Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

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

Document Type : Original Article

Authors
1 Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran
2 Department of Physics, Sharif University of Technology, Tehran, Iran
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.
Keywords
Subjects

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Volume 3, Issue 3
Summer 2026
Pages 113-128

  • Receive Date 31 July 2026
  • Revise Date 03 August 2026
  • Accept Date 21 August 2026
  • First Publish Date 21 August 2026
  • Publish Date 01 August 2026