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What Is Gibbs's Canonical Distribution?

Published online by Cambridge University Press:  01 January 2022

Kevin Davey
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Abstract

Although the canonical distribution is one of the central tools of statistical mechanics, the reason for its effectiveness is poorly understood. This is due in part to the fact that there is no clear consensus on what it means to use the canonical distribution to describe a system in equilibrium with a heat bath. I examine some traditional views as to what sort of thing we should take the canonical distribution to represent. I argue that a less explored alternative, according to which the canonical distribution represents a time ensemble of sorts, has a number of advantages that rival interpretations lack.

Type
Research Article
Information
Philosophy of Science , Volume 76 , Issue 5 , December 2009 , pp. 970 - 983
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

Thanks to Brandon Fogel, Nick Huggett, and John Norton for their feedback and suggestions.

References

Boltzmann, L. (1964), Lectures on Gas Theory. Berkeley: University of California Press.CrossRefGoogle Scholar
Earman, J., and Redei, M. (1996), “Why Ergodic Theory Does Not Explain the Success of Statistical Mechanics”, Why Ergodic Theory Does Not Explain the Success of Statistical Mechanics 47:63–78.Google Scholar
Einstein, A. (1903), “A Theory of the Foundations of Thermodynamics”, A Theory of the Foundations of Thermodynamics 11:170–187.Google Scholar
Ford, G., Kac, M., and Mazur, P. (1965), “Statistical Mechanics of Assemblies of Coupled Oscillators”, Statistical Mechanics of Assemblies of Coupled Oscillators 6 (4): 504–515..Google Scholar
Gibbs, J. Willard (1981), Elementary Principles in Statistical Mechanics. Woodbridge, CT: Ox Bow.Google Scholar
Huerta, M., and Robertson, H. (1969), “Entropy, Information Theory, and the Approach to Equilibrium of Coupled Harmonic Oscillator Systems”, Entropy, Information Theory, and the Approach to Equilibrium of Coupled Harmonic Oscillator Systems 1 (3): 393–414..Google Scholar
Huerta, M., and Robertson, H. (1971), “Approach to Equilibrium of Coupled Harmonic Oscillator Systems II”, Approach to Equilibrium of Coupled Harmonic Oscillator Systems II 3 (2): 171–189..Google Scholar
Malament, D., and Zabell, S. (1980), “Why Gibbs Phase Averages Work—the Role of Ergodic Theory”, Why Gibbs Phase Averages Work—the Role of Ergodic Theory 47:339–349.Google Scholar
Sklar, L. (1993), Physics and Chance. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Tegmark, M., and Yeh, L. (1994), “Steady States of Harmonic Oscillator Chains and Shortcomings of Harmonic Heat Baths”, Steady States of Harmonic Oscillator Chains and Shortcomings of Harmonic Heat Baths 202:342–262.Google Scholar