Abstract
A non-equilibrium ensemble is formulated and the partition function of a system in non-equilibrium transient state is derived by a method based upon the maximization of the Boltzmann’s entropy constrained by the non-linear Boltzmann-kinetic equation. We consider a logical sensation, which expresses that the characteristic function in a non-equilibrium ensemble that has a form similar to the equilibrium one. The connection between the N-particles to one-particle partition function is obtained and the time-dependent thermodynamic functions as well as transport kinetics coefficients can then be calculated. On the other hand by combining the phenomenological theory of irreversible processes and the results of the kinetic theory of irreversible processes obtained from the Boltzmann-kinetic equation for a dilute gas, a non-equilibrium ensemble method has been formulated for dilute gases as a parallel extension to the Gibbs ensemble method in equilibrium statistical mechanics. This method is distinct from those of McLennan, Zubarev and Sobouti. The main distinguishing feature is, the use of an irreversible kinetic equation (i.e., The Boltzmann-kinetic equation) instead of the time reversal invariant Liouville equation.
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