Equations of Motion in Nonequilibrium Statistical Mechanics

Abstract

Exact equations of motion for the space- and time-dependent thermodynamic coordinates of a many-body system are derived directly from the Liouville equation. This is done by definining a generalized canonical density operator depending only upon present values of the thermodynamic coordinates. This operator is used no matter how far the system is from equilibrium. An explicit expression for the entropy of a system possibly not in equilibrium is given in terms of this operator. The equation of motion for the operator is derived, and the coupled, nonlinear, integrodifferential equations of motion for the thermodynamic coordinates follow immediately.