Nongeneralizability of Tsallis Entropy by means of Kolmogorov-Nagumo averages under pseudo-additivity

Abstract

As additivity is a characteristic property of the classical information measure, Shannon entropy, pseudo-additivity is a characteristic property of Tsallis entropy. Renyi generalized Shannon entropy by means of Kolmogorov-Nagumo averages, by imposing additivity as a constraint.In this paper we show that there exists no generalization for Tsallis entropy, by means of Kolmogorov-Nagumo averages, which preserves the pseudo-additivity.