Generating functionals, consistency, and uniqueness in the integral equation theory of liquids

TL;DR

This paper explores the relationships between generating functionals, thermodynamic consistency, and solution uniqueness in liquid integral equation theory, proposing a new automatic closure derivation approach and presenting initial results.

Contribution

It introduces a novel method for automatically deriving closures that satisfy thermodynamic consistency and solution uniqueness in liquid integral equations.

Findings

Numerical examples illustrate the relations between functionals, consistency, and uniqueness.

A new approach for automatic closure derivation is proposed.

Initial results demonstrate the feasibility of the method.

Abstract

We discuss and illustrate through numerical examples the relations between generating functionals, thermodynamic consistency (in particular the virial-free energy one), and uniqueness of the solution, in the integral equation theory of liquids. We propose a new approach for deriving closures automatically satisfying such characteristics. Results from a first exploration of this program are presented and discussed.