The Photon Gas in Classical Mechanics: A Statistical-Mechanical Treatment of Classical Field Theory

Abstract

The thermodynamics of cavity radiation is usually introduced through the quantum theory of a photon gas. In contrast, we investigate which features of thermal radiation follow from classical electrodynamics alone. We show, using two complementary approaches, that the proportionalities between energy density, radiation pressure, and energy flux arise without invoking photons or quantum statistics. The first approach is based on explicit solutions of Maxwell's equations and spatio-temporal averaging of electromagnetic waves. The second approach develops the classical statistical mechanics of the electromagnetic field from first principles by constructing the canonical Hamiltonian, implementing the gauge constraints, formulating the partition function as a functional integral, and evaluating the corresponding field correlation functions. By combining wave analysis, statistical mechanics, constrained Hamiltonian dynamics, and functional methods within a single classical framework, this work provides a coherent classical formulation of electromagnetic radiation thermodynamics.