Temperature-dependent evolution of coherence, entropy, and photon statistics in photoluminescence

Photoluminescence (PL) is a fundamental light–matter interaction in which absorbed photons are re-emitted, playing a key role in science and engineering. Although the PL is often modeled using a non-zero chemical potential in Planck’s law to account for deviations from equilibrium, its explicit temperature dependence has not been formulated. Here, we derive a fundamental relationship expressing the chemical potential as a function of temperature, material properties, and excitation conditions, enabling a treatment of the PL analogous to thermal radiation and Planck’s law. This framework captures temperature-dependent spectral emission, entropy, temporal coherence, and photon statistics, revealing a range where the emission rate is quasi-conserved, linked to the observed blueshift, followed by a rapid transition to thermal behavior. These results establish a unified thermodynamic description of the PL, clarifying how temperature governs its optical properties, thereby providing a rigorous basis for temperature-controlled light sources with engineered coherence and thermal photon statistics.