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Epsilon-Ergodicity and the Success of Equilibrium Statistical Mechanics

Published online by Cambridge University Press:  01 April 2022

Peter B. M. Vranas
Peter B. M. Vranas*
Affiliation:
Department of Philosophy, University of Michigan
*
†Send requests for reprints to the author, Department of Philosophy, The University of Michigan, 2215 Angeli Hall, Ann Arbor MI 48109, USA; e-mail: vranas@umich.edu.
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Abstract

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 defense of absolute continuity to support epsilon-continuity, and I prove that, for epsilon-ergodic systems, every epsilon-continuous invariant probability measure is very close to the microcanonical.

Type
Research Article
Information
Philosophy of Science , Volume 65 , Issue 4 , December 1998 , pp. 688 - 708
Copyright
Copyright © Philosophy of Science Association 1998

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Footnotes

‡

I am very grateful to Robert Batterman, James Joyce, and Lawrence Sklar for extensive discussion. Thanks also to Stephen Leeds, David Malament, and Peter Railton for help. Versions of this paper were presented at the seventy-second annual meeting of the Pacific Division of the American Philosophical Association (Los Angeles, March 1998) and at the Twentieth World Congress of Philosophy (Boston, August 1998).

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