Kinetic theory approach to irreversible thermodynamics of radiation and matter

Thermodynamics of irreversible processes in a radiation field is formulated, based on kinetic theory, by treating nonequilibrium radiation as a nonequilibrium photon gas interacting with matter (e.g., a dilute plasma). A set of Boltzmann equations is taken for kinetic equations for nonequilibrium photons and a dilute gas mixture. The kinetic equations then are used to derive the evolution equations for macroscopic variables necessary for describing temporal and spatial evolution of irreversible processes in the system of matter and radiation. The modified moment method is applied to rigorously subject the evolution equations to the requirements of the thermodynamic laws. It is shown that the entropy differential can be calculated in terms of a compensation differential and a nonvanishing dissipation term and that the entropy balance equation is reducible to a simpler differential equation for a new function B related to the entropy by a Legendre-type transformation and computable in terms of a form of entropy production only. A method of calculating nonequilibrium corrections for the distribution functions for photons and matter is presented. The formalism presented provides a method of computing transport coefficients and studying irreversible processes in matter and radiation from the statistical mechanical viewpoint in a unified manner consistent with thermodynamic laws.