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Entropy - A Guide for the Perplexed

In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford, GB: Oxford University Press. pp. 115-142 (2011)

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  1. Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements.Carlton M. Caves, Christopher A. Fuchs, Kiran K. Manne & Joseph M. Renes - 2004 - Foundations of Physics 34 (2):193-209.
    We prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures, as opposed to the restricted class of orthogonal projection-valued measures used in the original theorem. The advantage of this method is that it works for two-dimensional quantum systems and even for vector spaces over rational fields—settings where the standard theorem fails. Furthermore, unlike the method necessary for proving the original result, the present one is rather elementary. In the case of a qubit, we (...)
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  • The Spin-Echo System Reconsidered.D. A. Lavis - 2004 - Foundations of Physics 34 (4):669-688.
    Simple models have played an important role in the discussion of foundational issues in statistical mechanics. Among them the spin-echo system is of particular interest since it can be realized experimentally. This has led to inferences being drawn about approaches to the foundations of statistical mechanics, particularly with respect to the use of coarse-graining. We examine these claims with the help of computer simulations.
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  • Bell’s Theorem.Abner Shimony - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: The Metaphysics Research Lab.
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  • ”Relative state’ formulation of quantum mechanics.Hugh Everett - 1957 - Reviews of Modern Physics 29 (3):454--462.
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  • The principle of anomaly in quantum mechanics.Hans Reichenbach - 1948 - Dialectica 2 (3‐4):337-350.
    SummaryThe following two questions are examined: 1o Do the unobservable parameters possess precise, though unknown, values ? 2o If these unobservable values were known, would it be possible to make precise predictions of the reults of later measurements ?The answer is shown to be negative; the questions, therefore, are not meaningless, being capable of a falsification. The inquiry leads to the establishment of a principle of anomaly, more precisely speaking, of causal anomaly, which is to be added to Heisenberg's principle (...)
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  • Chaos and algorithmic complexity.Robert W. Batterman & Homer White - 1996 - Foundations of Physics 26 (3):307-336.
    Our aim is to discover whether the notion of algorithmic orbit-complexity can serve to define “chaos” in a dynamical system. We begin with a mostly expository discussion of algorithmic complexity and certain results of Brudno, Pesin, and Ruelle (BRP theorems) which relate the degree of exponential instability of a dynamical system to the average algorithmic complexity of its orbits. When one speaks of predicting the behavior of a dynamical system, one usually has in mind one or more variables in the (...)
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  • On Zurek’s Derivation of the Born Rule.Maximilian Schlosshauer & Arthur Fine - 2005 - Foundations of Physics 35 (2):197-213.
    Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or “envariance” [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions that have implicitly entered into it, emphasizing issues that any such derivation is likely to face.
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  • Zur Quantenmechanik der Stoßvorgänge.Max Born - 1926 - Zeitschrift für Physik 37 (12):863-867.
    Durch eine Untersuchung der Stoßvorgänge wird die Auffassung entwickelt, daß die Quantenmechanik in der Schrödingerschen Form nicht nur die stationären Zustände, sondern auch die Quantensprünge zu beschreiben gestattet.
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  • A Relativistic Version of the Ghirardi–Rimini–Weber Model.Roderich Tumulka - 2006 - Journal of Statistical Physics 125:821-840.
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  • Modal Interpretations of Quantum Mechanics.Olimpia Lombardi & Dennis Dieks - forthcoming - Stanford Encyclopedia of Philosophy.
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  • An Essay towards solving a Problem in the Doctrine of Chances.T. Bayes - 1763 - Philosophical Transactions 53:370-418.
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  • The Significance of the Ergodic Decomposition of Stationary Measures for the Interpretation of Probability.Jan Von Plato - 1982 - Synthese 53 (3):419 - 432.
    De Finetti's representation theorem is a special case of the ergodic decomposition of stationary probability measures. The problems of the interpretation of probabilities centred around de Finetti's theorem are extended to this more general situation. The ergodic decomposition theorem has a physical background in the ergodic theory of dynamical systems. Thereby the interpretations of probabilities in the cases of de Finetti's theorem and its generalization and in ergodic theory are systematically connected to each other.
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  • Dispositional Probabilities.James H. Fetzer - 1970 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1970:473 - 482.
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  • What Was Born's Statistical Interpretation?Linda Wessels - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:187-200.
    The statistical interpretation introduced by Born in mid-1926 is not the interpretation now associated with his name. Born's own understanding of that interpretation is revealed by looking at some of its roots in Born's earlier work with Franck on collisions, his collaboration with Jordan on that topic, his contributions to matrix mechanics, his attempt in collaboration with Wiener at an operator formulation of quantum mechanics, and at the exposition of the interpretation in Born's first papers on a wave mechanical treatment (...)
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  • Probabilistic Explanations.James H. Fetzer - 1982 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1982:194-207.
    The purpose of this paper is to provide a systematic defense of the single-case propensity account of probabilistic explanation from the criticisms advanced by Hanna and by Humphreys and to offer a critical appraisal of the aleatory conception advanced by Humphreys and of the deductive-nomological-probabilistic approach Railton has proposed. The principal conclusion supported by this analysis is that the Requirements of Maximal Specificity and of Strict Maximal Specificity afford the foundation for completely objective explanations of probabilistic explananda, so long as (...)
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  • The Problem of Irreversibility.John Earman - 1986 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:226 - 233.
    After reviewing recent literature from physics and philosophy, it is concluded that we are still far from having a satisfying explanation of the nature and origins of irreversibility. It is proposed that the most fruitful approach to this problem is to concentrate on conditions needed for a rigorous derivation of the Boltzmann equation.
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  • The Propensity Interpretation of the Calculus of Probability, and the Quantum Theory.Karl R. Popper - 1957 - In Stefan Körner (ed.), Observation and Interpretation: A Symposium of Philosophers and Physicists. Butterworth. pp. 65--70.
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  • Quantum Theory of Probability and Decisions.David Deutsch - 1999 - Proceedings of the Royal Society of London:3129--37.
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  • The ergodic hierarchy.Roman Frigg & Joseph Berkovitz - 2011 - Stanford Encyclopedia of Philosophy.
    The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss how its applications in these fields.
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  • Theories of Probability.Terrence Fine - 1973 - Academic Press.
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  • Is there a stability problem for Bayesian noncommutative probabilities?Giovanni Valente - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (4):832-843.
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  • Everett and the Born rule.Alastair I. M. Rae - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (3):243-250.
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  • Re-conceiving quantum theories in terms of information-theoretic constraints.Armond Duwell - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (1):181-201.
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  • What could be objective about probabilities?Tim Maudlin - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):275-291.
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  • The problem of time's arrow historico-critically reexamined.Roberto Torretti - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (4):732-756.
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  • Relativistic Invariance and Modal Interpretations.John Earman & Laura Ruetsche - 2005 - Philosophy of Science 72 (4):557-583.
    A number of arguments have been given to show that the modal interpretation of ordinary nonrelativistic quantum mechanics cannot be consistently extended to the relativistic setting. We find these arguments inconclusive. However, there is a prima facie reason to think that a tension exists between the modal interpretation and relativistic invariance; namely, the best candidate for a modal interpretation adapted to relativistic quantum field theory, a prescription due to Rob Clifton, comes out trivial when applied to a number of systems (...)
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  • Von Neumann’s Entropy Does Not Correspond to Thermodynamic Entropy.Meir Hemmo & Orly Shenker - 2006 - Philosophy of Science 73 (2):153-174.
    Von Neumann argued by means of a thought experiment involving measurements of spin observables that the quantum mechanical quantity is conceptually equivalent to thermodynamic entropy. We analyze Von Neumann's thought experiment and show that his argument fails. Over the past few years there has been a dispute in the literature regarding the Von Neumann entropy. It turns out that each contribution to this dispute addressed a different special case. In this paper we generalize the discussion and examine the full matrix (...)
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  • Deterministic chaos and the nature of chance.John A. Winnie - 1996 - In John Earman & John D. Norton (eds.), The Cosmos of Science: Essays of Exploration. University of Pitsburgh Press. pp. 299--324.
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  • Determinism and Chance from a Humean Perspective.Roman Frigg & Carl Hoefer - 2010 - In Thomas Uebel, Stephan Hartmann, Wenceslao Gonzalez, Marcel Weber, Dennis Dieks & Friedrich Stadler (eds.), The Present Situation in the Philosophy of Science. Springer. pp. 351--72.
    On the face of it ‘deterministic chance’ is an oxymoron: either an event is chancy or deterministic, but not both. Nevertheless, the world is rife with events that seem to be exactly that: chancy and deterministic at once. Simple gambling devices like coins and dice are cases in point. On the one hand they are governed by deterministic laws – the laws of classical mechanics – and hence given the initial condition of, say, a coin toss it is determined whether (...)
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  • Mises redux.Richard C. Jeffrey - 2010 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. New York: Routledge.
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  • Mathematics and plausible reasoning.George Pólya - 1968 - Princeton, N.J.,: Princeton University Press.
    2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive (...)
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  • Deterministic versus indeterministic descriptions: Not that different after all?Charlotte Werndl - 2009 - In Alexander Hieke & Hannes Leitgeb (eds.), Reduction, Abstraction, Analysis. Ontos. pp. 63-78.
    The guiding question of this paper is: how similar are deterministic descriptions and indeterministic descriptions from a predictive viewpoint? The deterministic and indeterministic descriptions of concern in this paper are measure-theoretic deterministic systems and stochastic processes, respectively. I will explain intuitively some mathematical results which show that measure-theoretic deterministic systems and stochastic processes give more often the same predictions than one might perhaps have expected, and hence that from a predictive viewpoint these descriptions are quite similar.
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  • Probability: A Philosophical Introduction.D. H. Mellor - 2004 - Routledge.
    This book: * assumes no mathematical background and keeps the technicalities to a minimum * explains the most important applications of probability theory to ...
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  • The Physics of Time Asymmetry.Paul Davies - 1974 - University of California Press.
    The physics of time asymmetry has never been a single well-defined subject, but more a collection of consistency problems which arise in almost all branches ...
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  • How determinism can fail in classical physics and how quantum physics can (sometimes) provide a cure.John Earman - 2008 - Philosophy of Science 75 (5):817-829.
    Various fault modes of determinism in classical physics are outlined. It is shown how quantum mechanics can cure some forms of classical indeterminism. †To contact the author, please write to: Department of HPS, University of Pittsburgh, 1017 Cathedral of Learning, Pittsburgh, PA 15260; e‐mail: [email protected].
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  • Why typicality does not explain the approach to equilibrium.Roman Frigg - 2011 - In .
    Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of typicality-based explanations (...)
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  • On schizophrenic experiences of the neutron or why we should believe in the many‐worlds interpretation of quantum theory.Lev Vaidman - 1990 - International Studies in the Philosophy of Science 12 (3):245 – 261.
    This is a philosophical paper in favor of the many-worlds interpretation of quantum theory. The necessity of introducing many worlds is explained by analyzing a neutron interference experiment. The concept of the “measure of existence of a world” is introduced and some difficulties with the issue of probability in the framework of the MWI are resolved.
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  • Entanglement, Upper Probabilities and Decoherence in Quantum Mechanics.Patrick Suppes & Stephan Hartmann - 2009 - In Mauro Dorato et al (ed.), EPSA 2007: Launch of the European Philosophy of Science Association. Springer. pp. 93--103.
    Quantum mechanical entangled configurations of particles that do not satisfy Bell’s inequalities, or equivalently, do not have a joint probability distribution, are familiar in the foundational literature of quantum mechanics. Nonexistence of a joint probability measure for the correlations predicted by quantum mechanics is itself equivalent to the nonexistence of local hidden variables that account for the correlations (for a proof of this equivalence, see Suppes and Zanotti, 1981). From a philosophical standpoint it is natural to ask what sort of (...)
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  • Schrödinger's philosophy of quantum mechanics.Michel Bitbol - 1998 - Boston: Kluwer Academic Publishers.
    This book is the final outcome of two projects. My first project was to publish a set of texts written by Schrodinger at the beginning of the 1950's for his seminars and lectures at the Dublin Institute for Advanced Studies. These almost completely forgotten texts contained important insights into the interpretation of quantum mechanics, and they provided several ideas which were missing or elusively expressed in SchrOdinger's published papers and books of the same period. However, they were likely to be (...)
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  • Quantum theory and the schism in physics.Karl Raimund Popper - 1982 - New York: Routledge.
    The basic theme of Popper's philosophy--that something can come from nothing--is related to the present situation in physical theory. Popper carries his investigation right to the center of current debate in quantum physics. He proposes an interpretation of physics--and indeed an entire cosmology--which is realist, conjectural, deductivist and objectivist, anti-positivist, and anti-instrumentalist. He stresses understanding, reminding us that our ignorance grows faster than our conjectural knowledge.
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  • Incompleteness, Nonlocality, and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics.Michael Redhead - 1987 - New York: Oxford University Press.
    Aiming to unravel the mystery of quantum mechanics, this book is concerned with questions about action-at-a-distance, holism, and whether quantum mechanics gives a complete account of microphysical reality. With rigorous arguments and clear thinking, the author provides an introduction to the philosophy of physics.
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  • Is there a reversibility paradox? Recentering the debate on the thermodynamic time arrow.Alon Drory - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):889-913.
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  • The justification of probability measures in statistical mechanics.Kevin Davey - 2008 - Philosophy of Science 75 (1):28-44.
    According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low-entropy macrostates are less probable than high-entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law is unhelpful at best and wrong at worst, and will argue that certain puzzles sometimes associated with the (...)
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  • A Quantum Mechanical Supertask.John D. Norton - 1999 - Foundations of Physics 29 (8):1265-1302.
    That quantum mechanical measurement processes are indeterministic is widely known. The time evolution governed by the differential Schrödinger equation can also be indeterministic under the extreme conditions of a quantum supertask, the quantum analogue of a classical supertask. Determinism can be restored by requiring normalizability of the supertask state vector, but it must be imposed as an additional constraint on the differential Schrödinger equation.
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  • Boltzmann's work in statistical physics.Jos Uffink - 2008 - Stanford Encyclopedia of Philosophy.
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  • Modal interpretations of quantum mechanics.Michael Dickson - 2008 - Stanford Encyclopedia of Philosophy.
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  • Is logic empirical?Guido Bacciagaluppi - unknown
    The philosophical debate about quantum logic between the late 1960s and the early 1980s was generated mainly by Putnam's claims that quantum mechanics empirically motivates introducing a new form of logic, that such an empirically founded quantum logic is the `true' logic, and that adopting quantum logic would resolve all the paradoxes of quantum mechanics. Most of that debate focussed on the latter claim, reaching the conclusion that it was mistaken. This chapter will attempt to clarify the possible misunderstandings surrounding (...)
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  • When are probabilistic explanations possible?Patrick Suppes & Mario Zanotti - 1981 - Synthese 48 (2):191 - 199.
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  • Time, quantum mechanics, and tense.Simon Saunders - 1996 - Synthese 107 (1):19 - 53.
    The relational approach to tense holds that the now, passage, and becoming are to be understood in terms of relations between events. The debate over the adequacy of this framework is illustrated by a comparative study of the sense in which physical theories, (in)deterministic and (non)relativistic, can lend expression to the metaphysics at issue. The objective is not to settle the matter, but to clarify the nature of this metaphysics and to establish that the same issues are at stake in (...)
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  • Time, quantum mechanics, and decoherence.Simon Saunders - 1995 - Synthese 102 (2):235 - 266.
    State-reduction and the notion of actuality are compared to passage through time and the notion of the present; already in classical relativity the latter give rise to difficulties. The solution proposed here is to treat both tense and value-definiteness as relational properties or facts as relations; likewise the notions of change and probability. In both cases essential characteristics are absent: temporal relations are tenselessly true; probabilistic relations are deterministically true. The basic ideas go back to Everett, although the technical development (...)
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