Interacting systems with zero thermodynamic curvature

TL;DR

This paper explores the concept of zero thermodynamic curvature in interacting systems, demonstrating that such systems can have nontrivial interactions and proposing an extension to Ruppeiner's conjecture.

Contribution

It reveals the existence of systems with zero curvature but nontrivial interactions and discusses two viable Ruppeiner metrics, extending the understanding of thermodynamic geometry.

Findings

Existence of systems with zero curvature and nontrivial interactions.

The ideal gas is the only system with both curvature scalars vanishing.

Proposed an extension to Ruppeiner's conjecture.

Abstract

We review a conjecture by Ruppeiner that relates the nature of interparticle interactions to the sign of the thermodynamic curvature scalar $R$, paying special attention to the case of zero curvature. We highlight the underappreciated fact that there are two Ruppeiner metrics that are equally viable in principle, which are obtained by restricting to systems of constant volume and constant particle number, respectively. We then demonstrate the existence of thermodynamic systems with vanishing curvature scalar but nontrivial interactions. Information about interactions in these systems is obtained by carrying out an inversion procedure on the virial coefficients. Finally, we show using the virial expansion that the ideal gas is the unique physical system for which both curvature scalars vanish. This leads us to propose an extension to Ruppeiner's conjecture.