经典力学中的光子气体：经典场论的统计力学处理
The Photon Gas in Classical Mechanics: A Statistical-Mechanical Treatment of Classical Field Theory
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中文总结 AI 辅助
该研究从经典电动力学出发，通过两种互补方法推导电磁辐射热力学的核心比例关系，构建了自洽的经典框架，无需依赖光子或量子统计。
中文摘要 AI 辅助
空腔辐射的热力学通常通过光子气体的量子理论引入。与之相反，我们研究仅从经典电动力学出发，热辐射会呈现哪些特征。我们通过两种互补方法证明，能量密度、辐射压强与能流之间的比例关系无需引入光子或量子统计即可推导得出。第一种方法基于麦克斯韦方程的显式解，对电磁波进行时空平均；第二种方法从第一性原理出发构建电磁场的经典统计力学，具体包括构造正则哈密顿量、实施规范约束、将配分函数表述为泛函积分，以及计算对应的场关联函数。本研究将波分析、统计力学、约束哈密顿动力学与泛函方法整合至单一经典框架，为电磁辐射热力学提供了自洽的经典表述。
英文摘要
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.
