In this chapter, we examine equilibrium radiation, which represents our third and final application of statistical mechanics to independent particles beyond the dilute limit. For simplicity in mathematically modeling the radiant field, we apply the methods of statistical thermodynamics to electromagnetic waves enclosed in a cubical blackbody cavity. The enclosed radiation is at both thermal and radiative equilibrium if the walls of the cavity are at constant temperature with equal rates of emission and absorption, respectively.

Bose–Einstein Statistics for the Photon Gas

From a quantum perspective, the electromagnetic radiation within a blackbody cavity can be modeled as an assembly of independent photons. Given this representation, we recall from Section 5.9 that photons are particles of zero spin; hence, a photon gas must follow Bose–Einstein statistics, whose equilibrium particle distribution, following Eq. (3.31), is normally given by

However, in comparison to the usual assumptions associated with Eq. (14.1), photons do not obey particle conservation as they are constantly being formed and destroyed at the walls of a blackbody cavity. Of course, thermodynamic equilibrium still mandates conservation of energy at these same walls. As a result, nothing prevents, for example, the replacement of one incoming photon with two outgoing photons, each having half its energy.