Permittivity and one-particle distribution functions in the thermodynamics of a Coulomb system

Using the grand canonical distribution and the virial theorem, we show that the Gibbs thermodynamic potential of a nonrelativistic system of charged particles is uniquely determined by its permittivity and the distribution functions of electrons and nuclei without using perturbation theory. This means that consistent approximations for the permittivity and one-particle distribution functions of electrons and nuclei must be used to calculate thermodynamic functions of the Coulomb system. To construct such self-consistent approximations, we propose using a decoupling procedure based on separating the ‘`connected" and "regular" parts of the temperature Green’s functions in the equations of motion. We consider the self-consistent Hartree–Fock approximation corresponding to this procedure.