Information-theoretical derivation of an extended thermodynamical description of radiative systems

Abstract

A radiative equation of the Cattaneo-Vernotte type is derived from information theory and the radiative transfer equation. The equation thus derived is a radiative analog of the equation that is used for the description of hyperbolic heat conduction. It is shown, without recourse to any phenomenological assumption, that radiative transfer may be included in a natural way in the framework of extended irreversible thermodynamics ͑EIT͒.

Wavefronts in time-delayed reaction-diffusion systems. Theory and comparison to experiment

“…Let n(x, t) stand for the fraction of particles that at time t are at position x. Denoting by n + (x, t) and n − (x, t) the fraction of particles which are arriving from the left and from the right respectively, then n(x, t) = n + (x, t) + n − (x, t). (14) We denote by p the probability of jumping in the same direction as the previous jump, i.e. the probability that the particle persists in its direction after completing a step, whereas q = 1 − p is the probability for jumping in the opposite direction.…”

Extended Irreversible Thermodynamics of Chemically Reacting Systems

“…Before closing this paper, we would like to mention that, in some way, this result is not surprising because the same conclusion has recently been reached for radiative transfer, which is nothing but a transformation of one species of matter into another by the interchange of photons; that is, it may be viewed as an special case of a chemically reacting system. The reason why, in contrast to what was done in refs and , we have not made use of statistical mechanics but of kinetic theory is that the radiative transfer equation is much simpler mathematically than the Boltzmann equation and, within information statistical theory, the use of the chemical rate of reaction as an additional constraint leads to extremely complicated equations except for some simple systems for which one may not consistently evaluate the entropy density of the overall system…”