Radiative transfer and irreversibility

Abstract

The irreversibility of the interaction of radiation with matter is investigated by considering a stationary isothermal gas that emits the resonance line of atoms with only two discrete energy levels. In order to describe such a situation microscopically, the steady-state balance of the occupation numbers of the atomic levels and the equation of radiative transfer have to be taken into account simultaneously. The explicit expressions for the non-equilibrium entropies and temperatures of the radiation field and of the gas of the two-level atoms are derived in a systematic way. In the framework of the model considered, the kinetic temperature is an upper limit for both the radiant temperature and the excitation temperature. The local production of radiant entropy, integrated over the whole spectral line, is always positive, but, as a result of non-coherent scattering, it can be negative in certain frequency intervals. The radiant entropy produced by the entire atmosphere is, however, positive for every frequency emitted. Likewise, the total local entropy production is, in agreement with the Second Law, always positive. It is further shown that an anisotropic radiation field has a smaller entropy density and a greater production of radiant entropy than the isotropic radiation field of equal spectral distribution of energy. As an example, an atmosphere is treated numerically that emits a spectral line of large optical thickness under extreme non-equilibrium conditions.