从热力学观点推导具有经典零点辐射的Classical Physics的普朗克黑体谱
Derivations of the Planck Blackbody Spectrum from Thermodynamic Ideas in Classical Physics with Classical Zero-Point Radiation
摘要：
基于热力学思想，在包含经典零点辐射的经典物理中，给出了普朗克黑体谱的两种新的推导方法。应用于谐振子或辐射简正模的热力学第一和第二定律要求正则势$ϕ(ω/T)$是对应于振荡频率与温度之比的单个变量的函数。热力学第二定律涉及极值的思想，它可以应用于热辐射。我们对Planck谱的第一次推导是基于正则势$ϕ(ω/T)$是一个单调函数的思想，当在低温零点能和高温能量均分之间插值时，它的所有导数都是单调的;单调性行为排除了正则势给出$ω/T.$比的优选值。我们对普朗克谱的第二次推导是基于以下要求：在恒温的有隔板的盒子中辐射的亥姆霍兹自由能的变化在热平衡时应是最小的。最后，当选取传统普朗克谱中的每个简正模的光谱能量作为忽略低温零点能的传统普朗克谱时，在高温下，Casimir能量随分块位置的变化对应于零点能的缺失，从而将零点能的概念嵌入到传统普朗克谱中.强调了热辐射与经典物理中的零点辐射和时空结构的密切联系。
英文摘要：
Based upon thermodynamic ideas, two new derivations of the Planck blackbody spectrum are given within classical physics which includes classical zero-point radiation. The first and second laws of thermodynamics, applied to a harmonic oscillator or a radiation normal mode, require that the canonical potential $ϕ(ω/T)$ is a function of a single variable corresponding to the ratio of the oscillation frequency to the temperature. The second law of thermodynamics involves extremum ideas which may be applied to thermal radiation. Our first derivation of the Planck spectrum is based upon the idea that the canonical potential $ϕ(ω/T)$ is a monotonic function and all its derivatives are monotonic when interpolating between zero-point energy at low temperature and energy equipartition at high temperature; the monotonic behavior precludes the canonical potential from giving a preferred value for the ratio $ω/T.$ Our second derivation of the Planck spectrum is based upon the requirement that the change in the Helmholtz free energy of the radiation in a partitioned box held at constant temperature should be a minimum at thermal equilibrium. Finally, the change in Casimir energy with change in partition position for the radiation in a partitioned box is shown to correspond at high temperature to the absence of zero-point energy when the spectral energy per normal mode is chosen as the traditional Planck spectrum which omits zero-point energy at low temperature; thus the idea of zero-point energy is embedded in the traditional Planck spectrum. It is emphasized that thermal radiation is intimately connected with zero-point radiation and the structure of spacetime in classical physics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
