Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-06-13T03:35:27.107Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermodynamic Entropy and Its Relation to Probability in Classical Mechanics

Published online by Cambridge University Press:  01 January 2022

Kevin Davey
Get access Rights & Permissions [Opens in a new window]

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
Information
Philosophy of Science , Volume 78 , Issue 5 , December 2011 , pp. 955 - 975
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.)

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 75:28–44.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., 39–54. 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