黑体辐射的数字随机性
The digital randomness of black-body radiation
摘要：
本文在经典柯尔莫哥洛夫概率论的框架下，分析了黑体辐射光谱分量随机能量的分数部分的统计性质。除了能量的整数部分（满足著名的普朗克-玻色分布），其分数部分（与“舍入误差”有关）的实现已经由二进制序列表示，如z = 0.001011000010.证明了0-s和1-s在不同位置所实现的二进制变量是独立的。根据独立性条件，可以恢复分数部分z的原始分布。如果这些二元变量具有相同的分布，那么它们描述了一个与温度无关的随机能量，其期望值就是零点能量。因此，零点波动可以被认为是一个理想的随机数发生器的物理代表。
英文摘要：
The statistical properties of the fractional part of the random energy of a spectral component of black-body radiation have been analysed in the frame of classical Kolmogorovian probability theory. Besides the integer part of the energy (which satisfies the well-known Planck-Bose distribution), the realizations of its fractional part (related to 'round-off errors') has been represented by binary sequences, like z = 0.001011000010.... It has been shown that the binary variables realized by the 0-s and 1-s at different positions are independent. From the condition of independence the original distribution of the fractional part z can be recovered. If these binary variables have the same distribution, then they describe a temperature-independent random energy, whose expectation value is just the zero-point energy. Thus, the zero-point fluctuation can be considered as a physical representative of an ideal random number generator.
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