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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.

References

Denbigh, Kenneth G., and Redhead, Michael L. G.. 1989. “Gibbs’ Paradox and Non-uniform Convergence.” Synthese 81 (3): 283–312.CrossRefGoogle Scholar
Dieks, Dennis. 2011. “The Gibbs Paradox Revisited.” In Explanation, Prediction, and Confirmation, ed. Dieks, D., Gonzalez, W. J., Hartmann, S., Uebel, T., and Weber, M., 367–77. Dordrecht: Springer.CrossRefGoogle Scholar
Gibbs, J. Willard. 1875/1931. “On the Equilibrium of Heterogeneous Substances.” Repr. in The Collected Works of J. Willard Gibbs, Vol. 1, Thermodynamics, 55–353. New York: Longman.Google Scholar
Jaynes, Edwin T. 1992. “The Gibbs Paradox.” In Maximum Entropy and Bayesian Methods, ed. Smith, C. R., Erickson, G. J., and Neudorfer, P. O., 1–22. Dordrecht: Kluwer.Google Scholar
Nagle, John F. 2004. “Regarding the Entropy of Distinguishable Particles.” Journal of Statistical Physics 117 (5–6): 1047–62.CrossRefGoogle Scholar
Schrödinger, Erwin. 1946. Statistical Thermodynamics. Cambridge: Cambridge University Press.Google Scholar
Swendsen, Robert H. 2002. “Statistical Mechanics of Classical Systems with Distinguishable Particles.” Journal of Statistical Physics 107 (5–6): 1143–66.CrossRefGoogle Scholar
Swendsen, Robert H.. 2006. “Statistical Mechanics of Colloids and Boltzmann's Definition of the Entropy.” American Journal of Physics 74 (3): 187–90.CrossRefGoogle Scholar
Swendsen, Robert H.. 2008. “Gibbs’ Paradox and the Definition of Entropy.” Entropy 10:15–18.CrossRefGoogle Scholar
Van Kampen, N. G. 1984. “The Gibbs Paradox.” In Essays in Theoretical Physics: In Honour of Dirk ter Haar, ed. Parry, W. E., 303–12. Oxford: Pergamon.Google Scholar
Versteegh, Marijn A. M., and Dieks, Dennis. 2011. “The Gibbs Paradox and the Distinguishability of Identical Particles.” American Journal of Physics 79 (7): 741–46.CrossRefGoogle Scholar