Remarks on the Pseudo-Additivity in the Axiomatization of Tsallis Entropy

Abstract

In this paper, we discuss the application of pseudo-additivity in axiomatic systems developed for Tsallis entropy and the influence of independence of systems in the entropy of composition. Although the axiomatization of Tsallis entropy has a long history and various axiomatic systems based on pseudo-additivity have been proposed, there are still unresolved questions. We present an overview of such axiomatic systems and highlight some topics, in particular theoretical considerations or some applications, which can be viewed as bottlenecks of a concrete system. Then, we offer solutions for these critical topics, which can be viewed as a contribution to the axiomatization of Tsallis entropy.