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We examine in detail the mechanisms behind thermalization and Bose-Einsteincondensation of a gas of photons in a dye-filled microcavity. We derive amicroscopic quantum model, based on that of a standard laser, and show how thismodel can reproduce the behavior of recent experiments. Using the rate equationapproximation of this model, we show how a thermal distribution of photonsarises. We go on to describe how the non-equilibrium effects in our model cancause thermalization to break down as one moves away from the experimentalparameter values. In particular, we examine the effects of changing cavitylength, and of altering the vibrational spectrum of the dye molecules. We areable to identify two measures which quantify whether the system is in thermalequilibrium. Using these we plot "phase diagrams" distinguishing BEC andstandard lasing regimes. Going beyond the rate equation approximation, ourquantum model allows us to investigate both the second order coherence,$g^{(2)}$, and the linewidth of the emission from the cavity. We show how thelinewidth collapses as the system transitions to a Bose condensed state, andcompare the results to the Schawlow--Townes linewidth.

Thermalization and breakdown of thermalization in photon condensates