从Casimir能量和零点辐射的自然最大熵原理导出黑体辐射谱
Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation
摘要：
通过数值计算，零点辐射的普朗克谱满足自然的最大熵原理，而光谱的替代选择不。具体地说，如果我们考虑一组有导电壁的盒子，每个盒子在盒子中的不同位置放置一个分区，使得在盒子的集合中，分区在体积上均匀间隔，那么普朗克光谱对应于随机辐射的光谱（在低频时每个简正模式具有恒定能量kT，在高频时每个简正模式具有零点能量（1/2）hw）这在盒子的集合上为每个盒子的辐射能量提供了最大的均匀性。分析涉及卡西米尔能量和零点辐射，这通常不会出现在热力学分析。为了简单起见，分析是在一个空间维度的波。
英文摘要：
By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes, each with a partition placed at a different location in the box, so that across the collection of boxes the partitions are uniformly spaced across the volume, then the Planck spectrum correspond to that spectrum of random radiation (having constant energy kT per normal mode at low frequencies and zero-point energy (1/2)hw per normal mode at high frequencies) which gives maximum uniformity across the collection of boxes for the radiation energy per box. The analysis involves Casimir energies and zero-point radiation which do not usually appear in thermodynamic analyses. For simplicity, the analysis is presented for waves in one space dimension.
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