Comments on "On q-non-extensive statistics with non-Tsallisian entropy"

TL;DR

This paper critiques a recent derivation of a generalized entropy based on GSK axioms, corrects the derivation, and proposes a new axiomatic framework for such entropies, emphasizing their role in generalized statistical mechanics.

Contribution

It identifies a flaw in the previous derivation of a generalized entropy and introduces a new axiomatic system to accurately characterize these entropies.

Findings

The original entropy class violates the fourth GSK axiom.

A corrected entropy class consistent with all GSK axioms is derived.

A new axiomatic system for generalized entropies is proposed.

Abstract

Recently, in [P. Jizba and J. Korbel, Physica A 444, 2016, 808-827], four generalized Shannon-Khinchin [GSK] axioms have been proposed and a generalized entropy which uniquely satisfies the GSK axioms has been derived. In this comment, we show that the unique class of the entropies derived in the aforementioned paper is not correct, as it violates the fourth GSK axiom, and we derive the correct one. Nevertheless, the class of entropies proposed in the commented paper still can serve as a basis for generalized statistical mechanics. We propose a new axiomatic system which characterizes the class of entropies.