Temperature-Dependent Evolution of Photoluminescence: A Thermodynamic and Optical Perspective

Photoluminescence (PL) occurs when absorbed photons excite electrons, followed by thermalization and light emission, and plays an important role in science and engineering. Traditionally, PL is described by introducing a nonzero chemical potential into Planck's law to account for deviations from purely thermal emission. Assigning a chemical potential at a fixed temperature is straightforward, but its temperature dependence has remained unresolved. Here, we derive a fundamental relationship expressing the chemical potential as a function of temperature, material properties, and excitation conditions. This allows temperature-dependent PL to be analyzed in direct analogy to Planck's law and blackbody radiation. Our framework provides a unified description of the PL thermodynamic and optical properties, including spectral emission, entropy generation, temporal coherence, and photon statistics, capturing the transition from narrowband, pump-induced emission to broadband thermal radiation. Beyond its fundamental significance, this model provides a framework for the design of tunable light sources.