Thermodynamic stability conditions for nonadditive composable entropies

TL;DR

This paper examines the thermodynamic stability conditions of nonadditive, composable entropies, revealing that for Tsallis and κ-generalized entropies, stability is linked to positive heat capacity, regardless of entropy concavity.

Contribution

It clarifies the relationship between stability conditions and entropy properties for nonadditive entropies, challenging the assumption that concavity alone ensures stability.

Findings

TSC of Tsallis entropy is equivalent to positive heat capacity.

TSC of κ-generalized Boltzmann entropy is also linked to positive heat capacity.

Concavity of entropy does not necessarily imply thermodynamic stability.

Abstract

The thermodynamic stability conditions (TSC) of nonadditive and composable entropies are discussed. Generally the concavity of a nonadditive entropy with respect to internal energy is not necessarily equivalent to the corresponding TSC. It is shown that both the TSC of Tsallis' entropy and that of the $\kappa$-generalized Boltzmann entropy are equivalent to the positivity of the standard heat capacity.