Comment on "Third Law of thermodynamics as a key test of generalized entropies"

TL;DR

This paper critically examines previous claims about the violation of the third law of thermodynamics by Tsallis entropy, clarifying the conditions under which the entropy maximization is valid.

Contribution

It demonstrates that Tsallis entropy does not violate the third law for certain q-intervals because no maximizing distribution exists there.

Findings

Tsallis entropy maximization is valid only for q ≥ 1.

No distribution maximizes Tsallis entropy for q ≤ 0 and 0<q<1.

Previous claims about violations are based on invalid assumptions.

Abstract

Bento \textit{et al.} [Phys. Rev. E 91, 022105 (2015)] state that the Tsallis entropy violates the third law of thermodynamics for $q \leq 0$ and $0<q<1$. We show that their results are valid only for $q \geq 1$, since there is no distribution maximizing the Tsallis entropy for the intervals $q \leq 0$ and $0<q<1$ compatible with the system energy expression.