Thermodynamic consistency between the energy and virial routes in the mean spherical approximation for soft potentials

TL;DR

This paper proves that for soft potentials with finite Fourier transforms, the virial and energy routes yield equivalent thermodynamic results within a broad class of approximations, including the mean spherical approximation.

Contribution

It establishes a general proof of thermodynamic consistency between the virial and energy routes for a class of soft potential approximations.

Findings

Virial and energy routes are equivalent for soft potentials with finite Fourier transforms.

The proof applies to a broad class of approximations including the mean spherical approximation.

Thermodynamic consistency is established for these approximations.

Abstract

It is proven that, for any soft potential characterized by a finite Fourier transform $\widetilde{\phi}(k)$, the virial and energy thermodynamic routes are equivalent for approximations such that the Fourier transform of the total correlation function divided by the density $\rho$ is an arbitrary function of $\rho\beta\widetilde{\phi}(k)$, where $\beta$ is the inverse temperature. This class includes the mean spherical approximation as a particular case.