On the self-consistency conditions in the statistical thermodynamics of the Coulomb system

The thermodynamic potential for a homogeneous and isotropic equilibrium nonrelativistic system of electrons and nuclei interacting with each other according to the Coulomb law is considered. Using the virial theorem and exact relations for the Green functions, it is shown that the thermodynamic functions of the Coulomb system are uniquely determined by the single-particle Green functions of electrons and nuclei outside the framework of perturbation theory. On this basis, self-consistency conditions are formulated for the thermodynamic functions that determine the applicability of the approximations used for single-particle Green functions.