Equation of state for five-dimensional hyperspheres from the chemical-potential route

TL;DR

This paper derives an analytical equation of state for five-dimensional hard hyperspheres using the chemical-potential route, comparing it with other methods and analyzing deviations from simulation data.

Contribution

It introduces an analytical expression for the contact value of the pair distribution function in five dimensions and compares multiple thermodynamic routes for the first time.

Findings

All routes are exact up to third density order.

Compressibility and chemical-potential routes show smaller deviations from simulations than the virial route.

Linear interpolations improve the accuracy of the equation of state.

Abstract

We use the Percus-Yevick approach in the chemical-potential route to evaluate the equation of state of hard hyperspheres in five dimensions. The evaluation requires the derivation of an analytical expression for the contact value of the pair distribution function between particles of the bulk fluid and a solute particle with arbitrary size. The equation of state is compared with those obtained from the conventional virial and compressibility thermodynamic routes and the associated virial coefficients are computed. The pressure calculated from all routes is exact up to third density order, but it deviates with respect to simulation data as density increases, the compressibility and the chemical-potential routes exhibiting smaller deviations than the virial route. Accurate linear interpolations between the compressibility route and either the chemical-potential route or the virial one are constructed.