Shannon, Levy, and Tsallis: A Note

Pushpa Rathie, University of Brasilia
Sergio Da Silva, Federal University of Santa Catarina

Abstract

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 Levy stable distributions. The Tsallis distribution is found to be just one special case of the Levy, and not the other way around.