Validity of the third law of thermodynamics for the Tsallis entropy

TL;DR

This paper demonstrates that Tsallis entropy adheres to the third law of thermodynamics across all regimes when using complete deformed functions, correcting previous claims of violations in certain parameter ranges.

Contribution

It clarifies the validity of the third law for Tsallis entropy by employing complete deformed functions, resolving prior misconceptions about its regime-dependent violations.

Findings

Tsallis entropy satisfies the third law for all q values when using complete functions.

The division between regimes q<1 and q>1 is inherent in the deformed functions' structure.

Escort-averaging is unnecessary with the complete deformed functions.

Abstract

Bento \textit{et al.} [Phys. Rev. E 91, 022105 (2015)] recently stated that the Tsallis entropy violates the third law of thermodynamics for $0 < q <1$ in the sub-additive regime. We first show that the division between the regimes $q < 1$ and $q > 1$ is already inherent in the fundamental incomplete structure of the deformed logarithms and exponentials underlying the Tsallis entropy. Then, we provide the complete deformed functions and show that the Tsallis entropy conforms to the third law of thermodynamics for both super-additive $q < 1$ and sub-additive $q > 1$ regimes. Finally, we remark that the Tsallis entropy does not require the use of escort-averaging scheme once it is expressed in terms of the complete deformed functions.