Modified Robertson projection operator method and irreversible thermodynamics

Abstract

A modified Robertson projection operator is used to obtain the evolution equation for the projected distribution function as well as various macroscopic evolution equations. These evolution equations, although not as yet proved to be consistent with the thermodynamic laws, form a basis for a formal theory of macroscopic processes. On introducing some approximations to the projected propagator we construct an approximate, thermodynamically consistent evolution equation (kinetic equation) and develop a thermodynamically consistent theory of irreversible processes with the approximate evolution equation so obtained. The mathematical structure of the theory of irreversible processes thus formulated can be brought into harmony with the theory based on the Boltzmann equation and the generalized Boltzmann equation, which was previously developed and reported in the literature. The Maxwell–Cattaneo–Vernotte type constitutive equations are derived on making a number of approximations on the exact evolution equations for the stress and the heat flux.