The Boltzmann equation and nonequilibrium ensemble method

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Abstract
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.