Nonequilibrium ensemble dynamics.

The ensemble theory of Gibbs has been universally accepted as a theoretical foundation for dealing with thermodynamic systems in the equilibrium state. No comparable theory has gained wide acceptance in nonequilibrium statistical mechanics. We would like to propose a formalism for nonequilibrium systems which follows the spirit of Gibbs's ensemble theory. We will show that such a nonequilibrium ensemble dynamics may be employed to derive, in a straightforward manner, (1) formal equations for the time evolution of the macroscopic features of the system, (2) the existence of a nonequilibrium entropy function which is a nondecreasing function of time, (3) the Onsager reciprocity theorem, and (4) the fluctuation-dissipation theorem. Just as Gibbs's ensemble dynamics may be justified by demonstrating that the mean-square fluctuation of the macroscopic properties of certain thermodynamic systems is small, so we will show that the mean-square fluctuation in the time evolution of the macroscopic properties is small for certain classes of thermodynamic systems.