Thermal and mechanical equilibrium among weakly interacting systems in generalized thermostatistics framework

TL;DR

This paper investigates the conditions for thermal and mechanical equilibrium between weakly interacting systems within the generalized Sharma-Mittal entropy framework, analyzing stability and the roles of temperature and pressure.

Contribution

It introduces a detailed analysis of equilibrium and stability conditions in generalized thermostatistics using Sharma-Mittal entropy, connecting thermodynamic stability with entropy concavity and energy convexity.

Findings

Thermodynamic evolution is governed by temperature and pressure.

Stability conditions relate to entropy concavity and energy convexity.

Equilibrium analysis applies in both entropy and energy representations.

Abstract

We consider two statistically independent systems described by the same entropy belonging to the two-parameter family of Sharma-Mittal. Assuming a weak interaction among the systems, allowing in this way an exchange of heat and work, we analyze, both in the entropy representation and in the energy representation, the evolution toward the equilibrium. The thermodynamics evolution is controlled by two scalar quantities identified with the temperature and the pressure of the system. The thermodynamical stability conditions of the equilibrium state are analyzed in both representations. Their relationship with the concavity conditions for the entropy and with the convexity conditions for the energy are spotlighted.