Maximum entropy principle for Renyi's and Tsallis' entropies

TL;DR

This paper rederives the equilibrium probability distributions that maximize Renyi and Tsallis entropies, introducing new normalized forms that differ from traditional partition function-based forms.

Contribution

It presents novel S-forms of the maximum entropy distributions for Renyi and Tsallis entropies, normalized with their respective entropies.

Findings

New S-forms of equilibrium distributions derived

Distributions normalized with entropies instead of partition functions

Provides alternative formulations for non-extensive entropy maximization

Abstract

The equilibrium distributions of probabilities providing maximality of Renyi and Tsallis entropies are rederived. New S-forms of them are found which are normalised with corresponding entropies in contrast to the usual Z-forms normalised with partition functions.