Kinetic equations for the Green functions describing equilibrium states of a gas

Abstract

The hierarchy equations of general Green functions describing an imperfect Fermi gas of an arbitrary density can be transformed into closed equations, rigorously in the bulk limit. The latter equations are greatly simplified with the assumption that the system is in a homogeneous stationary state. It is shown that the simplified equations, the kinetic equations for the homogeneous stationary states, are satisfied by the Green functions defined with the grand-canonical density operator. This fact and basic thermodynamic arguments establish that the grand-canonical ensemble theory in the bulk limit correctly describes the thermodynamic equilibrium states of the system.