Information-theoretical approach to radiative transfer

Abstract

The maximum entropy formalism is used to obtain the radiation and matter distribution functions for radiative systems is steady nonequilibrium states, under the gray approximation. The radiation distribution function is expanded in a smallness parameter, which vanishes at equilibrium. In the first near-equilibrium approximation, we derive the results of near-equilibrium diffusion theory. This may be regarded as an analogue to the kinetic-theoretical result, according to which in the first Enskog approximation, the Fourier heat conduction equation is obtained. The theory is also developed up to the second order, leading to results which apply to situations further away from equilibrium than those corresponding to near-equilibrium diffusion theory. A simple application is analyzed.