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The Gibbs Paradox and the Definition of Entropy in Statistical Mechanics

Published online by Cambridge University Press:  01 January 2022

Peter M. Ainsworth
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Abstract

This article considers the Gibbs paradox and its implications for three definitions of entropy in statistical mechanics: (i) the “classical” Boltzmann entropy (SB1); (ii) the modified Boltzmann entropy that is usually proposed in response to the paradox (SB2); and (iii) a generalized version of the latter (SB2G). It is argued that (i) notwithstanding a recent suggestion to the contrary, the paradox does imply that SB1 is not a satisfactory definition of entropy; (ii) SB2 is undermined by “second-order” versions of the paradox; and (iii) SB2G solves the paradox but is not a satisfactory definition of entropy.

Type
Research Article
Information
Philosophy of Science , Volume 79 , Issue 4 , October 2012 , pp. 542 - 560
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

I am very grateful for the financial support of the Leverhulme Trust. I gave talks on the Gibbs paradox at the University of Bristol's philosophy department's “work in progress” seminar and the British Society of the Philosophy of Science's annual conference (2011); thanks to the audiences of both for helpful discussions.

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