Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T12:16:48.769Z Has data issue: false hasContentIssue false
  • English
  • Français

The Gibbs Paradox and the Definition of Entropy in Statistical Mechanics

Published online by Cambridge University Press:  01 January 2022

Peter M. Ainsworth
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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