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ArticleOriginal scientific text

Title

Canonical distributions and phase transitions

Authors 1, 2

Affiliations

  1. School of Operations Research and Industrial Engineering Cornell University, Ithaca, NY 14853, USA
  2. Department of Mathematics, Iowa State University, Ames, IA 50011, USA

Abstract

Entropy maximization subject to known expected values is extended to the case where the random variables involved may take on positive infinite values. As a result, an arbitrary probability distribution on a finite set may be realized as a canonical distribution. The Rényi entropy of the distribution arises as a natural by-product of this realization. Starting with the uniform distributionon a proper subset of a set, the canonical distribution of equilibriumstatistical mechanics may be used to exhibit an elementary phase transition, characterized by discontinuity of the partition function.

Keywords

ENG
canonical distribution, canonical ensemble, Gibbs state, phase transition, entropy maximization, Rényi entropy

Bibliography

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Discussiones Mathematicae Probability and Statistics
2000/20/2
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Pages:
167-176
Main language of publication
English
Received
1999-02-03
Accepted
2000-03-15
Published
2000

DOI: 10.7151/dmps.1009

Exact and natural sciences