Comments on "A two-parameter generalization of Shannon-Khinchin Axioms and the uniqueness theorem"

TL;DR

This paper corrects and extends a two-parameter entropy class originally proposed by Wada and Suyari, deriving a consistent class of entropies using the maxent principle and axiomatic approaches.

Contribution

It fixes errors in Wada and Suyari's entropy class and shows equivalence with a maxent-derived class through modified initial conditions.

Findings

Corrected the Wada-Suyari entropy class.

Established equivalence with a maxent-derived entropy class.

Provided a consistent two-parameter entropy framework.

Abstract

Wada and Suyari proposed a two-parameter generalization of Shannon-Khinchin axioms (TGSK axioms) [T. Wada and H. Suyari, Physics Letters A, 368(3)]. We derive a new class of entropies which differs from Wada-Suyari's class by fixing the incorrectness which occurs in the mentioned paper. Also, we consider a two-parameter class of entropies derived from the maxent principle proposed in [Kaniadakis, G. and Lissia, M. and Scarfone, AM, Physica A: Statistical Mechanics and its Applications, 340(1)]. We rederived this class by changing initial condition, obtaining the same class as our class derived from TGSK axioms.