Entropy and Temperature of Electromagnetic Radiation

Electromagnetic (EM) radiation is both wave and heat. Waves are characterized by spectral distribution, spatial distribution, time coherence, spatial coherence, energy flux, and polarization. Heat, namely energy transferred from a hot body to a cold one, is characterized by its energy and entropy, and the ratio between them is the temperature. Here we calculate the entropy and temperature of a single radiation mode from the wave properties of the radiation. Using the Heisenberg uncertainty principle and Planck law, we calculate, from the optical properties of the radiation, the number of modes and their occupation number. Then we calculate the entropy and temperature of a single-mode EM radiation. It is shown that the entropy of a single-mode varies from zero for low occupation number, namely in the quantum limit to one Boltzmann constant for high occupation number, namely in the classical limit. The temperature varies from zero Kelvin in the quantum limit to infinity at high energies in the classical limit. This analysis is consistent with Fourier optics and statistical mechanics namely: Stephan-Boltzmann Law, Wein Law, Zipf law, IT File’s entropy, and the canonical distribution.