Thermodynamic stability conditions for nonadditive composable entropies

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.Comment: 6pages; Contribution to a topical issue of Continuum Mechanics and Thermodynamics (CMT), edited by M. Sugiyam