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.

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

References in corpus (5)

• Statistical mechanics in the context of special relativity
• Non Linear Kinetics underlying Generalized Statistics
• General pseudoadditivity of composable entropy prescribed by existence of equilibrium
• A new one parameter deformation of the exponential function
• On the thermodynamic stability conditions of Tsallis' entropy

Cited by in corpus (13)

• Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions
• Maximum entropy principle and power-law tailed distributions
• Relativistic Entropy and Related Boltzmann Kinetics
• Thermodynamic equilibrium and its stability for Microcanonical systems described by the Sharma-Taneja-Mittal entropy
• k-Deformed Fourier Transform
• Physical origin of the power-law tailed statistical distributions
• Relativistic Roots of $\kappa$-Entropy
• Relativistic kinetics and power-law tailed distributions
• Power-Law tailed statistical distributions and Lorentz transformations
• Properties of the Nonextensive Gaussian entropy
• Thermal and mechanical equilibrium among weakly interacting systems in generalized thermostatistics framework
• Intensive variables in the framework of the non-extensive thermostatistics
• Composable entropy and deviation from macroscopic equilibrium