Thermodynamics of extensive but nonadditive systems: modified Gibbs-Duhem equation in the dipolar gas

TL;DR

This paper explores the thermodynamics of nonadditive systems, demonstrating that shape-dependent entropy leads to violations of the Gibbs-Duhem equation, with numerical and experimental implications for dipolar gases.

Contribution

It introduces a modified Gibbs-Duhem equation for nonadditive systems and confirms its violation through numerical analysis of dipolar gases.

Findings

Shape dependence of entropy density causes Gibbs-Duhem violation.

Numerical evidence confirms the violation in dipolar gases.

Potential observability in cold-atom experiments.

Abstract

Thermodynamic properties of extensive but nonadditive systems are investigated. The precise definitions of additivity and extensivity are presented, and we will see that additivity derives several important properties including the shape-independence of the thermodynamic functions, the concavity of the entropy, and the equivalence of ensembles. In nonadditive systems, some of the above properties can be violated. It is pointed out that the shape-dependence of the entropy density in a nonadditive system results in the violation of the Gibbs-Duhem equation. As an example, the dipolar gas is numerically studied and the violation of the Gibbs-Duhem equation is confirmed. The predicted violation of the Gibbs-Duhem equation should be observable in cold-atom experiment with polarized dipolar gas.