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Boltzmann, Gibbs, and the Concept of Equilibrium

Published online by Cambridge University Press:  01 January 2022

David A. Lavis
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Abstract

The Boltzmann and Gibbs approaches to statistical mechanics have very different definitions of equilibrium and entropy. The problems associated with this are discussed, and it is suggested that they can be resolved, to produce a version of statistical mechanics incorporating both approaches, by redefining equilibrium not as a binary property (being/not being in equilibrium) but as a continuous property (degrees of equilibrium) measured by the Boltzmann entropy and by introducing the idea of thermodynamic-like behavior for the Boltzmann entropy. The Kac ring model is used as an example to test the proposals.

Type
New Approaches to Equilibrium in Thermodynamics and Statistical Mechanics
Information
Philosophy of Science , Volume 75 , Issue 5: Proceedings of the 2006 Biennial Meeting of the Philosophy of Science Association. Part II: Symposia Papers. Edited by Cristina Bicchieri and Jason Alexander , December 2008 , pp. 682 - 696
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

This is a modified version of the paper presented at the twentieth biennial meeting of the Philosophy of Science Association, Vancouver, Canada, November 2006. I am grateful to the organizers for giving me the opportunity to contribute to the conference and to Roman Frigg for many useful discussions.

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