Particle-photon radiative interactions and thermalization

We analyze the statistical properties of radiative transitions for a molecular system possessing discrete, equally spaced, energy levels, interacting with thermal radiation at constant temperature. A radiative fluctuation-dissipation theorem is derived and the particle velocity distribution analyzed. It is shown analytically that, neglecting molecular collisions, the velocity distribution function cannot be Gaussian, as the equilibrium value for the kurtosis $\kappa$ is different from $\kappa =3$. A Maxwellian velocity distribution can be recovered in the limit of small radiative friction.