Equations of Motion in Nonequilibrium Statistical Mechanics. II. Energy Transport

Abstract

The exact equations of motion for the space-and time-dependent coordinates of an arbitrary many-body system have been derived previously. These equations are partial integro-differential equations whose kernels are generalizations of time-correlation functions. In this paper the equations are rewritten using flux operators satisfying conservation equations, and the memory-retaining nonlocal generalizations of the equations of nonequilibrium thermodynamics are obtained. The formalism is applied to energy transport, and the usual expression for heat conductivity is derived without making the usual assumptions. Finally, a simple function is assumed for the kernel, and the equation then reduces to a well-known heat-conduction and -wave equation.