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Zbl 1154.94351
Rathie, P.N.; Da Silva, S.
Shannon, Lévy, and Tsallis: A note. (English)
[J] Appl. Math. Sci., Ruse 2, No. 25-28, 1359-1363 (2008). ISSN 1312-885X; ISSN 1314-7552/e

Summary: The Tsallis nonextensive entropy of the statistical physics literature exactly matches the previously defined Havrda-Charvat structural $\alpha$-entropy of information theory. We offer three novel results by optimizing Shannon and Havrda-Charvat entropies under different sets of conditions. The results yield generalized $t$-distributions that encompass the entire family of Lévy stable distributions. The Tsallis distribution is found to be just one special case of the Lévy, and not the other way around.

MSC 2000:: *94A17 Measures of information
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
60G20 Generalized stochastic processes
60G52 Stable processes

Keywords: Shannon entropy; Gibbs extensive entropy; Havrda-Charvat structural $\alpha$-entropy; Tsallis nonextensive entropy; Lévy stable distributions

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