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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1009,
author = {K.B. Athreya and J.D.H. Smith},
title = {Canonical distributions and phase transitions},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {20},
year = {2000},
pages = {167-176},
zbl = {0978.82036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1009}
}
K.B. Athreya; J.D.H. Smith. Canonical distributions and phase transitions. Discussiones Mathematicae Probability and Statistics, Tome 20 (2000) pp. 167-176. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1009/
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