Shannon himself had seen in his lifetime (Shannon, Bell Syst Tech J 27:379-423 and 623-656, 1948). As pointed out by Alfred Rényi (1961), in his essential paper (Rényi, Proc. of the 4th Berkeley Symposium on Mathematics, Statistics and Probability, 547-561, 1961) on generalized information measures, for other sorts of problems other quantities may serve just as well as measures of information, or even better. This would be supported either by their operational significance or by a set of natural postulates characterizing them, or preferably by both. Thus, the idea of generalized entropies arises in scientific literature.We analyze here some new measures of Entropy, very useful to be applied on Biocomputing (Ulanowicz and Hannon, Proc R Soc Lond B 232:181-192, 1987; Volkenstein, Entropy and Information. Series: Progress in Mathematical Physics, 2009). PMID:20865562
Classification of 5-S Epileptic EEG Recordings Using Distribution Entropy and Sample Entropy
Li, Peng; Karmakar, Chandan; Yan, Chang; Palaniswami, Marimuthu; Liu, Changchun
2016-01-01
Epilepsy is an electrophysiological disorder of the brain, the hallmark of which is recurrent and unprovoked seizures. Electroencephalogram (EEG) measures electrical activity of the brain that is commonly applied as a non-invasive technique for seizure detection. Although a vast number of publications have been published on intelligent algorithms to classify interictal and ictal EEG, it remains an open question whether they can be detected using short-length EEG recordings. In this study, we proposed three protocols to select 5 s EEG segment for classifying interictal and ictal EEG from normal. We used the publicly-accessible Bonn database, which consists of normal, interical, and ictal EEG signals with a length of 4097 sampling points (23.6 s) per record. In this study, we selected three segments of 868 points (5 s) length from each recordings and evaluated results for each of them separately. The well-studied irregularity measure—sample entropy (SampEn)—and a more recently proposed complexity measure—distribution entropy (DistEn)—were used as classification features. A total of 20 combinations of input parameters m and τ for the calculation of SampEn and DistEn were selected for compatibility. Results showed that SampEn was undefined for half of the used combinations of input parameters and indicated a large intra-class variance. Moreover, DistEn performed robustly for short-length EEG data indicating relative independence from input parameters and small intra-class fluctuations. In addition, it showed acceptable performance for all three classification problems (interictal EEG from normal, ictal EEG from normal, and ictal EEG from interictal) compared to SampEn, which showed better results only for distinguishing normal EEG from interictal and ictal. Both SampEn and DistEn showed good reproducibility and consistency, as evidenced by the independence of results on analysing protocol. PMID:27148074
NASA Astrophysics Data System (ADS)
Foster, K.
1994-09-01
This document is a description of a computer program called Format( )MEDIC( )Input. The purpose of this program is to allow the user to quickly reformat wind velocity data in the Model Evaluation Database (MEDb) into a reasonable 'first cut' set of MEDIC input files (MEDIC.nml, StnLoc.Met, and Observ.Met). The user is cautioned that these resulting input files must be reviewed for correctness and completeness. This program will not format MEDb data into a Problem Station Library or Problem Metdata File. A description of how the program reformats the data is provided, along with a description of the required and optional user input and a description of the resulting output files. A description of the MEDb is not provided here but can be found in the RAS Division Model Evaluation Database Description document.
Fano resonances and entanglement entropy
Eisler, Viktor; Garmon, Savannah Sterling
2010-11-01
We study the entanglement in the ground state of a chain of free spinless fermions with a single side-coupled impurity. We find a logarithmic scaling for the entanglement entropy of a segment neighboring the impurity. The prefactor of the logarithm varies continuously and contains an impurity contribution described by a one-parameter function while the contribution of the unmodified boundary enters additively. The coefficient is found explicitly by pointing out similarities with other models involving interface defects. The proposed formula gives excellent agreement with our numerical data. If the segment has an open boundary, one finds a rapidly oscillating subleading term in the entropy that persists in the limit of large block sizes. The particle-number fluctuation inside the subsystem is also reported. It is analogous with the expression for the entropy scaling, however, with a simpler functional form for the coefficient.
Convex accelerated maximum entropy reconstruction
NASA Astrophysics Data System (ADS)
Worley, Bradley
2016-04-01
Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm - called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm - is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra.
Quantum geometry and gravitational entropy
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Gravitational entropy of cosmic expansion
NASA Astrophysics Data System (ADS)
Sussman , R. A.
2014-09-01
We apply a recent proposal to define ``gravitational entropy'' to the expansion of cosmic voids within the framework of non-perturbative General Relativity. By considering CDM void configurations compatible with basic observational constraints, we show that this entropy grows from post-inflationary conditions towards a final asymptotic value in a late time fully non-linear regime described by the Lemaître- Tolman-Bondi (LTB) dust models. A qualitatively analogous behavior occurs if we assume a positive cosmological constant consistent with a Λ-CDM background model. However, the Λ term introduces a significant suppression of entropy growth with the terminal equilibrium value reached at a much faster rate.
Construction of microcanonical entropy on thermodynamic pillars.
Campisi, Michele
2015-05-01
A question that is currently highly debated is whether the microcanonical entropy should be expressed as the logarithm of the phase volume (volume entropy, also known as the Gibbs entropy) or as the logarithm of the density of states (surface entropy, also known as the Boltzmann entropy). Rather than postulating them and investigating the consequence of each definition, as is customary, here we adopt a bottom-up approach and construct the entropy expression within the microcanonical formalism upon two fundamental thermodynamic pillars: (i) The second law of thermodynamics as formulated for quasistatic processes: δQ/T is an exact differential, and (ii) the law of ideal gases: PV=k(B)NT. The first pillar implies that entropy must be some function of the phase volume Ω. The second pillar singles out the logarithmic function among all possible functions. Hence the construction leads uniquely to the expression S=k(B)lnΩ, that is, the volume entropy. As a consequence any entropy expression other than that of Gibbs, e.g., the Boltzmann entropy, can lead to inconsistencies with the two thermodynamic pillars. We illustrate this with the prototypical example of a macroscopic collection of noninteracting spins in a magnetic field, and show that the Boltzmann entropy severely fails to predict the magnetization, even in the thermodynamic limit. The uniqueness of the Gibbs entropy, as well as the demonstrated potential harm of the Boltzmann entropy, provide compelling reasons for discarding the latter at once. PMID:26066159
Entanglement entropy of scattering particles
NASA Astrophysics Data System (ADS)
Peschanski, Robi; Seki, Shigenori
2016-07-01
We study the entanglement entropy between the two outgoing particles in an elastic scattering process. It is formulated within an S-matrix formalism using the partial wave expansion of two-body states, which plays a significant role in our computation. As a result, we obtain a novel formula that expresses the entanglement entropy in a high energy scattering by the use of physical observables, namely the elastic and total cross sections and a physical bound on the impact parameter range, related to the elastic differential cross-section.
Whose Entropy: A Maximal Entropy Analysis of Phosphorylation Signaling
NASA Astrophysics Data System (ADS)
Remacle, F.; Graeber, T. G.; Levine, R. D.
2011-07-01
High throughput experiments, characteristic of studies in systems biology, produce large output data sets often at different time points or under a variety of related conditions or for different patients. In several recent papers the data is modeled by using a distribution of maximal information-theoretic entropy. We pose the question: `whose entropy' meaning how do we select the variables whose distribution should be compared to that of maximal entropy. The point is that different choices can lead to different answers. Due to the technological advances that allow for the system-wide measurement of hundreds to thousands of events from biological samples, addressing this question is now part of the analysis of systems biology datasets. The analysis of the extent of phosphorylation in reference to the transformation potency of Bcr-Abl fusion oncogene mutants is used as a biological example. The approach taken seeks to use entropy not simply as a statistical measure of dispersion but as a physical, thermodynamic, state function. This highlights the dilemma of what are the variables that describe the state of the signaling network. Is what matters Boolean, spin-like, variables that specify whether a particular phosphorylation site is or is not actually phosphorylated. Or does the actual extent of phosphorylation matter. Last but not least is the possibility that in a signaling network some few specific phosphorylation sites are the key to the signal transduction even though these sites are not at any time abundantly phosphorylated in an absolute sense.
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)
The Effect of Input-Based Instruction Type on the Acquisition of Spanish Accusative Clitics
ERIC Educational Resources Information Center
White, Justin
2015-01-01
The purpose of this paper is to compare structured input (SI) with other input-based instructional treatments. The input-based instructional types include: input flood (IF), text enhancement (TE), SI activities, and focused input (FI; SI without implicit negative feedback). Participants included 145 adult learners enrolled in an intermediate…
Quantum Kaniadakis entropy under projective measurement
NASA Astrophysics Data System (ADS)
Ourabah, Kamel; Hamici-Bendimerad, Amel Hiba; Tribeche, Mouloud
2015-09-01
It is well known that the von Neumann entropy of a quantum state does not decrease with a projective measurement. This property holds for Tsallis and Rényi entropies as well. We show that the recently introduced quantum version of the Kaniadakis entropy preserves this property.
Quantum Kaniadakis entropy under projective measurement.
Ourabah, Kamel; Hamici-Bendimerad, Amel Hiba; Tribeche, Mouloud
2015-09-01
It is well known that the von Neumann entropy of a quantum state does not decrease with a projective measurement. This property holds for Tsallis and Rényi entropies as well. We show that the recently introduced quantum version of the Kaniadakis entropy preserves this property. PMID:26465433
Remainder terms for some quantum entropy inequalities
Carlen, Eric A.; Lieb, Elliott H.
2014-04-15
We consider three von Neumann entropy inequalities: subadditivity; Pinsker's inequality for relative entropy; and the monotonicity of relative entropy. For these we state conditions for equality, and we prove some new error bounds away from equality, including an improved version of Pinsker's inequality.
Entropy: A new measure of stock market volatility?
NASA Astrophysics Data System (ADS)
Bentes, Sonia R.; Menezes, Rui
2012-11-01
When uncertainty dominates understanding stock market volatility is vital. There are a number of reasons for that. On one hand, substantial changes in volatility of financial market returns are capable of having significant negative effects on risk averse investors. In addition, such changes can also impact on consumption patterns, corporate capital investment decisions and macroeconomic variables. Arguably, volatility is one of the most important concepts in the whole finance theory. In the traditional approach this phenomenon has been addressed based on the concept of standard-deviation (or variance) from which all the famous ARCH type models - Autoregressive Conditional Heteroskedasticity Models- depart. In this context, volatility is often used to describe dispersion from an expected value, price or model. The variability of traded prices from their sample mean is only an example. Although as a measure of uncertainty and risk standard-deviation is very popular since it is simple and easy to calculate it has long been recognized that it is not fully satisfactory. The main reason for that lies in the fact that it is severely affected by extreme values. This may suggest that this is not a closed issue. Bearing on the above we might conclude that many other questions might arise while addressing this subject. One of outstanding importance, from which more sophisticated analysis can be carried out, is how to evaluate volatility, after all? If the standard-deviation has some drawbacks shall we still rely on it? Shall we look for an alternative measure? In searching for this shall we consider the insight of other domains of knowledge? In this paper we specifically address if the concept of entropy, originally developed in physics by Clausius in the XIX century, which can constitute an effective alternative. Basically, what we try to understand is, which are the potentialities of entropy compared to the standard deviation. But why entropy? The answer lies on the fact
Entropy of dynamical social networks
NASA Astrophysics Data System (ADS)
Zhao, Kun; Karsai, Marton; Bianconi, Ginestra
2012-02-01
Dynamical social networks are evolving rapidly and are highly adaptive. Characterizing the information encoded in social networks is essential to gain insight into the structure, evolution, adaptability and dynamics. Recently entropy measures have been used to quantify the information in email correspondence, static networks and mobility patterns. Nevertheless, we still lack methods to quantify the information encoded in time-varying dynamical social networks. In this talk we present a model to quantify the entropy of dynamical social networks and use this model to analyze the data of phone-call communication. We show evidence that the entropy of the phone-call interaction network changes according to circadian rhythms. Moreover we show that social networks are extremely adaptive and are modified by the use of technologies such as mobile phone communication. Indeed the statistics of duration of phone-call is described by a Weibull distribution and is significantly different from the distribution of duration of face-to-face interactions in a conference. Finally we investigate how much the entropy of dynamical social networks changes in realistic models of phone-call or face-to face interactions characterizing in this way different type human social behavior.
Entropy algebras and Birkhoff factorization
NASA Astrophysics Data System (ADS)
Marcolli, Matilde; Tedeschi, Nicolas
2015-11-01
We develop notions of Rota-Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deformations arising from quantum information measures such as the von Neumann entropy. We consider examples related to Manin's renormalization and computation program, to Markov random fields and to counting functions and zeta functions of algebraic varieties.
Coherent Informational Energy and Entropy.
ERIC Educational Resources Information Center
Avramescu, Aurel
1980-01-01
Seeks to provide a common theoretical foundation for all known bibliometric laws by assimilating a systemic view of the information transfer process with a thermodynamic process, i.e., the conduction of heat in solids. The resulting diffusion model establishes new definitions for informational energy and entropy consistent with corresponding…
Rigorous entropy-energy arguments
NASA Astrophysics Data System (ADS)
Simon, Barry; Sokal, Alan D.
1981-08-01
We present a method for making rigorous various arguments which predict that certain situations are unstable because of a balance of energy vs. entropy. As applications, we give yet another proof that the two-dimensional plane rotor has no spontaneous magnetization and we make rigorous Thouless' arguments on the one-dimensional Ising model with coupling J/n 2.
Entanglement entropy in particle decay
NASA Astrophysics Data System (ADS)
Lello, Louis; Boyanovsky, Daniel; Holman, Richard
2013-11-01
The decay of a parent particle into two or more daughter particles results in an entangled quantum state as a consequence of conservation laws in the decay process. Recent experiments at Belle and BaBar take advantage of quantum entanglement and the correlations in the time evolution of the product particles to study CP and T violations. If one (or more) of the product particles are not observed, their degrees of freedom are traced out of the pure state density matrix resulting from the decay, leading to a mixed state density matrix and an entanglement entropy. This entropy is a measure of the loss of information present in the original quantum correlations of the entangled state. We use the Wigner-Weisskopf method to construct an approximation to this state that evolves in time in a manifestly unitary way. We then obtain the entanglement entropy from the reduced density matrix of one of the daughter particles obtained by tracing out the unobserved states, and follow its time evolution. We find that it grows over a time scale determined by the lifetime of the parent particle to a maximum, which when the width of the parent particle is narrow, describes the phase space distribution of maximally entangled Bell-like states. The method is generalized to the case in which the parent particle is described by a wave packet localized in space. Possible experimental avenues to measure the entanglement entropy in the decay of mesons at rest are discussed.
Alternative Multiview Maximum Entropy Discrimination.
Chao, Guoqing; Sun, Shiliang
2016-07-01
Maximum entropy discrimination (MED) is a general framework for discriminative estimation based on maximum entropy and maximum margin principles, and can produce hard-margin support vector machines under some assumptions. Recently, the multiview version of MED multiview MED (MVMED) was proposed. In this paper, we try to explore a more natural MVMED framework by assuming two separate distributions p1( Θ1) over the first-view classifier parameter Θ1 and p2( Θ2) over the second-view classifier parameter Θ2 . We name the new MVMED framework as alternative MVMED (AMVMED), which enforces the posteriors of two view margins to be equal. The proposed AMVMED is more flexible than the existing MVMED, because compared with MVMED, which optimizes one relative entropy, AMVMED assigns one relative entropy term to each of the two views, thus incorporating a tradeoff between the two views. We give the detailed solving procedure, which can be divided into two steps. The first step is solving our optimization problem without considering the equal margin posteriors from two views, and then, in the second step, we consider the equal posteriors. Experimental results on multiple real-world data sets verify the effectiveness of the AMVMED, and comparisons with MVMED are also reported. PMID:26111403
NASA Technical Reports Server (NTRS)
Mushotzky, R.
2008-01-01
I will discuss how one can determine the origin of the 'extra entropy' in groups and clusters and the feedback needed in models of galaxy formation. I will stress the use of x-ray spectroscopy and imaging and the critical value that Con-X has in this regard.
NASA Technical Reports Server (NTRS)
Tumer, Kagan; Oza, Nikunj C.; Clancy, Daniel (Technical Monitor)
2001-01-01
Using an ensemble of classifiers instead of a single classifier has been shown to improve generalization performance in many pattern recognition problems. However, the extent of such improvement depends greatly on the amount of correlation among the errors of the base classifiers. Therefore, reducing those correlations while keeping the classifiers' performance levels high is an important area of research. In this article, we explore input decimation (ID), a method which selects feature subsets for their ability to discriminate among the classes and uses them to decouple the base classifiers. We provide a summary of the theoretical benefits of correlation reduction, along with results of our method on two underwater sonar data sets, three benchmarks from the Probenl/UCI repositories, and two synthetic data sets. The results indicate that input decimated ensembles (IDEs) outperform ensembles whose base classifiers use all the input features; randomly selected subsets of features; and features created using principal components analysis, on a wide range of domains.
A violation of the covariant entropy bound?
NASA Astrophysics Data System (ADS)
Masoumi, Ali; Mathur, Samir D.
2015-04-01
Several arguments suggest that the entropy density at high energy density ρ should be given by the expression s =K √{ρ /G } , where K is a constant of order unity. On the other hand the covariant entropy bound requires that the entropy on a light sheet be bounded by A /4 G , where A is the area of the boundary of the sheet. We find that in a suitably chosen cosmological geometry, the above expression for s violates the covariant entropy bound. We consider different possible explanations for this fact, in particular, the possibility that entropy bounds should be defined in terms of volumes of regions rather than areas of surfaces.
q-entropy for symbolic dynamical systems
NASA Astrophysics Data System (ADS)
Zhao, Yun; Pesin, Yakov
2015-12-01
For symbolic dynamical systems we use the Carathéodory construction as described in (Pesin 1997 Dimension Theory in Dynamical Systems, ConTemporary Views and Applications (Chicago: University of Chicago Press)) to introduce the notions of q-topological and q-metric entropies. We describe some basic properties of these entropies and in particular, discuss relations between q-metric entropy and local metric entropy. Both q-topological and q-metric entropies are new invariants respectively under homeomorphisms and metric isomorphisms of dynamical systems.
Towards information inequalities for generalized graph entropies.
Sivakumar, Lavanya; Dehmer, Matthias
2012-01-01
In this article, we discuss the problem of establishing relations between information measures for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the Rényi entropy have been considered for this study. Our main results involve establishing formal relationships, by means of inequalities, between these two kinds of measures. Further, we also state and prove inequalities connecting the classical partition-based graph entropies and partition-independent entropy measures. In addition, several explicit inequalities are derived for special classes of graphs. PMID:22715375
Entropy-Corrected Holographic Dark Energy
NASA Astrophysics Data System (ADS)
Wei, Hao
2009-10-01
The holographic dark energy (HDE) is now an interesting candidate of dark energy, which has been studied extensively in the literature. In the derivation of HDE, the black hole entropy plays an important role. In fact, the entropy-area relation can be modified due to loop quantum gravity or other reasons. With the modified entropy-area relation, we propose the so-called “entropy-corrected holographic dark energy" (ECHDE) in the present work. We consider many aspects of ECHDE and find some interesting results. In addition, we briefly consider the so-called “entropy-corrected agegraphic dark energy" (ECADE).
Generalized gravitational entropy from total derivative action
NASA Astrophysics Data System (ADS)
Dong, Xi; Miao, Rong-Xin
2015-12-01
We investigate the generalized gravitational entropy from total derivative terms in the gravitational action. Following the method of Lewkowycz and Maldacena, we find that the generalized gravitational entropy from total derivatives vanishes. We compare our results with the work of Astaneh, Patrushev, and Solodukhin. We find that if total derivatives produced nonzero entropy, the holographic and the field-theoretic universal terms of entanglement entropy would not match. Furthermore, the second law of thermodynamics could be violated if the entropy of total derivatives did not vanish.
Renyi entropy measures of heart rate Gaussianity.
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. PMID:16402599
Nonparametric entropy estimation using kernel densities.
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. PMID:19897106
Entropy-Based Financial Asset Pricing
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-based financial asset pricing.
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 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; Lin, Naiguo; Wilber, Mark
2011-01-01
Earth's bow shock is a transition layer that causes an irreversible change in the state of plasma that is stationary in time. Theories predict entropy increases across the bow shock but entropy has never been directly measured. Cluster and Double Star plasma experiments measure 3D plasma distributions upstream and downstream of the bow shock that allow calculation of Boltzmann's entropy function H and his famous H-theorem, dH/dt O. We present the first direct measurements of entropy density changes across Earth's bow shock. We will show that this entropy generation may be part of the processes that produce the non-thermal plasma distributions is consistent with a kinetic entropy flux model derived from the collisionless Boltzmann equation, giving strong support that solar wind's total entropy across the bow shock remains unchanged. As far as we know, our results are not explained by any existing shock models and should be of interests to theorists.
Universal crossovers between entanglement entropy and thermal entropy
NASA Astrophysics Data System (ADS)
Swingle, Brian; Senthil, T.
2013-01-01
We postulate the existence of universal crossover functions connecting the universal parts of the entanglement entropy to the low-temperature thermal entropy in gapless quantum many-body systems. These scaling functions encode the intuition that the same low-energy degrees of freedom which control low-temperature thermal physics are also responsible for the long-range entanglement in the quantum ground state. We demonstrate the correctness of the proposed scaling form and determine the scaling function for certain classes of gapless systems whose low-energy physics is described by a conformal field theory. We also use our crossover formalism to argue that local systems which are “natural” can violate the boundary law at most logarithmically. In particular, we show that several non-Fermi-liquid phases of matter have entanglement entropy that is at most of order Ld-1log(L) for a region of linear size L thereby confirming various earlier suggestions in the literature. We also briefly apply our crossover formalism to the study of fluctuations in conserved quantities and discuss some subtleties that occur in systems that spontaneously break a continuous symmetry.
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.
Phonon Entropy of Alloying in Dilute Vanadium Alloys
NASA Astrophysics Data System (ADS)
Delaire, Olivier; Swan-Wood, Tabitha; Kresch, Max; Fultz, Brent
2005-03-01
We investigate the entropic effects associated with changes in the phonon modes of vanadium upon dilute substitutional alloying. Using inelastic neutron scattering, we have measured the phonon DOS and the phonon entropy of mixing in V - 6%X, with X a transition metal impurity. We study trends for impurities across the d-series and down several columns of the periodic table. We show that for Ni, Pd and Pt impurities, the phonon entropy of alloying is large and negative, and in the case of Pt it results in a negative total entropy of mixing for 6% impurities. A Born-von Karman model was used to invert the experimental DOS curves and showed that the phonon stiffening down this column is associated with an increases in 1NN longitudinal inter-atomic force-constants. The changes in the phonon DOS for impurities across the 3d series are also correlated with the previously measured changes in the superconducting temperature Tc. Ab-initio DFT simulations were used to compute the effect of impurities on the electronic and phonon properties of vanadium, and are compared to the experimental results. This work was supported by DOE through the BES Grant DE-FG03-0346055 and BES-MS, W-31-109-ENG-38.
Quantum information entropies for position-dependent mass Schrödinger problem
Yañez-Navarro, G.; Sun, Guo-Hua; Dytrych, T.; Launey, K.D.; Dong, Shi-Hai; Draayer, J.P.
2014-09-15
The Shannon entropy for the position-dependent Schrödinger equation for a particle with a nonuniform solitonic mass density is evaluated in the case of a trivial null potential. The position S{sub x} and momentum S{sub p} information entropies for the three lowest-lying states are calculated. In particular, for these states, we are able to derive analytical solutions for the S{sub x} entropy as well as for the Fourier transformed wave functions, while the S{sub p} quantity is calculated numerically. We notice the behavior of the S{sub x} entropy, namely, it decreases as the mass barrier width narrows and becomes negative beyond a particular width. The negative Shannon entropy exists for the probability densities that are highly localized. The mass barrier determines the stability of the system. The dependence of S{sub p} on the width is contrary to the one for S{sub x}. Some interesting features of the information entropy densities ρ{sub s}(x) and ρ{sub s}(p) are demonstrated. In addition, the Bialynicki-Birula–Mycielski (BBM) inequality is tested for a number of states and found to hold for all the cases.
Nonequilibrium thermodynamics and maximum entropy production in the Earth system
NASA Astrophysics Data System (ADS)
Kleidon, Axel
2009-02-01
The Earth system is maintained in a unique state far from thermodynamic equilibrium, as, for instance, reflected in the high concentration of reactive oxygen in the atmosphere. The myriad of processes that transform energy, that result in the motion of mass in the atmosphere, in oceans, and on land, processes that drive the global water, carbon, and other biogeochemical cycles, all have in common that they are irreversible in their nature. Entropy production is a general consequence of these processes and measures their degree of irreversibility. The proposed principle of maximum entropy production (MEP) states that systems are driven to steady states in which they produce entropy at the maximum possible rate given the prevailing constraints. In this review, the basics of nonequilibrium thermodynamics are described, as well as how these apply to Earth system processes. Applications of the MEP principle are discussed, ranging from the strength of the atmospheric circulation, the hydrological cycle, and biogeochemical cycles to the role that life plays in these processes. Nonequilibrium thermodynamics and the MEP principle have potentially wide-ranging implications for our understanding of Earth system functioning, how it has evolved in the past, and why it is habitable. Entropy production allows us to quantify an objective direction of Earth system change (closer to vs further away from thermodynamic equilibrium, or, equivalently, towards a state of MEP). When a maximum in entropy production is reached, MEP implies that the Earth system reacts to perturbations primarily with negative feedbacks. In conclusion, this nonequilibrium thermodynamic view of the Earth system shows great promise to establish a holistic description of the Earth as one system. This perspective is likely to allow us to better understand and predict its function as one entity, how it has evolved in the past, and how it is modified by human activities in the future.
Ramdani, Sofiane; Bonnet, Vincent; Tallon, Guillaume; Lagarde, Julien; Bernard, Pierre Louis; Blain, Hubert
2016-08-01
Entropy measures are often used to quantify the regularity of postural sway time series. Recent methodological developments provided both multivariate and multiscale approaches allowing the extraction of complexity features from physiological signals; see "Dynamical complexity of human responses: A multivariate data-adaptive framework," in Bulletin of Polish Academy of Science and Technology, vol. 60, p. 433, 2012. The resulting entropy measures are good candidates for the analysis of bivariate postural sway signals exhibiting nonstationarity and multiscale properties. These methods are dependant on several input parameters such as embedding parameters. Using two data sets collected from institutionalized frail older adults, we numerically investigate the behavior of a recent multivariate and multiscale entropy estimator; see "Multivariate multiscale entropy: A tool for complexity analysis of multichannel data," Physics Review E, vol. 84, p. 061918, 2011. We propose criteria for the selection of the input parameters. Using these optimal parameters, we statistically compare the multivariate and multiscale entropy values of postural sway data of non-faller subjects to those of fallers. These two groups are discriminated by the resulting measures over multiple time scales. We also demonstrate that the typical parameter settings proposed in the literature lead to entropy measures that do not distinguish the two groups. This last result confirms the importance of the selection of appropriate input parameters. PMID:26372426
Bacterial chemotaxis and entropy production
Županović, Paško; Brumen, Milan; Jagodič, Marko; Juretić, Davor
2010-01-01
Entropy production is calculated for bacterial chemotaxis in the case of a migrating band of bacteria in a capillary tube. It is found that the speed of the migrating band is a decreasing function of the starting concentration of the metabolizable attractant. The experimentally found dependence of speed on the starting concentration of galactose, glucose and oxygen is fitted with power-law functions. It is found that the corresponding exponents lie within the theoretically predicted interval. The effect of the reproduction of bacteria on band speed is considered, too. The acceleration of the band is predicted due to the reproduction rate of bacteria. The relationship between chemotaxis, the maximum entropy production principle and the formation of self-organizing structure is discussed. PMID:20368258
[Multiscale entropy analysis of electrocardiogram].
Wang, Jun; Ning, Xinbao; Li, Jin; Ma, Qianli; Xu, Yinlin; Bian, Chunhua
2007-10-01
Using the algorithm proposed by Costa M, et al., we studied the multiscale entropy (MSE) of electrocardiogram. The sample entropy (SampEn) of the healthy subjects was found to be higher than that of the subjects with coronary heart disease or myocardial infarction. The healthy subjects' complexity was found to be the highest. The SampEn of the subjects with coronary heart disease was noted to be only slightly higher than that of the subjects with myocardial infarction. These findings show that the complexity of the subjects with coronary heart disease or myocardial infarction is distinctly lower than the complexity of the healthy ones, and the subjects suffereing from coronary heart disease are liable to the onset of myocardial infarction. PMID:18027679
Entropy of unimodular lattice triangulations
NASA Astrophysics Data System (ADS)
Knauf, Johannes F.; Krüger, Benedikt; Mecke, Klaus
2015-02-01
Triangulations are important objects of study in combinatorics, finite element simulations and quantum gravity, where their entropy is crucial for many physical properties. Due to their inherent complex topological structure even the number of possible triangulations is unknown for large systems. We present a novel algorithm for an approximate enumeration which is based on calculations of the density of states using the Wang-Landau flat histogram sampling. For triangulations on two-dimensional integer lattices we achieve excellent agreement with known exact numbers of small triangulations as well as an improvement of analytical calculated asymptotics. The entropy density is C=2.196(3) consistent with rigorous upper and lower bounds. The presented numerical scheme can easily be applied to other counting and optimization problems.
Entropy favours open colloidal lattices
NASA Astrophysics Data System (ADS)
Mao, Xiaoming; Chen, Qian; Granick, Steve
2013-03-01
Burgeoning experimental and simulation activity seeks to understand the existence of self-assembled colloidal structures that are not close-packed. Here we describe an analytical theory based on lattice dynamics and supported by experiments that reveals the fundamental role entropy can play in stabilizing open lattices. The entropy we consider is associated with the rotational and vibrational modes unique to colloids interacting through extended attractive patches. The theory makes predictions of the implied temperature, pressure and patch-size dependence of the phase diagram of open and close-packed structures. More generally, it provides guidance for the conditions at which targeted patchy colloidal assemblies in two and three dimensions are stable, thus overcoming the difficulty in exploring by experiment or simulation the full range of conceivable parameters.
Preserved entropy and fragile magnetism
NASA Astrophysics Data System (ADS)
Canfield, Paul C.; Bud’ko, Sergey L.
2016-08-01
A large swath of quantum critical and strongly correlated electron systems can be associated with the phenomena of preserved entropy and fragile magnetism. In this overview we present our thoughts and plans for the discovery and development of lanthanide and transition metal based, strongly correlated systems that are revealed by suppressed, fragile magnetism, quantum criticality, or grow out of preserved entropy. We will present and discuss current examples such as YbBiPt, YbAgGe, YbFe2Zn20, PrAg2In, BaFe2As2, CaFe2As2, LaCrSb3 and LaCrGe3 as part of our motivation and to provide illustrative examples.
NASA Astrophysics Data System (ADS)
Fodor, Petru; Vyhnalek, Brian; Kaufman, Miron
2013-03-01
We investigate mixing in Dean flows by solving numerically the Navier-Stokes equation for a circular channel. Tracers of two chemical species are carried by the fluid. The centrifugal forces, experienced as the fluid travels along a curved trajectory, coupled with the fluid incompressibility induce cross-sectional rotating flows (Dean vortices). These transversal flows promote the mixing of the chemical species. We generate images for different cross sections along the trajectory. The mixing efficiency is evaluated using the Shannon entropy. Previously we have found, P. S. Fodor and M. Kaufman, Modern Physics Letters B 25, 1111 (2011), this measure to be useful in understanding mixing in the staggered herringbone mixer. The mixing entropy is determined as function of the Reynolds number, the angle of the cross section and the observation scale (number of bins). Quantitative comparison of the mixing in the Dean micromixer and in the staggered herringbone mixer is attempted.
Preserved entropy and fragile magnetism.
Canfield, Paul C; Bud'ko, Sergey L
2016-08-01
A large swath of quantum critical and strongly correlated electron systems can be associated with the phenomena of preserved entropy and fragile magnetism. In this overview we present our thoughts and plans for the discovery and development of lanthanide and transition metal based, strongly correlated systems that are revealed by suppressed, fragile magnetism, quantum criticality, or grow out of preserved entropy. We will present and discuss current examples such as YbBiPt, YbAgGe, YbFe2Zn20, PrAg2In, BaFe2As2, CaFe2As2, LaCrSb3 and LaCrGe3 as part of our motivation and to provide illustrative examples. PMID:27377181
Entropy of adsorption of mixed surfactants from solutions onto the air/water interface
Chen, L.-W.; Chen, J.-H.; Zhou, N.-F.
1995-01-01
The partial molar entropy change for mixed surfactant molecules adsorbed from solution at the air/water interface has been investigated by surface thermodynamics based upon the experimental surface tension isotherms at various temperatures. Results for different surfactant mixtures of sodium dodecyl sulfate and sodium tetradecyl sulfate, decylpyridinium chloride and sodium alkylsulfonates have shown that the partial molar entropy changes for adsorption of the mixed surfactants were generally negative and decreased with increasing adsorption to a minimum near the maximum adsorption and then increased abruptly. The entropy decrease can be explained by the adsorption-orientation of surfactant molecules in the adsorbed monolayer and the abrupt entropy increase at the maximum adsorption is possible due to the strong repulsion between the adsorbed molecules.
Coverage-adjusted entropy estimation.
Vu, Vincent Q; Yu, Bin; Kass, Robert E
2007-09-20
Data on 'neural coding' have frequently been analyzed using information-theoretic measures. These formulations involve the fundamental and generally difficult statistical problem of estimating entropy. We review briefly several methods that have been advanced to estimate entropy and highlight a method, the coverage-adjusted entropy estimator (CAE), due to Chao and Shen that appeared recently in the environmental statistics literature. This method begins with the elementary Horvitz-Thompson estimator, developed for sampling from a finite population, and adjusts for the potential new species that have not yet been observed in the sample-these become the new patterns or 'words' in a spike train that have not yet been observed. The adjustment is due to I. J. Good, and is called the Good-Turing coverage estimate. We provide a new empirical regularization derivation of the coverage-adjusted probability estimator, which shrinks the maximum likelihood estimate. We prove that the CAE is consistent and first-order optimal, with rate O(P)(1/log n), in the class of distributions with finite entropy variance and that, within the class of distributions with finite qth moment of the log-likelihood, the Good-Turing coverage estimate and the total probability of unobserved words converge at rate O(P)(1/(log n)(q)). We then provide a simulation study of the estimator with standard distributions and examples from neuronal data, where observations are dependent. The results show that, with a minor modification, the CAE performs much better than the MLE and is better than the best upper bound estimator, due to Paninski, when the number of possible words m is unknown or infinite. PMID:17567838
Entropy estimation and Fibonacci numbers
NASA Astrophysics Data System (ADS)
Timofeev, Evgeniy A.; Kaltchenko, Alexei
2013-05-01
We introduce a new metric on a space of right-sided infinite sequences drawn from a finite alphabet. Emerging from a problem of entropy estimation of a discrete stationary ergodic process, the metric is important on its own part and exhibits some interesting properties. Notably, the number of distinct metric values for a set of sequences of length m is equal to Fm+3 - 1, where Fm is a Fibonacci number.
NASA Astrophysics Data System (ADS)
Garattini, Remo
A simple model of space-time foam, made by two different types of wormholes in a semiclassical approximation, is taken under examination: one type is a collection of Nw Schwarzschild wormholes, while the other one is made by Schwarzschild-Anti-de Sitter wormholes. The area quantization related to the entropy via the Bekenstein-Hawking formula hints a possible selection between the two configurations. Application to the charged black hole are discussed.
Economics and Maximum Entropy Production
NASA Astrophysics Data System (ADS)
Lorenz, R. D.
2003-04-01
Price differentials, sales volume and profit can be seen as analogues of temperature difference, heat flow and work or entropy production in the climate system. One aspect in which economic systems exhibit more clarity than the climate is that the empirical and/or statistical mechanical tendency for systems to seek a maximum in production is very evident in economics, in that the profit motive is very clear. Noting the common link between 1/f noise, power laws and Self-Organized Criticality with Maximum Entropy Production, the power law fluctuations in security and commodity prices is not inconsistent with the analogy. There is an additional thermodynamic analogy, in that scarcity is valued. A commodity concentrated among a few traders is valued highly by the many who do not have it. The market therefore encourages via prices the spreading of those goods among a wider group, just as heat tends to diffuse, increasing entropy. I explore some empirical price-volume relationships of metals and meteorites in this context.
Entropy of random entangling surfaces
NASA Astrophysics Data System (ADS)
Solodukhin, Sergey N.
2012-09-01
We consider the situation when a globally defined four-dimensional field system is separated on two entangled sub-systems by a dynamical (random) two-dimensional surface. The reduced density matrix averaged over ensemble of random surfaces of fixed area and the corresponding average entropy are introduced. The average entanglement entropy is analyzed for a generic conformal field theory in four dimensions. Two important particular cases are considered. In the first, both the intrinsic metric on the entangling surface and the spacetime metric are fluctuating. An important example of this type is when the entangling surface is a black hole horizon, the fluctuations of which cause necessarily the fluctuations in the spacetime geometry. In the second case, the spacetime is considered to be fixed. The detailed analysis is carried out for the random entangling surfaces embedded in flat Minkowski spacetime. In all cases, the problem reduces to an effectively two-dimensional problem of random surfaces which can be treated by means of the well-known conformal methods. Focusing on the logarithmic terms in the entropy, we predict the appearance of a new ln ln(A) term. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.
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.
Quality evaluation of adaptive optical image based on DCT and Rényi entropy
NASA Astrophysics Data System (ADS)
Xu, Yuannan; Li, Junwei; Wang, Jing; Deng, Rong; Dong, Yanbing
2015-04-01
The adaptive optical telescopes play a more and more important role in the detection system on the ground, and the adaptive optical images are so many that we need find a suitable method of quality evaluation to choose good quality images automatically in order to save human power. It is well known that the adaptive optical images are no-reference images. In this paper, a new logarithmic evaluation method based on the use of the discrete cosine transform(DCT) and Rényi entropy for the adaptive optical images is proposed. Through the DCT using one or two dimension window, the statistical property of Rényi entropy for images is studied. The different directional Rényi entropy maps of an input image containing different information content are obtained. The mean values of different directional Rényi entropy maps are calculated. For image quality evaluation, the different directional Rényi entropy and its standard deviation corresponding to region of interest is selected as an indicator for the anisotropy of the images. The standard deviation of different directional Rényi entropy is obtained as the quality evaluation value for adaptive optical image. Experimental results show the proposed method that the sorting quality matches well with the visual inspection.
Maximum entropy analysis of cosmic ray composition
NASA Astrophysics Data System (ADS)
Nosek, Dalibor; Ebr, Jan; Vícha, Jakub; Trávníček, Petr; Nosková, Jana
2016-03-01
We focus on the primary composition of cosmic rays with the highest energies that cause extensive air showers in the Earth's atmosphere. A way of examining the two lowest order moments of the sample distribution of the depth of shower maximum is presented. The aim is to show that useful information about the composition of the primary beam can be inferred with limited knowledge we have about processes underlying these observations. In order to describe how the moments of the depth of shower maximum depend on the type of primary particles and their energies, we utilize a superposition model. Using the principle of maximum entropy, we are able to determine what trends in the primary composition are consistent with the input data, while relying on a limited amount of information from shower physics. Some capabilities and limitations of the proposed method are discussed. In order to achieve a realistic description of the primary mass composition, we pay special attention to the choice of the parameters of the superposition model. We present two examples that demonstrate what consequences can be drawn for energy dependent changes in the primary composition.
Hypermnesia using auditory input.
Allen, J
1992-07-01
The author investigated whether hypermnesia would occur with auditory input. In addition, the author examined the effects of subjects' knowledge that they would later be asked to recall the stimuli. Two groups of 26 subjects each were given three successive recall trials after they listened to an audiotape of 59 high-imagery nouns. The subjects in the uninformed group were not told that they would later be asked to remember the words; those in the informed group were. Hypermnesia was evident, but only in the uninformed group. PMID:1447564
Liebetrau, A.M.
1983-10-01
Work is underway at Pacific Northwest Laboratory (PNL) to improve the probabilistic analysis used to model pressurized thermal shock (PTS) incidents in reactor pressure vessels, and, further, to incorporate these improvements into the existing Vessel Integrity Simulation Analysis (VISA) code. Two topics related to work on input distributions in VISA are discussed in this paper. The first involves the treatment of flaw size distributions and the second concerns errors in the parameters in the (Guthrie) equation which is used to compute ..delta..RT/sub NDT/, the shift in reference temperature for nil ductility transition.
Entropy bounds for hierarchical molecular networks.
Dehmer, Matthias; Borgert, Stephan; Emmert-Streib, Frank
2008-01-01
In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of non-hierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the entropy of a single hierarchical graph, we see that the derived bounds can also be used for characterizing graph classes. Our contribution is an important extension to previous results about the entropy of non-hierarchical networks because for practical applications hierarchical networks are playing an important role in chemistry and biology. In addition to the derivation of the entropy bounds, we provide a numerical analysis for two special graph classes, rooted trees and generalized trees, and demonstrate hereby not only the computational feasibility of our method but also learn about its characteristics and interpretability with respect to data analysis. PMID:18769487
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.
Entropy jump across an inviscid shock wave
NASA Technical Reports Server (NTRS)
Salas, Manuel D.; Iollo, Angelo
1995-01-01
The shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure are shown to be the same, however density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy, propagation equation cannot be used as a conservation law.
Entropy in an Arc Plasma Source
Kaminska, A.; Dudeck, M
2008-03-19
The entropy properties in a D.C. argon arc plasma source are studied. The local thermodynamical entropy relations are established for a set of uniform sub-systems (Ar, Ar{sup +}, e) in order to deduce the entropy balance equation in presence of dissipative effects and in the case of a thermal non equilibrium. Phenomenological linear laws are deduced in near equilibrium situation. The flow parameters inside the plasma source are calculated by a Navier-Stokes fluid description taking into account a thermal local non equilibrium. The entropy function is calculated in the plasma source using the values of the local variables obtained from the numerical code.
Constructing black hole entropy from gravitational collapse
NASA Astrophysics Data System (ADS)
Acquaviva, Giovanni; Ellis, George F. R.; Goswami, Rituparno; Hamid, Aymen I. M.
2015-03-01
Based on a recent proposal for the gravitational entropy of free gravitational fields, we investigate the thermodynamic properties of black hole formation through gravitational collapse in the framework of the semitetrad 1 +1 +2 covariant formalism. In the simplest case of an Oppenheimer-Snyder-Datt collapse, we prove that the change in gravitational entropy outside a collapsing body is related to the variation of the surface area of the body itself, even before the formation of horizons. As a result, we are able to relate the Bekenstein-Hawking entropy of the black hole end state to the variation of the vacuum gravitational entropy outside the collapsing body.
Link prediction based on path entropy
NASA Astrophysics Data System (ADS)
Xu, Zhongqi; Pu, Cunlai; Yang, Jian
2016-08-01
Information theory has been taken as a prospective tool for quantifying the complexity of complex networks. In this paper, first we study the information entropy or uncertainty of a path using the information theory. After that, we apply the path entropy to the link prediction problem in real-world networks. Specifically, we propose a new similarity index, namely Path Entropy (PE) index, which considers the information entropies of shortest paths between node pairs with penalization to long paths. Empirical experiments demonstrate that PE index outperforms the mainstream of link predictors.
Unrestrained Expansion - A Source of Entropy
NASA Astrophysics Data System (ADS)
Michaud, L. M.
2005-12-01
The paper examines the role of unrestrained expansion in atmospheric entropy production. Lack of mechanical equilibrium is shown to be a far larger producer of internally generated entropy than other internally generated entropy production processes. Isentropic expanders are used to explain atmospheric entropy production. Unrestrained expansion can account for the discrepancy between the energy that would be produced if the heat were carried by Carnot engines and the energy actually produced. Having an expander in more important to mechanical energy production than reducing friction losses. The method of analysis is also applicable to: the solar chimney and to the atmospheric vortex engine.
Beyond Gibbs-Boltzmann-Shannon: General Entropies -- The Gibbs-Lorentzian Example
NASA Astrophysics Data System (ADS)
Treumann, Rudolf; Baumjohann, Wolfgang
2014-08-01
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing Gibbs-Boltzmann-Shannon's entropy definition enabling construction of new forms of statistical mechanics. The general entropy may also be of importance in information theory and data analysis. Application to generalised Lorentzian phase space elements yields the Gibbs-Lorentzian power law probability distribution and statistical mechanics. The corresponding Boltzmann, Fermi and Bose-Einstein distributions are found. They apply only to finite temperature states including correlations. As a by-product any negative absolute temperatures are categorically excluded, supporting a recent ``no-negative T" claim.
Entropy bounds and dark energy
NASA Astrophysics Data System (ADS)
Hsu, Stephen D. H.
2004-07-01
Entropy bounds render quantum corrections to the cosmological constant Λ finite. Under certain assumptions, the natural value of Λ is of order the observed dark energy density ~10-10 eV4, thereby resolving the cosmological constant problem. We note that the dark energy equation of state in these scenarios is w≡p/ρ=0 over cosmological distances, and is strongly disfavored by observational data. Alternatively, Λ in these scenarios might account for the diffuse dark matter component of the cosmological energy density. Permanent address: Institute of Theoretical Science and Department of Physics, University of Oregon, Eugene, OR 97403.
NASA Astrophysics Data System (ADS)
The Arctic Research and Policy Act (Eos, June 26, 1984, p. 412) was signed into law by President Ronald Reagan this past July. One of its objectives is to develop a 5-year research plan for the Arctic. A request for input to this plan is being issued this week to nearly 500 people in science, engineering, and industry.To promote Arctic research and to recommend research policy in the Arctic, the new law establishes a five-member Arctic Research Commission, to be appointed by the President, and establishes an Interagency Arctic Research Policy Committee, to be composed of representatives from nearly a dozen agencies having interests in the region. The commission will make policy recommendations, and the interagency committee will implement those recommendations. The National Science Foundation (NSF) has been designated as the lead agency of the interagency committee.
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 dependence of Hawking radiation entropy
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 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}.
Entanglement entropy between real and virtual particles in ϕ4 quantum field theory
NASA Astrophysics Data System (ADS)
Ardenghi, Juan Sebastián
2015-04-01
The aim of this work is to compute the entanglement entropy of real and virtual particles by rewriting the generating functional of ϕ4 theory as a mean value between states and observables defined through the correlation functions. Then the von Neumann definition of entropy can be applied to these quantum states and in particular, for the partial traces taken over the internal or external degrees of freedom. This procedure can be done for each order in the perturbation expansion showing that the entanglement entropy for real and virtual particles behaves as ln (m0). In particular, entanglement entropy is computed at first order for the correlation function of two external points showing that mutual information is identical to the external entropy and that conditional entropies are negative for all the domain of m0. In turn, from the definition of the quantum states, it is possible to obtain general relations between total traces between different quantum states of a ϕr theory. Finally, discussion about the possibility of taking partial traces over external degrees of freedom is considered, which implies the introduction of some observables that measure space-time points where an interaction occurs.
Detection of Events in Biomedical Signals by a Rényi Entropy Measure
NASA Astrophysics Data System (ADS)
Gabarda, S.; Cristóbal, G.; Martínez-Alajarín, J.; Ruiz, R.
2006-10-01
Biomedical signals contain important information about the healthy condition of human beings. Anomalous events in these signals are commonly associated to diseases. The information content enclosed by time-frequency representations (TFR) of biomedical signals can be explored by means of different Rényi entropy measures. To be precise, Rényi entropy can be approached under different normalizations, producing different outcomes. The best choice depends upon the particularities of the application considered. In this paper we propose a new processing scheme to the problem of events detection in biomedical signals, based on a particular normalization of the Rény entropy measurement. As in the case of another TFR's, the pseudo-Wigner distribution (PWD) of a biomedical signal can take negative values and thus it cannot be properly interpreted as a probability density function. Therefore a complexity measure based on the classical Shannon entropy cannot be used and a generalized measure such as the Rényi entropy is required. Our method allows the identification of the events as the moments having the highest amount of information (entropy) along the temporal data. This provides localized information about normal and pathological events in biomedical signals. Therefore, the diagnosis of diseases is facilitated in this way. The method is illustrated with examples of application to phonocardiograms and electrocardiograms and result are discussed.
Entropy and generalized least square methods in assessment of the regional value of streamgages
Markus, M.; Vernon, Knapp H.; Tasker, Gary D.
2003-01-01
The Illinois State Water Survey performed a study to assess the streamgaging network in the State of Illinois. One of the important aspects of the study was to assess the regional value of each station through an assessment of the information transfer among gaging records for low, average, and high flow conditions. This analysis was performed for the main hydrologic regions in the State, and the stations were initially evaluated using a new approach based on entropy analysis. To determine the regional value of each station within a region, several information parameters, including total net information, were defined based on entropy. Stations were ranked based on the total net information. For comparison, the regional value of the same stations was assessed using the generalized least square regression (GLS) method, developed by the US Geological Survey. Finally, a hybrid combination of GLS and entropy was created by including a function of the negative net information as a penalty function in the GLS. The weights of the combined model were determined to maximize the average correlation with the results of GLS and entropy. The entropy and GLS methods were evaluated using the high-flow data from southern Illinois stations. The combined method was compared with the entropy and GLS approaches using the high-flow data from eastern Illinois stations. ?? 2003 Elsevier B.V. All rights reserved.
Lin, Shu-Kun |
1996-12-31
Gibbs paradox statement of entropy of mixing has been regarded as the theoretical foundation of statistical mechanics, quantum theory and biophysics. However, all the relevant chemical experimental observations and logical analyses indicate that the Gibbs paradox statement is false. I prove that this statement is wrong: Gibbs paradox statement implies that entropy decreases with the increase in symmetry (as represented by a symmetry number {sigma}; see any statistical mechanics textbook). From group theory any system has at least a symmetry number {sigma}=1 which is the identity operation for a strictly asymmetric system. It follows that the entropy of a system is equal to, or less than, zero. However, from either von Neumann-Shannon entropy formula (S(w) =-{Sigma}{sup {omega}} in p{sub 1}) or the Boltzmann entropy formula (S = in w) and the original definition, entropy is non-negative. Therefore, this statement is false. It should not be a surprise that for the first time, many outstanding problems such as the validity of Pauling`s resonance theory, the explanation of second order phase transition phenomena, the biophysical problem of protein folding and the related hydrophobic effect, etc., can be solved. Empirical principles such as Pauli principle (and Hund`s rule) and HSAB principle, etc., can also be given a theoretical explanation.
Negative specific heat of a magnetically self-confined plasma torus
Kiessling, Michael K.-H.; Neukirch, Thomas
2003-01-01
It is shown that the thermodynamic maximum-entropy principle predicts negative specific heat for a stationary, magnetically self-confined current-carrying plasma torus. Implications for the magnetic self-confinement of fusion plasma are considered. PMID:12576553
Extensive ground state entropy in supersymmetric lattice models
Eerten, Hendrik van
2005-12-15
We present the result of calculations of the Witten index for a supersymmetric lattice model on lattices of various type and size. Because the model remains supersymmetric at finite lattice size, the Witten index can be calculated using row-to-row transfer matrices and the calculations are similar to calculations of the partition function at negative activity -1. The Witten index provides a lower bound on the number of ground states. We find strong numerical evidence that the Witten index grows exponentially with the number of sites of the lattice, implying that the model has extensive entropy in the ground state.
Input Multiplicities in Process Control.
ERIC Educational Resources Information Center
Koppel, Lowell B.
1983-01-01
Describes research investigating potential effect of input multiplicity on multivariable chemical process control systems. Several simple processes are shown to exhibit the possibility of theoretical developments on input multiplicity and closely related phenomena are discussed. (JN)
Modeling and generating input processes
Johnson, M.E.
1987-01-01
This tutorial paper provides information relevant to the selection and generation of stochastic inputs to simulation studies. The primary area considered is multivariate but much of the philosophy at least is relevant to univariate inputs as well. 14 refs.
Invariant of dynamical systems: A generalized entropy
Meson, A.M.; Vericat, F. |
1996-09-01
In this work the concept of entropy of a dynamical system, as given by Kolmogorov, is generalized in the sense of Tsallis. It is shown that this entropy is an isomorphism invariant, being complete for Bernoulli schemes. {copyright} {ital 1996 American Institute of Physics.}
The Origins of the Entropy Concept
NASA Astrophysics Data System (ADS)
Darrigol, Olivier
To this day entropy remains a strange, difficult, and multiform concept. Even the great Henri Poincaré renounced precisely defining energy and entropy. In order to justify the success of the two laws of thermodynamics for his students at the Sorbonne, he turned to history:
Ehrenfest's Lottery--Time and Entropy Maximization
ERIC Educational Resources Information Center
Ashbaugh, Henry S.
2010-01-01
Successful teaching of the Second Law of Thermodynamics suffers from limited simple examples linking equilibrium to entropy maximization. I describe a thought experiment connecting entropy to a lottery that mixes marbles amongst a collection of urns. This mixing obeys diffusion-like dynamics. Equilibrium is achieved when the marble distribution is…
Campbell's Rule for Estimating Entropy Changes
ERIC Educational Resources Information Center
Jensen, William B.
2004-01-01
Campbell's rule for estimating entropy changes is discussed in relation to an earlier article by Norman Craig, where it was proposed that the approximate value of the entropy of reaction was related to net moles of gas consumed or generated. It was seen that the average for Campbell's data set was lower than that for Craig's data set and…
Chemical Engineering Students' Ideas of Entropy
ERIC Educational Resources Information Center
Haglund, Jesper; Andersson, Staffan; Elmgren, Maja
2015-01-01
Thermodynamics, and in particular entropy, has been found to be challenging for students, not least due to its abstract character. Comparisons with more familiar and concrete domains, by means of analogy and metaphor, are commonly used in thermodynamics teaching, in particular the metaphor "entropy is disorder." However, this particular…
Progress in High-Entropy Alloys
Gao, Michael C
2013-12-01
Strictly speaking, high-entropy alloys (HEAs) refer to single-phase, solid-solution alloys with multiprincipal elements in an equal or a near-equal molar ratio whose configurational entropy is tremendously high. This special topic was organized to reflect the focus and diversity of HEA research topics in the community.
Entropy and Certainty in Lossless Data Compression
ERIC Educational Resources Information Center
Jacobs, James Jay
2009-01-01
Data compression is the art of using encoding techniques to represent data symbols using less storage space compared to the original data representation. The encoding process builds a relationship between the entropy of the data and the certainty of the system. The theoretical limits of this relationship are defined by the theory of entropy in…
Entropy and Information: A Multidisciplinary Overview.
ERIC Educational Resources Information Center
Shaw, Debora; Davis, Charles H.
1983-01-01
Cites representative extensions of concept of entropy (measure of the amount of energy unavailable for useful work; from the second law of thermodynamics) noting basic relationships between entropy, order, information, and meaning in such disciplines as biology, economics, information science, the arts, and religion. Seventy-eight references are…
Entropy Generation in a Chemical Reaction
ERIC Educational Resources Information Center
Miranda, E. N.
2010-01-01
Entropy generation in a chemical reaction is analysed without using the general formalism of non-equilibrium thermodynamics at a level adequate for advanced undergraduates. In a first approach to the problem, the phenomenological kinetic equation of an elementary first-order reaction is used to show that entropy production is always positive. A…
Entropy estimation of very short symbolic sequences
NASA Astrophysics Data System (ADS)
Lesne, Annick; Blanc, Jean-Luc; Pezard, Laurent
2009-04-01
While entropy per unit time is a meaningful index to quantify the dynamic features of experimental time series, its estimation is often hampered in practice by the finite length of the data. We here investigate the performance of entropy estimation procedures, relying either on block entropies or Lempel-Ziv complexity, when only very short symbolic sequences are available. Heuristic analytical arguments point at the influence of temporal correlations on the bias and statistical fluctuations, and put forward a reduced effective sequence length suitable for error estimation. Numerical studies are conducted using, as benchmarks, the wealth of different dynamic regimes generated by the family of logistic maps and stochastic evolutions generated by a Markov chain of tunable correlation time. Practical guidelines and validity criteria are proposed. For instance, block entropy leads to a dramatic overestimation for sequences of low entropy, whereas it outperforms Lempel-Ziv complexity at high entropy. As a general result, the quality of entropy estimation is sensitive to the sequence temporal correlation hence self-consistently depends on the entropy value itself, thus promoting a two-step procedure. Lempel-Ziv complexity is to be preferred in the first step and remains the best estimator for highly correlated sequences.
Generalized Entropic Uncertainty Relations with Tsallis' Entropy
NASA Technical Reports Server (NTRS)
Portesi, M.; Plastino, A.
1996-01-01
A generalization of the entropic formulation of the Uncertainty Principle of Quantum Mechanics is considered with the introduction of the q-entropies recently proposed by Tsallis. The concomitant generalized measure is illustrated for the case of phase and number operators in quantum optics. Interesting results are obtained when making use of q-entropies as the basis for constructing generalized entropic uncertainty measures.
Gosseries, Olivia; Schnakers, Caroline; Ledoux, Didier; Vanhaudenhuyse, Audrey; Bruno, Marie-Aurélie; Demertzi, Athéna; Noirhomme, Quentin; Lehembre, Rémy; Damas, Pierre; Goldman, Serge; Peeters, Erika; Moonen, Gustave; Laureys, Steven
Summary Monitoring the level of consciousness in brain-injured patients with disorders of consciousness is crucial as it provides diagnostic and prognostic information. Behavioral assessment remains the gold standard for assessing consciousness but previous studies have shown a high rate of misdiagnosis. This study aimed to investigate the usefulness of electroencephalography (EEG) entropy measurements in differentiating unconscious (coma or vegetative) from minimally conscious patients. Left fronto-temporal EEG recordings (10-minute resting state epochs) were prospectively obtained in 56 patients and 16 age-matched healthy volunteers. Patients were assessed in the acute (≤1 month post-injury; n=29) or chronic (>1 month post-injury; n=27) stage. The etiology was traumatic in 23 patients. Automated online EEG entropy calculations (providing an arbitrary value ranging from 0 to 91) were compared with behavioral assessments (Coma Recovery Scale-Revised) and outcome. EEG entropy correlated with Coma Recovery Scale total scores (r=0.49). Mean EEG entropy values were higher in minimally conscious (73±19; mean and standard deviation) than in vegetative/unresponsive wakefulness syndrome patients (45±28). Receiver operating characteristic analysis revealed an entropy cut-off value of 52 differentiating acute unconscious from minimally conscious patients (sensitivity 89% and specificity 90%). In chronic patients, entropy measurements offered no reliable diagnostic information. EEG entropy measurements did not allow prediction of outcome. User-independent time-frequency balanced spectral EEG entropy measurements seem to constitute an interesting diagnostic – albeit not prognostic – tool for assessing neural network complexity in disorders of consciousness in the acute setting. Future studies are needed before using this tool in routine clinical practice, and these should seek to improve automated EEG quantification paradigms in order to reduce the remaining false
Gosseries, Olivia; Schnakers, Caroline; Ledoux, Didier; Vanhaudenhuyse, Audrey; Bruno, Marie-Aurélie; Demertzi, Athéna; Noirhomme, Quentin; Lehembre, Rémy; Damas, Pierre; Goldman, Serge; Peeters, Erika; Moonen, Gustave; Laureys, Steven
2011-01-01
Monitoring the level of consciousness in brain-injured patients with disorders of consciousness is crucial as it provides diagnostic and prognostic information. Behavioral assessment remains the gold standard for assessing consciousness but previous studies have shown a high rate of misdiagnosis. This study aimed to investigate the usefulness of electroencephalography (EEG) entropy measurements in differentiating unconscious (coma or vegetative) from minimally conscious patients. Left fronto-temporal EEG recordings (10-minute resting state epochs) were prospectively obtained in 56 patients and 16 age-matched healthy volunteers. Patients were assessed in the acute (≤1 month post-injury; n=29) or chronic (>1 month post-injury; n=27) stage. The etiology was traumatic in 23 patients. Automated online EEG entropy calculations (providing an arbitrary value ranging from 0 to 91) were compared with behavioral assessments (Coma Recovery Scale-Revised) and outcome. EEG entropy correlated with Coma Recovery Scale total scores (r=0.49). Mean EEG entropy values were higher in minimally conscious (73±19; mean and standard deviation) than in vegetative/unresponsive wakefulness syndrome patients (45±28). Receiver operating characteristic analysis revealed an entropy cut-off value of 52 differentiating acute unconscious from minimally conscious patients (sensitivity 89% and specificity 90%). In chronic patients, entropy measurements offered no reliable diagnostic information. EEG entropy measurements did not allow prediction of outcome. User-independent time-frequency balanced spectral EEG entropy measurements seem to constitute an interesting diagnostic - albeit not prognostic - tool for assessing neural network complexity in disorders of consciousness in the acute setting. Future studies are needed before using this tool in routine clinical practice, and these should seek to improve automated EEG quantification paradigms in order to reduce the remaining false negative and
NASA Astrophysics Data System (ADS)
Kalaidzidis, Yannis L.; Gopta, Oxana; Kalaidzidis, Inna V.
2009-12-01
Originally the maximum entropy method for exponent deconvolution was restricted to the positive exponent's amplitudes by the entropy S(f, m) definition. It limits application of the method, since many experimental kinetics show both the rise and the decay, which manifest themselves as positive and negative amplitudes in the exponent spectrum. The generalization of entropy formulation for non-negative distribution (S. F. Gull and J. Skilling) overcomes this limitation. The drawback of the approach was, that m lost the meaning of the prior distribution, since that maximum of generalized S(f, m) is independent on m and achieved at f ≡ 0. It is significant problem when there are apriori information about possible spectrum behaviour. In the present work some assumptions of the entropy generalization was relaxed and alternative entropy formulation, with non-uniform prior was used for analysis of simulated and experimental data. The new approach was applied to spectra analysis of the absorption kinetics of the bacteriorhodopsin (bR—light driven proton pump from archea Halobacterium salinarium) photocycle. It was shown that the process of the intermediate M formation is non-exponential in the wild type bR. The non-exponential process could be interpreted as result of the protein conformational changes during proton transfer from the Shiff-base of bR.
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.
Trends of stellar entropy along stellar evolution
NASA Astrophysics Data System (ADS)
de Avellar, Guilherme Bronzato, Marcio; Alvares de Souza, Rodrigo; Horvath, Jorge Ernesto
2016-02-01
This paper is devoted to discussing the difference in the thermodynamic entropy budget per baryon in each type of stellar object found in the Universe. We track and discuss the actual decrease of the stored baryonic thermodynamic entropy from the most primitive molecular cloud up to the final fate of matter in black holes, passing through evolved states of matter as found in white dwarfs and neutron stars. We then discuss the case of actual stars with different masses throughout their evolution, clarifying the role of the virial equilibrium condition for the decrease in entropy and related issues. Finally, we discuss the role of gravity in driving the composition and the structural changes of stars with different Main Sequence masses during their evolution up to the final product. Particularly, we discuss the entropy of a black hole in this context arguing that the dramatic increase in its entropy, differently from the other cases, is due to the gravitational field itself.
The role of entropy in magnetotail dynamics
Birn, Joachim; Zaharia, Sorin; Hesse, Michael
2008-01-01
The role of entropy conservation and loss in magnetospheric dynamics, particularly in relation to substorm phases, is discussed on the basis of MHD theory and simulations, using comparisons with PIC simulations for validation. Entropy conservation appears to be a crucial element leading to the formation of thin embedded current sheets in the late substorm growth phase and the potential loss of equilibrium. Entropy loss (in the form of plasmoids) is essential in the earthward transport of flux tubes (bubbles, bursty bulk flows). Entropy loss also changes the tail stability properties and may render ballooning modes unstable and thus contribute to cross-tail variability. We illustrate these effects through results from theory and simulations. Entropy conservation also governs the accessibility of final states of evolution and the amount of energy that may be released.
Entropy of uremia and dialysis technology.
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. PMID:23343540