  The non-equilibrium-steady state (NEST) for photons in a cavity is
investigated theoretically. The NEST is caused by different parts of the cavity
being at distinct temperatures or by temperature gradients. By using a rate
equation based on the Lindblad equation, we derive an analytic expression for
the steady-state distribution of the photon spectrum. We predict differences
between the non-equilibrium steady state and a fit to the black-body spectrum
calculated via Planck's law with an effective temperature. For two bodies of
similar size at two temperatures which differ by a factor of two, the
difference would be more than 10%. We also show that cavity resonances have a
particularly large influence on the resulting non-equilibrium steady state of
the photons. The investigation of thermal spectra in the presence of more than
one temperature can be important for high-precision atomic clocks.
