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Shannon, Lévy, and Tsallis: a note. (English) Zbl 1154.94351
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.

94A17Measures of information, entropy
82C05Classical dynamic and nonequilibrium statistical mechanics (general)
60G20Generalized stochastic processes
60G51Processes with independent increments; Lévy processes
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