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Thermodynamic Entropy and Its Relation to Probability in Classical Mechanics

Published online by Cambridge University Press:  01 January 2022

Abstract

A gas relaxing into equilibrium is often taken to be a process in which a system moves from an “improbable” to a “probable” state. Given that the thermodynamic entropy increases during such a process, it is natural to conjecture that the thermodynamic entropy is a measure of the probability of a macrostate. For nonideal classical gases, however, I claim that there is no clear sense in which the thermodynamic entropy of a macrostate measures its probability. We must therefore reject the idea that (in classical mechanics) thermodynamic entropy and probability are connected in a deep and general way.

Type
Research Article
Copyright
Copyright © The Philosophy of Science Association

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References

Adib, A. 2004. “Does the Boltzmann Principle Need a Dynamical Correction?”Journal of Statistical Physics 117 (3/4): 581–97.CrossRefGoogle Scholar
Berdichevskii, V. 1988. “The Connection between Thermodynamic Entropy and Probability.”Journal of Applied Mathematics and Mechanics 52 (6): 947–57.CrossRefGoogle Scholar
Callendar, C. 1999. “Reducing Thermodynamics to Statistical Mechanics: The Case of Entropy.”Journal of Philosophy 96 (7): 348–73.Google Scholar
Campisi, M. 2005. “On the Mechanical Foundations of Thermodynamics: The Generalized Helmholtz Theorem.”Studies in History and Philosophy of Modern Physics 36:275–90.CrossRefGoogle Scholar
Davey, K. 2008. “Justification in Statistical Mechanics.”Philosophy of Science 75:2844.CrossRefGoogle Scholar
Fowler, R. H. 1955. Statistical Mechanics: The Theory of the Properties of Matter in Equilibrium. Cambridge: Cambridge University Press.Google Scholar
Gallavotti, G. 1999. Statistical Mechanics: A Short Treatise. Berlin: Springer.CrossRefGoogle Scholar
Gibbs, J. 1981. Elementary Principles in Statistical Mechanics. Woodbridge, CT: Ox Bow.Google Scholar
Goldstein, S. 2001. “Boltzmann's Approach to Statistical Mechanics.” In Chance in Physics: Foundations and Perspectives, ed. Bricmont, J. et al., 3954. New York: Springer.CrossRefGoogle Scholar
Helmholtz, H. 1884a. “Principien der Statik monocyklischer Systeme.” Borchardt-Crelles Journal für die reine und angewandte Mathematik 97:111–40. Repr. in Wissenschafltliche Abhandlungen, Vol. 3, ed. G. Wiedemann, 142–62, 179–202 (Leipzig: Barth, 1895).Google Scholar
Helmholtz, H.. 1884b. “Studien zur Statik monocyklischer Systeme.” Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin 1:159–77. Repr. in Wissenschafltliche Abhandlungen, Vol. 3, ed. G. Wiedemann, 163–78 (Leipzig: Barth, 1895).Google Scholar
Hertz, P. 1910. “Uber die mechanischen Grundlagen der Thermodynamik.”Annals of Physics 338 (13): 537–52.Google Scholar
Huang, K. 1963. Statistical Mechanics. Hoboken, NJ: Wiley.Google Scholar
Jaynes, E. T. 1965. “Gibbs vs Boltzmann Entropies.”American Journal of Physics 33:391–98.CrossRefGoogle Scholar
Khinchin, A. I. 1949. Mathematical Foundations of Statistical Mechanics. New York: Dover.Google Scholar