  Photoluminescence (PL) is a light-matter quantum interaction associated with
the chemical potential of light formulated by the Generalized Planck's law.
Without knowing the inherent temperature dependence of chemical potential, the
Generalized Planck's law is insufficient to characterize PL(T). Recent
experiments showed that PL at low temperatures conserves the emitted photon
rate, accompanied by a blue-shift and transition to thermal emission at a
higher temperature. Here, we theoretically study temperature-dependent PL by
including phononic interactions in a detailed balance analysis. Our solution
validates recent experiments and predicts important relations, including i) An
inherent relation between emissivity and the quantum efficiency of a system,
ii) A universal point defined by the pump and the temperature where the
emission rate is fixed to any material, iii) A new phonon-induced quenching
mechanism, and iv) Thermalization of the photon spectrum. These findings are
relevant to and important for all photonic fields where the temperature is
dominant.
