Classical Density Functional Theory: Representability and Universal Bounds

TL;DR

This paper establishes bounds on the minimum free energy of classical particle systems given a specific density, applicable in both canonical and grand-canonical ensembles, under certain interaction decay conditions.

Contribution

It introduces universal bounds on the free energy for classical systems based on the one-particle density, advancing theoretical understanding of density functional theory.

Findings

Derived upper and lower bounds on free energy

Applicable to systems with fast-decaying pair potentials

Addresses both canonical and grand-canonical ensembles

Abstract

We provide upper and lower bounds on the lowest free energy of a classical system at given one-particle density $\rho(x)$. We study both the canonical and grand-canonical cases, assuming the particles interact with a pair potential which decays fast enough at infinity.