Statistical thermodynamics of the Coulomb system and adiabatic approximation

It is shown that the Gibbs thermodynamic potential for a system of electrons and identical nuclei of the same sort in the adiabatic approximation for a subsystem of nuclei is determined by the thermodynamic characteristics of a uniform electron liquid in a compensating positive background and a subsystem of nuclei interacting between each other through the effective potential. It is established that this potential, in addition to the Coulomb interaction of nuclei between each other, is determined by the equilibrium nonuniform density of electrons, being in the Coulomb field of identical nuclei.