Interacting fluids in an arbitrary external field

TL;DR

This paper introduces a new method for analyzing the equilibrium properties of interacting fluids under arbitrary external fields, providing exact solutions in one dimension and a recurrence relation for three-dimensional cases.

Contribution

The paper develops a novel, exact method applicable in any dimension for studying interacting fluids, including a recurrence relation for the pair distribution function in 3D.

Findings

Exact results for 1D systems match previous methods

Derived explicit entropy and free energy functionals

Recurrence relation for 3D pair distribution functions

Abstract

We present new method for studying the equilibrium properties of interacting fluids in an arbitrary external filed. The method is valid in any dimension and it yields an exact results in one dimension. Using this approach, we derive a recurrence relation for the pair distribution function of a three dimensional in-homogeneous fluids, constitute of spherical molecules with arbitrary nearest neighbour interaction that extends to two molecules diameter. By integrating this recurrence relation, we get an explicit expressions for the entropy and free energy functionals as a functionals of the density and the pair distribution function. We show that for one dimensional systems, our results coincide exactly with previously derived one using a completely different approach.