Addendum to "Free-energy functional of the Debye-H\"uckel model of simple fluids"

TL;DR

This paper updates and simplifies free-energy functionals for the Debye-Hückel model of simple fluids, maintaining thermodynamic consistency and connecting to previous approaches, while discussing non-uniqueness issues.

Contribution

Provides simpler, equivalent free-energy functionals for the Debye-Hückel model, linking to earlier methods and addressing non-uniqueness concerns.

Findings

New simpler functionals with same properties

Relation to Lado and Olivares-McQuarrie approaches

Discussion on non-uniqueness of functionals

Abstract

In previous publications [arXiv:1608.08430, arXiv:1704.06502], the authors have proposed Debye-H\"uckel-approximate free-energy functionals of the pair distribution functions for one-component fluid and two-component plasmas. These functionals yield the corresponding Debye-H\"uckel integral equations when they are minimized with respect to the pair distribution functions, lead to correct thermodynamic relations and fulfill the virial theorem. In the present addendum, we update our results by providing simpler functionals that have the same properties. We relate these functionals to the approaches of Lado [Phys. Rev. A 8:2548, 1973] and of Olivares and McQuarrie [J. Chem. Phys. 65:3604, 1976]. We also discuss briefly the non-uniqueness issue that is raised by these results.