Results for 'Entropy'

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  1. Abner Shimony.Carnap On Entropy - 1975 - In Jaakko Hintikka (ed.), Rudolf Carnap, Logical Empiricist: Materials and Perspectives. D. Reidel Pub. Co.. pp. 381.
     
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  2.  9
    Maximum Entropy and Probability Kinematics Constrained by Conditionals.Stefan Lukits - 2015 - Entropy 17 (4):1690-1700.
    Two open questions of inductive reasoning are solved: (1) does the principle of maximum entropy (pme) give a solution to the obverse Majerník problem; and (2) is Wagner correct when he claims that Jeffrey’s updating principle (jup) contradicts pme? Majerník shows that pme provides unique and plausible marginal probabilities, given conditional probabilities. The obverse problem posed here is whether pme also provides such conditional probabilities, given certain marginal probabilities. The theorem developed to solve the obverse Majerník problem demonstrates that (...)
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  3.  21
    Logical Entropy: Introduction to Classical and Quantum Logical Information Theory.David Ellerman - 2018 - Entropy 20 (9):679.
    Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this (...)
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  4. Entropy - A Guide for the Perplexed.Roman Frigg & Charlotte Werndl - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press. pp. 115-142.
    Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the (...)
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  5. Quantifying Privacy in Terms of Entropy for Context Aware Services.Athanasios S. Voulodimos & Charalampos Z. Patrikakis - 2009 - Identity in the Information Society 2 (2):155-169.
    In this paper, we address the issue of privacy protection in context aware services, through the use of entropy as a means of measuring the capability of locating a user’s whereabouts and identifying personal selections. We present a framework for calculating levels of abstraction in location and personal preferences reporting in queries to a context aware services server. Finally, we propose a methodology for determining the levels of abstraction in location and preferences that should be applied in user data (...)
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  6. An Introduction to Logical Entropy and its Relation to Shannon Entropy.David Ellerman - 2013 - International Journal of Semantic Computing 7 (2):121-145.
    The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite set--just as the usual logical notion of probability based on the Boolean (...)
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  7.  38
    Bertrand’s Paradox and the Maximum Entropy Principle.Nicholas Shackel & Darrell P. Rowbottom - forthcoming - Philosophy and Phenomenological Research.
    An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand’s chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, that (...)
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  8.  67
    Entropy in Evolution.John Collier - 1986 - Biology and Philosophy 1 (1):5-24.
    Daniel R. Brooks and E. O. Wiley have proposed a theory of evolution in which fitness is merely a rate determining factor. Evolution is driven by non-equilibrium processes which increase the entropy and information content of species together. Evolution can occur without environmental selection, since increased complexity and organization result from the likely capture at the species level of random variations produced at the chemical level. Speciation can occur as the result of variation within the species which decreases the (...)
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  9.  82
    Horizon Entropy.Ted Jacobson & Renaud Parentani - 2003 - Foundations of Physics 33 (2):323-348.
    Although the laws of thermodynamics are well established for black hole horizons, much less has been said in the literature to support the extension of these laws to more general settings such as an asymptotic de Sitter horizon or a Rindler horizon (the event horizon of an asymptotic uniformly accelerated observer). In the present paper we review the results that have been previously established and argue that the laws of black hole thermodynamics, as well as their underlying statistical mechanical content, (...)
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  10.  62
    Eschatology and Entropy: An Alternative to Robert John Russell's Proposal.Klaus Nürnberger - 2012 - Zygon 47 (4):970-996.
    Traditional eschatology clashes with the theory of entropy. Trying to bridge the gap, Robert John Russell assumes that theology and science are based on contradictory, yet equally valid, metaphysical assumptions, each one capable of questioning and impacting the other. The author doubts that Russell's proposal will convince empirically oriented scientists and attempts to provide a viable alternative. Historical‐critical analysis suggests that biblical future expectations were redemptive responses to changing human needs. Apocalyptic visions were occasioned by heavy suffering in postexilic (...)
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  11. Unitarity as Preservation of Entropy and Entanglement in Quantum Systems.Florian Hulpke, Uffe V. Poulsen, Anna Sanpera, Aditi Sen, Ujjwal Sen & Maciej Lewenstein - 2006 - Foundations of Physics 36 (4):477-499.
    The logical structure of Quantum Mechanics (QM) and its relation to other fundamental principles of Nature has been for decades a subject of intensive research. In particular, the question whether the dynamical axiom of QM can be derived from other principles has been often considered. In this contribution, we show that unitary evolutions arise as a consequences of demanding preservation of entropy in the evolution of a single pure quantum system, and preservation of entanglement in the evolution of composite (...)
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  12. Black-Hole Entropy as Causal Links.Djamel Dou & Rafael D. Sorkin - 2003 - Foundations of Physics 33 (2):279-296.
    We model a black hole spacetime as a causal set and count, with a certain definition, the number of causal links crossing the horizon in proximity to a spacelike or null hypersurface Σ. We find that this number is proportional to the horizon's area on Σ, thus supporting the interpretation of the links as the “horizon atoms” that account for its entropy. The cases studied include not only equilibrium black holes but ones far from equilibrium.
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  13.  94
    Choosing a Definition of Entropy That Works.Robert H. Swendsen - 2012 - Foundations of Physics 42 (4):582-593.
    Disagreements over the meaning of the thermodynamic entropy and how it should be defined in statistical mechanics have endured for well over a century. In an earlier paper, I showed that there were at least nine essential properties of entropy that are still under dispute among experts. In this paper, I examine the consequences of differing definitions of the thermodynamic entropy of macroscopic systems.Two proposed definitions of entropy in classical statistical mechanics are (1) defining entropy (...)
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  14. On Classical and Quantum Logical Entropy.David Ellerman - manuscript
    The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of (...)
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  15. How Does the Entropy/Information Bound Work?Jacob D. Bekenstein - 2005 - Foundations of Physics 35 (11):1805-1823.
    According to the universal entropy bound, the entropy of a complete weakly self-gravitating physical system can be bounded exclusively in terms of its circumscribing radius and total gravitating energy. The bound’s correctness is supported by explicit statistical calculations of entropy, gedanken experiments involving the generalized second law, and Bousso’s covariant holographic bound. On the other hand, it is not always obvious in a particular example how the system avoids having too many states for given energy, and hence (...)
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  16.  59
    Quantum Model of Classical Mechanics: Maximum Entropy Packets. [REVIEW]P. Hájíček - 2009 - Foundations of Physics 39 (9):1072-1096.
    In a previous paper, a statistical method of constructing quantum models of classical properties has been described. The present paper concludes the description by turning to classical mechanics. The quantum states that maximize entropy for given averages and variances of coordinates and momenta are called ME packets. They generalize the Gaussian wave packets. A non-trivial extension of the partition-function method of probability calculus to quantum mechanics is given. Non-commutativity of quantum variables limits its usefulness. Still, the general form of (...)
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  17. On the Concept of Entropy for Quantum Decaying Systems.O. Civitarese & M. Gadella - 2013 - Foundations of Physics 43 (11):1275-1294.
    The classical concept of entropy was successfully extended to quantum mechanics by the introduction of the density operator formalism. However, further extensions to quantum decaying states have been hampered by conceptual difficulties associated to the particular nature of these states. In this work we address this problem, by (i) pointing out the difficulties that appear when one tries a consistent definition for this entropy, and (ii) building up a plausible formalism for it, which is based on the use (...)
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  18.  97
    Time Evolution in Macroscopic Systems. II. The Entropy.W. T. Grandy - 2004 - Foundations of Physics 34 (1):21-57.
    The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be defined unambiguously, but it is the time derivative or entropy production that governs ongoing processes in these systems. The differences in physical interpretation and thermodynamic role of entropy in equilibrium and nonequilibrium systems is emphasized and the observable aspects (...)
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  19.  98
    Probability Description and Entropy of Classical and Quantum Systems.Margarita A. Man’ko & Vladimir I. Man’ko - 2011 - Foundations of Physics 41 (3):330-344.
    Tomographic approach to describing both the states in classical statistical mechanics and the states in quantum mechanics using the fair probability distributions is reviewed. The entropy associated with the probability distribution (tomographic entropy) for classical and quantum systems is studied. The experimental possibility to check the inequalities like the position–momentum uncertainty relations and entropic uncertainty relations are considered.
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  20. Maximum Shannon Entropy, Minimum Fisher Information, and an Elementary Game.Shunlong Luo - 2002 - Foundations of Physics 32 (11):1757-1772.
    We formulate an elementary statistical game which captures the essence of some fundamental quantum experiments such as photon polarization and spin measurement. We explore and compare the significance of the principle of maximum Shannon entropy and the principle of minimum Fisher information in solving such a game. The solution based on the principle of minimum Fisher information coincides with the solution based on an invariance principle, and provides an informational explanation of Malus' law for photon polarization. There is no (...)
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  21. Vacuum Radiation, Entropy, and Molecular Chaos.Jean E. Burns - 2007 - Foundations of Physics 37 (12):1727-1737.
    Vacuum radiation causes a particle to make a random walk about its dynamical trajectory. In this random walk the root mean square change in spatial coordinate is proportional to t 1/2, and the fractional changes in momentum and energy are proportional to t −1/2, where t is time. Thus the exchange of energy and momentum between a particle and the vacuum tends to zero over time. At the end of a mean free path the fractional change in momentum of a (...)
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  22.  54
    Competing Definitions of Information Versus Entropy in Physics.Thomas Durt - 2011 - Foundations of Science 16 (4):315-318.
    As was mentioned by Nicolas Lori in his (Found Sci, 2010 ) commentary, the definition of Information in Physics is something about which not all authors agreed. According to physicists like me Information decreases when Entropy increases (so entropy would be a negative measure of information), while many physicists, seemingly the majority of them, are convinced of the contrary (even in the camp of Quantum Information Theoreticians). In this reply I reproduce, and make more precise, some of my (...)
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  23.  99
    Utility of Gambling When Events Are Valued: An Application of Inset Entropy[REVIEW]C. T. Ng, R. Duncan Luce & A. A. J. Marley - 2009 - Theory and Decision 67 (1):23-63.
    The present theory leads to a set of subjective weights such that the utility of an uncertain alternative (gamble) is partitioned into three terms involving those weights—a conventional subjectively weighted utility function over pure consequences, a subjectively weighted value function over events, and a subjectively weighted function of the subjective weights. Under several assumptions, this becomes one of several standard utility representations, plus a weighted value function over events, plus an entropy term of the weights. In the finitely additive (...)
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  24.  99
    Expanding the Area of Gravitational Entropy.R. B. Mann - 2003 - Foundations of Physics 33 (1):65-86.
    I describe how gravitational entropy is intimately connected with the concept of gravitational heat, expressed as the difference between the total and free energies of a given gravitational system. From this perspective one can compute these thermodyanmic quantities in settings that go considerably beyond Bekenstein's original insight that the area of a black hole event horizon can be identified with thermodynamic entropy. The settings include the outsides of cosmological horizons and spacetimes with NUT charge. However the interpretation of (...)
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  25.  69
    Characterizing Entropy in Statistical Physics and in Quantum Information Theory.Bernhard Baumgartner - 2014 - Foundations of Physics 44 (10):1107-1123.
    A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the axioms. First the Boltzmann–Planck formula is derived. Building on this formula, using the Law of Large Numbers—a basic theorem of probability theory—the von Neumann formula is deduced. Axioms used in older theories on the foundations are now derived facts.
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  26.  78
    Entropy of Formulas.Vera Koponen - 2009 - Archive for Mathematical Logic 48 (6):515-522.
    A probability distribution can be given to the set of isomorphism classes of models with universe {1, ..., n} of a sentence in first-order logic. We study the entropy of this distribution and derive a result from the 0–1 law for first-order sentences.
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  27.  35
    What Can the Quantum Liquid Say on the Brane Black Hole, the Entropy of an Extremal Black Hole, and the Vacuum Energy?G. E. Volovik - 2003 - Foundations of Physics 33 (2):349-368.
    Using quantum liquids one can simulate the behavior of the quantum vacuum in the presence of the event horizon. The condensed matter analogs demonstrate that in most cases the quantum vacuum resists formation of the horizon, and even if the horizon is formed different types of the vacuum instability develop, which are faster than the process of Hawking radiation. Nevertheless, it is possible to create the horizon on the quantum-liquid analog of the brane, where the vacuum life-time is long enough (...)
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  28.  64
    Quantum Mutual Entropy Defined by Liftings.Satoshi Iriyama & Masanori Ohya - 2011 - Foundations of Physics 41 (3):406-413.
    A lifting is a map from the state of a system to that of a compound system, which was introduced in Accardi and Ohya (Appl. Math. Optim. 39:33–59, 1999). The lifting can be applied to various physical processes.In this paper, we defined a quantum mutual entropy by the lifting. The usual quantum mutual entropy satisfies the Shannon inequality (Ohya in IEEE Trans. Inf. Theory 29(5):770–774, 1983), but the mutual entropy defined through the lifting does not satisfy this (...)
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  29.  65
    The Principle of Maximum Entropy and a Problem in Probability Kinematics.Stefan Lukits - 2014 - Synthese 191 (7):1-23.
    Sometimes we receive evidence in a form that standard conditioning (or Jeffrey conditioning) cannot accommodate. The principle of maximum entropy (MAXENT) provides a unique solution for the posterior probability distribution based on the intuition that the information gain consistent with assumptions and evidence should be minimal. Opponents of objective methods to determine these probabilities prominently cite van Fraassen’s Judy Benjamin case to undermine the generality of maxent. This article shows that an intuitive approach to Judy Benjamin’s case supports maxent. (...)
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  30.  55
    Aspects Concerning Entropy and Utility.A. R. Hoseinzadeh, G. R. Mohtashami Borzadaran & G. H. Yari - 2012 - Theory and Decision 72 (2):273-285.
    Expected utility maximization problem is one of the most useful tools in mathematical finance, decision analysis and economics. Motivated by statistical model selection, via the principle of expected utility maximization, Friedman and Sandow (J Mach Learn Res 4:257–291, 2003a) considered the model performance question from the point of view of an investor who evaluates models based on the performance of the optimal strategies that the models suggest. They interpreted their performance measures in information theoretic terms and provided new generalizations of (...)
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  31.  45
    On Clifford Space Relativity, Black Hole Entropy, Rainbow Metrics, Generalized Dispersion and Uncertainty Relations.Carlos Castro - 2014 - Foundations of Physics 44 (9):990-1008.
    An analysis of some of the applications of Clifford space relativity to the physics behind the modified black hole entropy-area relations, rainbow metrics, generalized dispersion and minimal length stringy uncertainty relations is presented.
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  32.  37
    Computing the Topological Entropy of Shifts.Christoph Spandl - 2007 - Mathematical Logic Quarterly 53 (4):493-510.
    Different characterizations of classes of shift dynamical systems via labeled digraphs, languages, and sets of forbidden words are investigated. The corresponding naming systems are analyzed according to reducibility and particularly with regard to the computability of the topological entropy relative to the presented naming systems. It turns out that all examined natural representations separate into two equivalence classes and that the topological entropy is not computable in general with respect to the defined natural representations. However, if a specific (...)
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  33.  79
    Three's a Crowd: On Causes, Entropy and Physical Eschatology. [REVIEW]Milan M. Ćirković & Vesna Milošević-Zdjelar - 2004 - Foundations of Science 9 (1):1-24.
    Recent discussions of theorigins of the thermodynamical temporal asymmetry (thearrow of time) by Huw Price and others arecritically assessed. This serves as amotivation for consideration of relationshipbetween thermodynamical and cosmologicalcauses. Although the project of clarificationof the thermodynamical explanandum is certainlywelcome, Price excludes another interestingoption, at least as viable as the sort ofAcausal-Particular approach he favors, andarguably more in the spirit of Boltzmannhimself. Thus, the competition of explanatoryprojects includes three horses, not two. Inaddition, it is the Acausal-Particular approachthat could benefit enormously (...)
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  34.  23
    Entropy and Art: An Essay on Disorder and Order.Rudolf Arnheim - 1973 - Journal of Aesthetics and Art Criticism 32 (2):280-281.
    This essay is an attempt to reconcile the disturbing contradiction between the striving for order in nature and in man and the principle of entropy implicit in the second law of thermodynamics - between the tendency toward greater organization and the general trend of the material universe toward death and disorder.
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  35.  27
    Predictive Statistical Mechanics and Macroscopic Time Evolution: Hydrodynamics and Entropy Production.Domagoj Kuić - 2016 - Foundations of Physics 46 (7):891-914.
    In the previous papers, it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy, subject to the constraint given by the Liouville equation averaged over the phase space, leads to a definition of the rate of entropy change for closed Hamiltonian systems without any additional assumptions. Here, we generalize this basic model and, with the introduction of the additional constraints which are equivalent to the hydrodynamic continuity equations, show that the (...)
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  36.  10
    Lexical Predictability During Natural Reading: Effects of Surprisal and Entropy Reduction.Matthew W. Lowder, Wonil Choi, Fernanda Ferreira & John M. Henderson - 2018 - Cognitive Science 42 (S4):1166-1183.
    What are the effects of word-by-word predictability on sentence processing times during the natural reading of a text? Although information complexity metrics such as surprisal and entropy reduction have been useful in addressing this question, these metrics tend to be estimated using computational language models, which require some degree of commitment to a particular theory of language processing. Taking a different approach, this study implemented a large-scale cumulative cloze task to collect word-by-word predictability data for 40 passages and compute (...)
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  37.  19
    Identities for Entropy Change Associated with the Time-Evolution of an Open System.Hiroki Majima & Akira Suzuki - 2015 - Foundations of Physics 45 (8):914-922.
    A general relation between entropy and an evolutionary superoperator is derived based on the theory of the real-time formulation. The formulation establishing the relation relies only on the framework of quantum statistical mechanics and the standard definition of the von Neumann entropy. Applying the theory of the imaginary-time formulation, a similar relation is obtained for the entropy change due to the change in reservoir temperatures. To show the usefulness of these formulas, we derived the expression for the (...)
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  38.  31
    Bayesian Model Learning Based on Predictive Entropy.Jukka Corander & Pekka Marttinen - 2006 - Journal of Logic, Language and Information 15 (1-2):5-20.
    Bayesian paradigm has been widely acknowledged as a coherent approach to learning putative probability model structures from a finite class of candidate models. Bayesian learning is based on measuring the predictive ability of a model in terms of the corresponding marginal data distribution, which equals the expectation of the likelihood with respect to a prior distribution for model parameters. The main controversy related to this learning method stems from the necessity of specifying proper prior distributions for all unknown parameters of (...)
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  39.  15
    Deformed Entropy and Information Relations for Composite and Noncomposite Systems.Vladimir N. Chernega, Olga V. Man’ko & Vladimir I. Man’ko - 2015 - Foundations of Physics 45 (7):783-798.
    The notion of conditional entropy is extended to noncomposite systems. The \-deformed entropic inequalities, which usually are associated with correlations of the subsystem degrees of freedom in bipartite systems, are found for the noncomposite systems. New entropic inequalities for quantum tomograms of qudit states including the single qudit states are obtained. The Araki–Lieb inequality is found for systems without subsystems.
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  40.  12
    On Entropy Production in the Madelung Fluid and the Role of Bohm’s Potential in Classical Diffusion.Eyal Heifetz, Roumen Tsekov, Eliahu Cohen & Zohar Nussinov - 2016 - Foundations of Physics 46 (7):815-824.
    The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow due to an expansion of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon (...) due to expansion is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the “force” accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum. (shrink)
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  41.  14
    On Entropy of Quantum Compound Systems.Noboru Watanabe - 2015 - Foundations of Physics 45 (10):1311-1329.
    We review some notions for general quantum entropies. The entropy of the compound systems is discussed and a numerical computation of the quantum dynamical systems is carried for the noisy optical channel.
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  42. Evolution as Entropy: Toward a Unified Theory of Biology.D. R. BROOKS - 1986 - University of Chicago Press.
    "By combining recent advances in the physical sciences with some of the novel ideas, techniques, and data of modern biology, this book attempts to achieve a new and different kind of evolutionary synthesis. I found it to be challenging, fascinating, infuriating, and provocative, but certainly not dull."--James H, Brown, University of New Mexico "This book is unquestionably mandatory reading not only for every living biologist but for generations of biologists to come."--Jack P. Hailman, Animal Behaviour , review of the first (...)
     
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  43. Reducing Thermodynamics to Statistical Mechanics: The Case of Entropy.Craig Callender - 1999 - Journal of Philosophy 96 (7):348-373.
  44.  50
    The Inert Vs. The Living State of Matter: Extended Criticality, Time Geometry, Anti-Entropy - An Overview.Giuseppe Longo & Maël Montévil - 2012 - Frontiers in Physiology 3:39.
    The physical singularity of life phenomena is analyzed by means of comparison with the driving concepts of theories of the inert. We outline conceptual analogies, transferals of methodologies and theoretical instruments between physics and biology, in addition to indicating significant differences and sometimes logical dualities. In order to make biological phenomenalities intelligible, we introduce theoretical extensions to certain physical theories. In this synthetic paper, we summarize and propose a unified conceptual framework for the main conclusions drawn from work spanning a (...)
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  45.  46
    Variation of Wavelet Entropy in Electroencephalogram Signal During Neurofeedback Training.Majid Ghoshuni, Mohammad Firoozabadi, Mohammad Ali Khalilzadeh & Mohammad Reza Hashemi Golpayegani - 2013 - Complexity 18 (3):18-23.
  46.  62
    Entropy and Information in Evolving Biological Systems.Daniel R. Brooks, John Collier, Brian A. Maurer, Jonathan D. H. Smith & E. O. Wiley - 1989 - Biology and Philosophy 4 (4):407-432.
    Integrating concepts of maintenance and of origins is essential to explaining biological diversity. The unified theory of evolution attempts to find a common theme linking production rules inherent in biological systems, explaining the origin of biological order as a manifestation of the flow of energy and the flow of information on various spatial and temporal scales, with the recognition that natural selection is an evolutionarily relevant process. Biological systems persist in space and time by transfor ming energy from one state (...)
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  47. Entropy Into the Greenhouse World.Jeremy Rifkin & Ted Howard - 1989
  48.  25
    Entropy in Relation to Incomplete Knowledge.Michael J. Zenzen - 1985
  49. Entropy: A New World View.Jeremy Rifkin - 1980 - Viking Press.
     
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  50. Entropy and Art.Rudolf Arnheim - 1971 - Berkeley: University of California Press.
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