Comments on "Nonextensive Entropies derived from Form Invariance of Pseudoadditivity"

TL;DR

This paper critically examines Suyari's axiomatic framework for nonextensive information content, broadening the class of functions considered and proposing a modified, more intuitive set of axioms.

Contribution

It expands the class of functions satisfying Suyari's axioms and introduces a modified axiomatic system with weaker, more intuitive conditions.

Findings

Havrda-Charvat entropy's information content satisfies Suyari's axioms

The class of functions satisfying Suyari's axioms is broader than originally defined

Some axioms are redundant and can be replaced with weaker conditions

Abstract

Recently, Suyari has defined nonextensive information content measure with unique class of functions which satisfies certain set of axioms. Nonextensive entropy is then defined as the appropriate expectation value of nonextensive information content [H. Suyari, Phys. Rev E 65 066118 (2002)]. In this comment we show that the class of functions determined by Suyari's axioms is actually wider than the one given by Suyari and we determine the class. Particularly, an information content corresponding to Havrda-Charvat entropy satisfies Suyari's axioms and does not belong to the class given by Suyari but belongs to our class. Moreover, some of the conditions from Suyari's set of axioms are redundant, and some of them can be replaced with more intuitive weaker ones. We give a modification of Suyari's axiomatic system with these weaker assumptions and define the corresponding information content measure.