Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-11T08:25:39.341Z Has data issue: false hasContentIssue false
  • English
  • Français

Why Gibbs Phase Averages Work—The Role of Ergodic Theory

Published online by Cambridge University Press:  01 April 2022

David B. Malament  and
Sandy L. Zabell
David B. Malament
Affiliation:
University of Chicago
Sandy L. Zabell
Affiliation:
University of Chicago
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose an “explanation scheme” for why the Gibbs phase average technique in classical equilibrium statistical mechanics works. Our account emphasizes the importance of the Khinchin-Lanford dispersion theorems. We suggest that ergodicity does play a role, but not the one usually assigned to it.

Type
Research Article
Information
Philosophy of Science , Volume 47 , Issue 3 , September 1980 , pp. 339 - 349
Copyright
Copyright © 1980 by 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

†

An earlier version of the paper was presented at the October 1978 meetings of the Philosophy of Science Association. Lawrence Sklar was the commentator. We are grateful to him and to Howard Stein for their remarks.

Support for this research was provided in part by National Science Foundation Grants Nos. SOC78-25046(D.M.) and MCS76-81435(S.Z.).

References

Billingsley, P. (1979), Probability and Measure. New York: Wiley.Google Scholar
Feller, W. (1971), An Introduction to Probability and Theory and its Applications, Vol. II (2nd ed.). New York: Wiley.Google Scholar
Friedman, K. S. (1976), “A Partial Vindication of Ergodic Theory,” Philosophy of Science 43: 151–162.CrossRefGoogle Scholar
Halmos, P. (1950), Measure Theory. Princeton: van Nostrand.CrossRefGoogle Scholar
Jaynes, E. T. (1973), “The Well-Posed Problem,” Foundations of Physics 3: 477–492.CrossRefGoogle Scholar
Khinchin, A. I. (1949), Mathematical Foundations of Statistical Mechanics. New York: Dover.Google Scholar
Lanford, O. (1973), “Entropy and Equilibrium States in Classical Statistical Mechanics,” in Statistical Mechanics and Mathematical Problems, Lenard, A. (ed.), Springer Verlag: 1–113.Google Scholar
Lavis, D. (1977), “The Role of Statistical Mechanics in Classical Physics,” British Journal for the Philosophy of Science 28: 255–279.CrossRefGoogle Scholar
Lebowitz, J. and Penrose, O. (1973), “Modern Ergodic Theory,” Physics Today 26: 23–29.CrossRefGoogle Scholar
Quay, P. (1978), “A Philosophical Explanation of the Explanatory Functions of Ergodic Theory,” Philosophy of Science 45: 47–59.Google Scholar
Rudin, W. (1959), “Measure Algebras on Abelian Groups,” Bulletin American Mathematical Society 65: 227–247.CrossRefGoogle Scholar
Sklar, L. (1973), “Statistical Explanation and Ergodic Theory,” Philosophy of Science 40: 194–212.CrossRefGoogle Scholar