期刊
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
卷 389, 期 16, 页码 3109-3116出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physa.2010.04.021
关键词
First digit law; Statistical physics; Mantissa distribution
资金
- National Natural Science Foundation of China [10721063, 10975003]
- Hui-Chun Chin and Tsung-Dao Lee Chinese Undergraduate Research Endowment (Chun-Tsung Endowment) at Peking University
- National Fund for Fostering Talents of Basic Science [J0630311, J0730316]
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 BC and FD distributions both fluctuate slightly in a periodic manner around Benford's distribution with respect to the temperature of the system, while the BE distribution conforms to it exactly whatever the temperature is. Thus 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. (C) 2010 Elsevier B.V. All rights reserved.
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