On the equivalence between the energy and virial routes to the equation of state of hard-sphere fluids

TL;DR

This paper demonstrates that the energy and virial routes to the equation of state for hard-sphere fluids are equivalent by using a limiting approach with square-shoulder interactions.

Contribution

It introduces a method to resolve the ill-defined energy route for hard-sphere fluids by considering a limiting case of square-shoulder interactions, establishing their equivalence.

Findings

Energy and virial routes yield the same equation of state for hard-sphere fluids.

The ambiguity in the energy route is resolved via a limiting process.

The approach confirms the theoretical equivalence of the two routes.

Abstract

The energy route to the equation of state of hard-sphere fluids is ill-defined since the internal energy is just that of an ideal gas and thus it is independent of density. It is shown that this ambiguity can be avoided by considering a square-shoulder interaction and taking the limit of vanishing shoulder width. The resulting hard-sphere equation of state coincides exactly with the one obtained through the virial route. Therefore, the energy and virial routes to the equation of state of hard-sphere fluids can be considered as equivalent.