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

TL;DR

This paper demonstrates that Tsallis entropy cannot be generalized using Kolmogorov-Nagumo averages while maintaining its pseudo-additivity property, highlighting a fundamental limitation in extending Tsallis entropy.

Contribution

It proves the non-existence of a Kolmogorov-Nagumo average-based generalization of Tsallis entropy that preserves pseudo-additivity.

Findings

No generalization of Tsallis entropy via Kolmogorov-Nagumo averages maintains pseudo-additivity.

Highlights a fundamental limitation in extending Tsallis entropy.

Contrasts with Renyi's successful generalization of Shannon entropy.

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.