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The Significant Digit Law in Statistical Physics

shizhao 添加于 2010-5-14 21:27 | 2344 次阅读 | 0 个评论

作者
Shao L, Ma B-Q
摘要
The occurrence of the nonzero leftmost digit, i.e., 1, 2, ..., 9, of numbers from many real world sources is not uniformly distributed as one might naively expect, but instead, the nature favors smaller ones according to a logarithmic distribution, named Benford's law. We investigate three kinds of widely used physical statistics, i.e., the Boltzmann-Gibbs (BG) distribution, the Fermi-Dirac (FD) distribution, and the Bose-Einstein (BE) distribution, and find that the BG and FD distributions both fluctuate slightly in a periodic manner around the Benford distribution with respect to the temperature of the system, while the BE distribution conforms to it exactly whatever the temperature is. Thus the Benford's law seems to present a general pattern for physical statistics and might be even more fundamental and profound in nature. Furthermore, various elegant properties of Benford's law, especially the mantissa distribution of data sets, are discussed.
详细资料
- 关键词: physics.data-an; cond-mat.stat-mech; hep-ph; math-ph; math.MP
- 文献种类:期刊
- 备注:arXiv:1005.0660v1; 21 latex pages, 5 figures, final version in journal publication
标签

本福特定律统计
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shizhao 的文献笔记订阅

理学家法兰克·本福特于1938年发现了以他姓命名的本福特定律(Benford's law)，这一规律描述了常用数字集和数据序列中数的首位数字分布。比如在实际生活中，以1为首位数字的数的出现机率约为总数的三成，接近期望值1/9的3倍。总体上说，1出现的几率是30.1%，2是17.6%，3是12.5%...9是4.6%。推广来说，越大的数，以它为首位的数出现的机率就越低。不过，并不是所有的数据集都符合本福特定律，比如彩票和电话号码就不遵守这一定律。但是现在北京大学物理系马伯强教授和研究生邵立晶的新发现为本福特定律的性质提供了新的见解。他们发现，物理学的三大统计学方法：Boltzmann-Gibbs分布、费米-狄拉克分布和玻色一爱因斯坦分布都符合本福特定律。研究人员认为，本福特定律可能是自然复杂性背后的一项基本原则。

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