The Boltzmann equation and nonequilibrium ensemble method

By combining the phenomenological theory of irreversible processes and the results of the kinetic theory of irreversible processes obtained from the Boltzmann equation for a dilute gas mixture, a nonequilibrium ensemble method is formulated for dilute classical gases as a parallel extension to the Gibbs ensemble method in equilibrium statistical mechanics. This method is distinct from those of McLennan and Zubarev. The main distinguishing features are: the use of an irreversible kinetic equation (i.e., the Boltzmann equation) instead of the time-reversal invariant Liouville equation; the extended Gibbs relation for calortropy; generalized hydrodynamic equations consistent with the second law of thermodynamics; and thermodynamical identifications of the parameters appearing in the nonequilibrium canonical distribution function. (C) 1995 American Institute of Physics.