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Explaining Thermodynamic-Like Behavior in Terms of Epsilon-Ergodicity

Published online by Cambridge University Press:  01 January 2022

Roman Frigg  and
Charlotte Werndl
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Abstract

Why do gases reach equilibrium when left to themselves? The canonical answer, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer is now widely regarded as flawed. We argue that some of the main objections in particular arguments based on the Kolmogorov-Arnold-Moser theorem and the Markus-Meyer theorem are beside the point. We then argue that something close to Boltzmann’s proposal is true: gases behave thermodynamic-like if they are epsilon-ergodic, that is, ergodic on the phase space except for a small region of measure epsilon. This answer is promising because there is evidence that relevant systems are epsilon-ergodic.

Type
Research Article
Information
Philosophy of Science , Volume 78 , Issue 4 , October 2011 , pp. 628 - 652
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

Authors are listed alphabetically. This work is fully collaborative. Earlier versions of this article have been presented at the 2010 British Society for the Philosophy of Science conference and at the Universities of Utrecht and Oxford; we would like to thank the audiences for valuable discussions. We also want to thank Scott Dumas, David Lavis, Pierre Lochak, and David Wallace for helpful comments. Roman Frigg also wishes to acknowledge support from the Spanish government research project FFI2008-01580/consolider ingenio CSD2009-0056.

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