Geodesic
Canonical distributions and phase transitions
Discussiones Mathematicae. Probability and Statistics, Tome 20 (2000) no. 2, pp. 167-176

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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: canonical distribution, canonical ensemble, Gibbs state, phase transition, entropy maximization, Rényi entropy 
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Athreya, K; Smith, J. Canonical distributions and phase transitions. Discussiones Mathematicae. Probability and Statistics, Tome 20 (2000) no. 2, pp. 167-176. http://geodesic.mathdoc.fr/item/DMPS_2000_20_2_a0/