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Why Equilibrium Statistical Mechanics Works: Universality and the Renormalization Group

Published online by Cambridge University Press:  01 April 2022

Robert W. Batterman
Robert W. Batterman*
Affiliation:
Department of Philosophy, Ohio State University
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Abstract

Discussions of the foundations of Classical Equilibrium Statistical Mechanics (SM) typically focus on the problem of justifying the use of a certain probability measure (the microcanonical measure) to compute average values of certain functions. One would like to be able to explain why the equilibrium behavior of a wide variety of distinct systems (different sorts of molecules interacting with different potentials) can be described by the same averaging procedure. A standard approach is to appeal to ergodic theory to justify this choice of measure. A different approach, eschewing ergodicity, was initiated by A. I. Khinchin. Both explanatory programs have been subjected to severe criticisms. This paper argues that the Khinchin type program deserves further attention in light of relatively recent results in understanding the physics of universal behavior.

Type
Research Article
Information
Philosophy of Science , Volume 65 , Issue 2 , June 1998 , pp. 183 - 208
Copyright
Copyright © Philosophy of Science Association 1998

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Footnotes

†

Send reprint requests to the author. Department of Philosophy, 350 University Hall, Ohio State University, Columbus, OH 43210.

‡

This material is based upon work supported by the National Science Foundation under Award No. SBR-9529052. I would like to thank Roger Jones, David Malament, and Abner Shimony for helpful comments and encouragement. A version of this paper was read at the 1997 APA Central division meetings in Pittsburgh. I would especially like to thank Yuri Balashov for his insightful criticisms as commentator there. I hope I have been able to address some of his worries.

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