ABSTRACT
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.