Nonequilibrium grand ensemble method for dense fluids

Abstract

A nonequilibrium grand ensemble method is developed for dense simple fluids by using an irreversible kinetic equation whose collision term is required to satisfy a few conditions. We show that the kinetic equation satisfying such conditions is sufficient for constructing a formal theory of irreversible processes, which is consistent with the thermodynamic laws, and an nonequilibrium extension of the Gibbs equilibrium ensemble theory. As in the equilibrium ensemble theory, nonequilibrium macroscopic (thermodynamic) variables are given in terms of the nonequilibrium partition function. This formal theory supplies the evolution equations for macroscopic observables which are consistent with the thermodynamic laws and an integral part of the nonequilibrium ensemble method. They generalize the classical hydrodynamic equations of Navier, Stokes, and Fourier to nonlinear transport processes occurring far from equilibrium. The evolution equations also include the constitutive equations for the fluid which describe transport properties of the substance when the collision term in the kinetic equation is explicitly modeled by taking into account the details of molecular collision events in the system.