The significant digit law in statistical physics
AbstractThe 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 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 389 (2010)
Issue (Month): 16 ()
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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/
First digit law; Statistical physics; Mantissa distribution;
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- David E. Giles, 2012. "Exact Asymptotic Goodness-of-Fit Testing For Discrete Circular Data, With Applications," Econometrics Working Papers 1201, Department of Economics, University of Victoria.
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