Free-energy functional of the Debye-Hückel model of two-component plasmas

We present a generalization of the Debye-Hückel 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-Hückel 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-Hückel 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-Hückel free energy are presented and discussed, including the virial theorem in the case of long-range interaction potentials.