Comment on "Generalized Shannon--Khinchin axioms and uniqueness theorem for pseudo-additive entropies" [Physica A 411 (2014) 138]

TL;DR

This paper discusses issues raised about hybrid entropies in statistical thermodynamics, attributing problems to specific mathematical rules, but concludes they remain useful in most applications.

Contribution

It clarifies the source of problems in hybrid entropies and affirms their continued applicability despite identified issues.

Findings

Problems linked to q-additive chain rule and escort distribution relations

Hybrid entropies remain useful in statistical thermodynamics

Clarification of mathematical foundations of hybrid entropies

Abstract

Recently in [Physica A 411 (2014) 138] Ili\'{c} and Stankovi\'{c} have suggested that there may be problem for the class of hybrid entropies introduced in [P.~Jizba and T.~Arimitsu, Physica A 340 (2004) 110]. In this Comment we point out that the problem can be traced down to the $q$-additive entropic chain rule and to a peculiar behavior of the DeFinetti--Kolmogorov relation for escort distributions. However, despite this, one can still safely use the proposed hybrid entropies in most of the statistical-thermodynamics considerations.