Continuity of a class of entropies and relative entropies

TL;DR

This paper investigates the continuity and stability of generalized entropy and relative entropy functions based on deformed logarithms, with applications to Tsallis' nonextensive thermostatistics.

Contribution

It introduces and analyzes the continuity of a class of entropies and relative entropies, demonstrating Lesche stability, especially for Tsallis entropy.

Findings

All considered entropies satisfy Lesche's stability condition.

Two distinct definitions of relative entropy are analyzed.

Tsallis entropy examples confirm the theoretical results.

Abstract

The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an application, all considered entropies are shown to satisfy Lesche's stability condition. The entropies of Tsallis' nonextensive thermostatistics are taken as examples.