Hydrodynamic description of Non-Equilibrium Radiation

Boris Rotstein, Eric Akkermans

Published 2022-07-03Version 1

Non-equilibrium radiation is addressed theoretically by means of a stochastic lattice-gas model. We consider a resonating transmission line composed of a chain of radiation resonators, each at a local equilibrium, whose boundaries are in thermal contact with two blackbody reservoirs at different temperatures. In the long chain limit, the stationary state of the non-equilibrium radiation is obtained in a closed form. The corresponding spectral energy density departs from the Planck expression, yet it obeys a useful scaling form. A macroscopic fluctuating hydrodynamic limit is obtained leading to a Langevin equation whose transport parameters are calculated. In this macroscopic limit, we identify a local temperature which characterises the spectral energy density. The generality of our approach is discussed and applications for the interaction of non-equilibrium radiation with matter are suggested.