Photon frequency diffusion process
  We introduce a stochastic multi-photon dynamics on reciprocal space. Assuming
isotropy, we derive the diffusion limit for a tagged photon to be a nonlinear
Markov process on frequency. The nonlinearity stems from the stimulated
emission. In the case of Compton scattering with thermal electrons, the
limiting process describes the dynamical fluctuations around the Kompaneets
equation. More generally, we construct a photon frequency diffusion process
which enables to include nonequilibrium effects. Modifications of the Planck
Law may thus be explored, where we focus on the low-frequency regime.
