Escort entropies and divergences and related canonical distribution

TL;DR

This paper introduces two-parameter families of entropies and divergences derived from Rényi and Tsallis frameworks, exploring their properties and deriving associated canonical distributions that unify and extend nonextensive thermodynamics results.

Contribution

It presents new two-parameter entropies and divergences based on escort distributions, and derives canonical distributions that generalize existing thermodynamic models.

Findings

Derived explicit forms of new entropies and divergences.

Established the canonical distribution associated with these entropies.

Connected the new framework with existing nonextensive thermodynamics results.

Abstract

We discuss two families of two-parameter entropies and divergences, derived from the standard R\'enyi and Tsallis entropies and divergences. These divergences and entropies are found as divergences or entropies of escort distributions. Exploiting the nonnegativity of the divergences, we derive the expression of the canonical distribution associated to the new entropies and a observable given as an escort-mean value. We show that this canonical distribution extends, and smoothly connects, the results obtained in nonextensive thermodynamics for the standard and generalized mean value constraints.