2024/09/28 by Ian Vega, Rodrigo, Juan, Vega, Ian · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cosmology and Gravitation Theories #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2409.19264
openalex publication_date 2024/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.