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Equilibrium in Gibbsian Statistical Mechanics

In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. London, UK: Routledge (2022)

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  1. The Dappled World: A Study of the Boundaries of Science.Nancy Cartwright - 1999 - New York, NY: Cambridge University Press.
    It is often supposed that the spectacular successes of our modern mathematical sciences support a lofty vision of a world completely ordered by one single elegant theory. In this book Nancy Cartwright argues to the contrary. When we draw our image of the world from the way modern science works - as empiricism teaches us we should - we end up with a world where some features are precisely ordered, others are given to rough regularity and still others behave in (...)
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  • Scientific reasoning: the Bayesian approach.Peter Urbach & Colin Howson - 1993 - Chicago: Open Court. Edited by Peter Urbach.
    Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...
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  • (2 other versions)The Dappled World: A Study of the Boundaries of Science.Nancy Cartwright - 1999 - Philosophy 75 (294):613-616.
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  • The Mathematical Theory of Communication.Claude E. Shannon & Warren Weaver - 1949 - University of Illinois Press.
    Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored (...)
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  • Critical Notices.Nancy Cartwright - 2003 - Philosophy and Phenomenological Research 66 (1):244-249.
    The Dappled World: A Study of the Boundaries of Science. nancy cartwright. Plato's Reception of Parmenides. john a. palmer.
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  • (1 other version)Physics and Chance.Lawrence Sklar - 1995 - British Journal for the Philosophy of Science 46 (1):145-149.
    Statistical mechanics is one of the crucial fundamental theories of physics, and in his new book Lawrence Sklar, one of the pre-eminent philosophers of physics, offers a comprehensive, non-technical introduction to that theory and to attempts to understand its foundational elements. Among the topics treated in detail are: probability and statistical explanation, the basic issues in both equilibrium and non-equilibrium statistical mechanics, the role of cosmology, the reduction of thermodynamics to statistical mechanics, and the alleged foundation of the very notion (...)
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  • A field guide to recent work on the foundations of statistical mechanics.Roman Frigg - 2008 - In Dean Rickles (ed.), The Ashgate Companion to Contemporary Philosophy of Physics. Ashgate. pp. 99-196.
    This is an extensive review of recent work on the foundations of statistical mechanics.
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  • Boltzmann's Approach to Statistical Mechanics.Sheldon Goldstein - unknown
    In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann’s analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann’s later work on the subject have little merit. Most twentieth century innovations – such as the identification of the state of a physical system with a probability distribution on its phase space, (...)
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  • Reducing thermodynamics to statistical mechanics: The case of entropy.Craig Callender - 1999 - Journal of Philosophy 96 (7):348-373.
    This article argues that most of the approaches to the foundations of statistical mechanics have severed their link with the original foundational project, the project of demonstrating how real mechanical systems can behave thermodynamically.
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  • Epsilon-ergodicity and the success of equilibrium statistical mechanics.Peter B. M. Vranas - 1998 - Philosophy of Science 65 (4):688-708.
    Why does classical equilibrium statistical mechanics work? Malament and Zabell (1980) noticed that, for ergodic dynamical systems, the unique absolutely continuous invariant probability measure is the microcanonical. Earman and Rédei (1996) replied that systems of interest are very probably not ergodic, so that absolutely continuous invariant probability measures very distant from the microcanonical exist. In response I define the generalized properties of epsilon-ergodicity and epsilon-continuity, I review computational evidence indicating that systems of interest are epsilon-ergodic, I adapt Malament and Zabell’s (...)
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  • Why ergodic theory does not explain the success of equilibrium statistical mechanics.John Earman & Miklós Rédei - 1996 - British Journal for the Philosophy of Science 47 (1):63-78.
    We argue that, contrary to some analyses in the philosophy of science literature, ergodic theory falls short in explaining the success of classical equilibrium statistical mechanics. Our claim is based on the observations that dynamical systems for which statistical mechanics works are most likely not ergodic, and that ergodicity is both too strong and too weak a condition for the required explanation: one needs only ergodic-like behaviour for the finite set of observables that matter, but the behaviour must ensure that (...)
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  • (1 other version)A field guide to recent work on the foundations of statistical mechanics.Roman Frigg - 2008 - In Dean Rickles (ed.), The Ashgate Companion to Contemporary Philosophy of Physics. Ashgate. pp. 99-196.
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  • The Principles of Statistical Mechanics.Richard C. Tolman - 1939 - Philosophy of Science 6 (3):381-381.
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  • Boltzmann and Gibbs: An attempted reconciliation.D. A. Lavis - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (2):245-273.
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  • Explaining Thermodynamic-Like Behavior in Terms of Epsilon-Ergodicity.Roman Frigg & Charlotte Werndl - 2011 - Philosophy of Science 78 (4):628-652.
    Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something (...)
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  • The Spin-Echo Experiments and the Second Law of Thermodynamics.T. M. Ridderbos & M. L. G. Redhead - 1998 - Foundations of Physics 28 (8):1237-1270.
    We introduce a simple model for so-called spin-echo experiments. We show that the model is a mincing system. On the basis of this model we study fine-grained entropy and coarse-grained entropy descriptions of these experiments. The coarse-grained description is shown to be unable to provide an explanation of the echo signals, as a result of the way in which it ignores dynamically generated correlations. This conclusion is extended to the general debate on the foundations of statistical mechanics. We emphasize the (...)
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  • Statistical explanation and ergodic theory.Lawrence Sklar - 1973 - Philosophy of Science 40 (2):194-212.
    Some philosphers of science of an empiricist and pragmatist bent have proposed models of statistical explanation, but have then become sceptical of the adequacy of these models. It is argued that general considerations concerning the purpose of function of explanation in science which are usually appealed to by such philosophers show that their scepticism is not well taken; for such considerations provide much the same rationale for the search for statistical explanations, as these philosophers have characterized them, as they do (...)
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  • Introduction to the Philosophy of Science.Merrilee H. Salmon, John Earman, Clark Glymour & James G. Lennox (eds.) - 1992 - Hackett Publishing Company.
    A reprint of the Prentice-Hall edition of 1992. Prepared by nine distinguished philosophers and historians of science, this thoughtful reader represents a cooperative effort to provide an introduction to the philosophy of science focused on cultivating an understanding of both the workings of science and its historical and social context. Selections range from discussions of topics in general methodology to a sampling of foundational problems in various physical, biological, behavioral, and social sciences. Each chapter contains a list of suggested readings (...)
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  • Implications of quantum theory in the foundations of statistical mechanics.David Wallace - manuscript
    An investigation is made into how the foundations of statistical mechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical differences are identified between classical and quantum mechanics (partly through analysis of technical work on quantum chaos by other authors). These imply that quantum mechanics significantly affects (...)
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  • Can the maximum entropy principle be explained as a consistency requirement?Jos Uffink - 1995 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 26 (3):223-261.
    The principle of maximum entropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in mathematical formulation and in intended scope, into the principle of maximum relative entropy or of minimum information. It has been claimed that these principles are singled out as unique methods of statistical inference that agree with (...)
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  • Why equilibrium statistical mechanics works: Universality and the renormalization group.Robert W. Batterman - 1998 - Philosophy of Science 65 (2):183-208.
    Discussions of the foundations of Classical Equilibrium Statistical Mechanics (SM) typically focus on the problem of justifying the use of a certain probability measure (the microcanonical measure) to compute average values of certain functions. One would like to be able to explain why the equilibrium behavior of a wide variety of distinct systems (different sorts of molecules interacting with different potentials) can be described by the same averaging procedure. A standard approach is to appeal to ergodic theory to justify this (...)
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  • The Physical Basis of the Direction of Time.Heinz Dieter Zeh - 1989 - Springer.
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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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  • Nought but molecules in motion.Jos Uffink - 1996 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 27 (3):373-387.
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  • Nonequilibrium statistical mechanics Brussels–Austin style.Robert C. Bishop - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (1):1-30.
    The fundamental problem on which Ilya Prigogine and the Brussels–Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time (...)
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  • The constraint rule of the maximum entropy principle.Jos Uffink - 1996 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 27 (1):47-79.
    The principle of maximum entropy is a method for assigning values to probability distributions on the basis of partial information. In usual formulations of this and related methods of inference one assumes that this partial information takes the form of a constraint on allowed probability distributions. In practical applications, however, the information consists of empirical data. A constraint rule is then employed to construct constraints on probability distributions out of these data. Usually one adopts the rule that equates the expectation (...)
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  • On How to Approach the Approach to Equilibrium.Joshua Luczak - 2016 - Philosophy of Science 83 (3):393-411.
    This article highlights the limitations of typicality accounts of thermodynamic behavior so as to promote an alternative line of research: understanding and accounting for the success of the techniques and equations physicists use to model the behavior of systems that begin away from equilibrium. This article also takes steps in this promising direction. It examines a technique commonly used to model the behavior of an important kind of system: a Brownian particle that has been introduced to an isolated fluid at (...)
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  • Randomness and probability in dynamical theories: On the proposals of the Prigogine school.Robert W. Batterman - 1991 - Philosophy of Science 58 (2):241-263.
    I discuss recent work in ergodic theory and statistical mechanics, regarding the compatibility and origin of random and chaotic behavior in deterministic dynamical systems. A detailed critique of some quite radical proposals of the Prigogine school is given. I argue that their conclusion regarding the conceptual bankruptcy of the classical conceptions of an exact microstate and unique phase space trajectory is not completely justified. The analogy they want to draw with quantum mechanics is not sufficiently close to support their most (...)
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  • The coarse-graining approach to statistical mechanics: how blissful is our ignorance?Katinka Ridderbos - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (1):65-77.
    In this paper I first argue that the objection which is most commonly levelled against the coarse-graining approach-viz. that it introduces an element of subjectivity into what ought to be a purely objective formalism-is ultimately unfounded. I then proceed to argue that two different objections to the coarse-graining approach indicate that it is an inadequate approach to statistical mechanics. The first objection is based on the fact that the appeal to appearances by the coarse-graining approach fails to justify the coarse-graining (...)
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  • On the brussels school's arrow of time in quantum theory.Vassilios Karakostas - 1996 - Philosophy of Science 63 (3):374-400.
    This paper examines the problem of founding irreversibility on reversible equations of motion from the point of view of the Brussels school's recent developments in the foundations of quantum statistical mechanics. A detailed critique of both their 'subdynamics' and 'transformation' theory is given. It is argued that the subdynamics approach involves a generalized form of 'coarse-graining' description, whereas, transformation theory cannot lead to truly irreversible processes pointing to a preferred direction of time. It is concluded that the Brussels school's conception (...)
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  • Reconsidering the concept of equilibrium in classical statistical mechanics.Janneke van Lith - 1999 - Philosophy of Science 66 (3):118.
    In the usual procedure of deriving equilibrium thermodynamics from classical statistical mechanics, Gibbsian fine-grained entropy is taken as the analogue of thermodynamical entropy. However, it is well known that the fine-grained entropy remains constant under the Hamiltonian flow. In this paper it is argued that we need not search for alternatives for fine-grained entropy, nor do we have to reject Hamiltonian dynamics, in order to solve the problem of the constancy of fine-grained entropy and, more generally, to account for the (...)
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  • Explaining statistical mechanics.J. P. Dougherty - 1993 - Studies in History and Philosophy of Science Part A 24 (5):843-866.
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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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  • Reductive relations in interpretations of probability.Jan Von Plato - 1981 - Synthese 48 (1):61 - 75.
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