On the uniqueness of flat thermodynamic geometries

Abstract

We investigate whether the ideal gas is the unique fluid equation of state corresponding to a flat thermodynamic geometry. Tentatively, we argue that the answer is no, and support this argument by exhibiting a choice of five virial coefficients that yield a thermodynamic curvature scalar which vanishes to fifth order in the number density. Furthermore, we see no obstructions in practice to finding coefficients that yield a curvature scalar which vanishes to all orders in the number density.