Comments on "Generalization of Shannon-Khinchin axioms to nonextensive systems and the uniqueness theorem for the nonextensive entropy"

TL;DR

This paper critiques Suyari's generalization of Shannon-Khinchin axioms, showing the class of entropies it defines is broader than originally proposed and providing a counterexample, while also generalizing the axioms for a new class of entropies.

Contribution

It demonstrates that Suyari's axioms encompass a wider class of entropies than initially claimed and extends these axioms to include recently introduced entropy classes.

Findings

Suyari's axioms define a broader entropy class than previously thought.

A counterexample shows the class is wider than Suyari's original proposal.

Generalized axioms include entropies based on pseudoadditive information content.

Abstract

Recently, Suyari has proposed a generalization of Shannon-Khinchin axioms, which determines a class of entropies containing the well-known Tsalis and Havrda-Charvat entropies [H. Suyari, IEEE Trans. Inf. Theory, vol. 50, pp. 1783-1787, Aug. 2004]. In this comment we show that the class of entropy functions determined by Suyari's axioms is wider than the one proposed by Suyari and give a counterexample. Additionally, we generalize Suyari's axioms characterizing recently introduced class of entropies obtained by averaging pseudoadditive information content introduced in [V. Ilic and M. Stankovic, "Comments on "Nonextensive Entropies derived from Form Invariance of Pseudoadditivity"" Submited, 2012].