A Projection Operator Approach to Extended Irreversible Thermodynamics

Abstract

Based on the projection·operator formalism established by Mori for Langevin equations, a general theory is formulated which is applicable to the description of transient irreversible processes. A time-smoothed density matrix (previously discussed by the present author) is used to define the projection operator in place of the equilibrium density matrix in Mori's formalism. It is shown that a statistical mechanical theory for transient processes can be developed in our formalism that dovetails perfectly with extended irreversible thermodynamics. 1 ) has been undeniably useful for the analysis of many phenomena in non-equilibrium macroscopic systems, it presents some very well-known limitations. The traditional theories are closely modeled on classical Fourier-N avier-Stokes theory, and it has long been accepted that they share the difficulty of predicting infinite propagation speeds for thermal ·and viscous disturbances. The parabolic character of the equations has been a source of concern. Mtiller 2 ) proposed that one way of generalizing linear irreversible thermodynamics was to modify the local-equilibrium assumption by introducing an extended entropy which depends on both the classical extensive variables and their fluxes. This proposal has given rise to the present form of extended irreversible thermodynamics. 3 )