Nonequilibrium ensemble method for dilute gases: Grand canonical ensemble

The nonequilibrium ensemble method is developed for dilute gases by using a nonequilibrium grand canonical ensemble distribution function. The underlying kinetic equation is an irreversible kinetic equation (e.g., the Boltzmann equation) satisfying a set of conditions that guarantee the existence of conservation laws and the H theorem. Such a kinetic equation is shown to give rise to a thermodynamically consistent theory of irreversible processes and an attendant nonequilibrium statistical thermodynamics completely parallel to statistical thermodynamics in the equilibrium Gibbs ensemble theory. It is shown that all macroscopic nonequilibrium variables are given in terms of the nonequilibrium grand canonical partition function for the system at arbitrary degree of removal from equilibrium.