Non-equilibrium ensembles and thermodynamic functions

A non-equilibrium ensemble is formulated and the partition function of a sy stem in non-equilibrium transient state is derived by a method based upon t he maximization of the Boltzmann's entropy constrained by non linear Boltzm ann kinetic equation. We consider a logical theorem which expresses that th e characteristic function in a non-equilibrium ensemble has a form similar to the equilibrium one. The connection between the N-particle to one-partic le non-equilibrium partition function is obtained and the time dependent th ermodynamic functions as well as transport kinetic coefficients can then be calculated.