Thermodynamic stability criterion and fluctuation theory in nonextensive thermodynamics

TL;DR

This paper develops a nonextensive thermodynamic formalism with dual Legendre structures, analyzing stability criteria and fluctuation theory, emphasizing the role of physical pressure and nonadditive volume in nonextensive systems.

Contribution

It introduces a dual formalism for nonextensive thermodynamics and clarifies the physical interpretation of stability criteria and fluctuations.

Findings

Physical pressure governs mechanical balance in nonextensive systems.

Stability criterion relates to heat capacity and isothermal compressibility.

Fluctuation theory is extended to nonextensive thermodynamics.

Abstract

We have constructed a nonextensive thermodynamic formalism consisting of two sets of parallel Legendre transformation structures in previous papers. One is the physical set and the other is the Lagrange set. In this paper we study the thermodynamic stability criterion with a dual interpretation of the thermodynamic relations and quantities. By recourse to the assumption that volume in nonextenstive system is nonadditive, we conclude that it is the physical pressure that is responsible for the mechanical balance between any two parts in a given nonextensive system. It is verified that in the physical set of transformation structures, the stability criterion can be expressed in terms of heat capacity and isothermal compressibility. We also discuss the fluctuation theory in nonextensive thermodynamics.