# Free-energy functional of the Debye-H\"uckel model of two-component plasmas

## TL;DR

This paper generalizes the Debye-Hückel free-energy functional to two-component plasmas with arbitrary interactions, enabling derivation of integral equations and ensuring thermodynamic consistency.

## Contribution

It introduces a new free-energy functional for two-component systems that reproduces Debye-Hückel equations and satisfies the virial theorem, extending previous one-component models.

## Key findings

- Derivation of the two-component Debye-Hückel integral equations
- The free-energy functional correctly reproduces internal energy density
- The model satisfies the virial theorem for long-range interactions

## Abstract

We present a generalization of the Debye-H\"uckel free-energy-density functional of simple fluids to the case of two-component systems with arbitrary interaction potentials. It allows one to obtain the two-component Debye-H\"uckel integral equations through its minimization with respect to the pair correlation functions, leads to the correct form of the internal energy density, and fulfills the virial theorem. It is based on our previous idea, proposed for the one-component Debye-H\"uckel approach, and which was published recently \cite{Piron16}. We use the Debye-Kirkwood charging method in the same way as in \cite{Piron16}, in order to build an expression of the free-energy density functional. Main properties of the two-component Debye-H\"uckel free energy are presented and discussed, including the virial theorem in the case of long-range interaction potentials.