Irreversible Processes in Liquids and the Density Matrix: Monatomic Molecules

Abstract

A density matrixρ̄ is introduced to describe a macroscopically small subvolume of an infinite, pure, monatomic liquid. It is assumed that the effect of molecular interactions across the wall bounding the subvolume may be represented by a random force which is a functional of the density matrix itself. The form of the functional is determined by expanding bothρ̄ and the random force potential as linear sums of a set of scalar, vector, and tensor variables, for which the time rates of change are calculated from the Von Neumann equation. It is shown that the system should relax in two stages to the local equilibrium whose decay is described by the Navier-Stokes equations and that the inertial effects which are important in the initial stage are described by the parameters in the imaginary part ofρ̄. From the low-frequency limiting forms of the pressure, heat flux, and rate equations, general expressions for the transport coefficients are written down.