有界系统的能量下界等价于有界系统的熵与能量比的Bekenstein上界
The lower bound on the energy for bounded systems is equivalent to the Bekenstein upper bound on the entropy to energy ratio for bounded systems
摘要：
采用多种方法证明了有界系统中熵能比（S/E）存在一个普适上界的假设。1981年，雅各布·D.贝肯斯坦发表了他的发现，S/E是有限的有效半径的系统，并提到了各种方法来推导S/E采用量子统计或热力学。可以看出，考虑到封闭腔内纵向本征模的能量差，可以得到类似的结果，就像马克斯·普朗克在1900年推导出黑体辐射光谱分布的正确公式一样。考虑到信息理论的方法，这个推导表明期望值的方差与测量这个期望值的概率的方差相同。这些研究结果的影响进行了讨论。
英文摘要：
Several approaches were used to proof the assumption that an universal upper bound on the entropy to energy ratio (S/E) exists in bounded systems. In 1981 Jacob D. Bekenstein published his findings that S/E is limited by the effective radius of the system and mentioned various approaches to derive S/E employing quantum statistics or thermodynamics. It can be shown that similar results are obtained considering the energetic difference of longitudinal eigenmodes inside a closed cavity like it was done by Max Planck in 1900 to derive the correct formula for the spectral distribution of the black-body radiation. Considering an information theoretical approach this derivation suggests that the variance of an expectation value is the same like the variance of the probability for measuring this expectation value. Implications of these findings are shortly discussed.
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