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The significant digit law in statistical physics

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  • Shao, Lijing
  • Ma, Bo-Qiang

Abstract

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 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.

Suggested Citation

  • Shao, Lijing & Ma, Bo-Qiang, 2010. "The significant digit law in statistical physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3109-3116.
  • Handle: RePEc:eee:phsmap:v:389:y:2010:i:16:p:3109-3116
    DOI: 10.1016/j.physa.2010.04.021
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    1. repec:eee:phsmap:v:486:y:2017:i:c:p:711-719 is not listed on IDEAS
    2. Sofia B. Villas-Boas & Qiuzi Fu & George Judge, 2015. "Is Benford’s Law a Universal Behavioral Theory?," Econometrics, MDPI, Open Access Journal, vol. 3(4), pages 1-11, October.
    3. Astrid Gamba & Giovanni Immordino & Salvatore Piccolo, 2016. "Corruption, Organized Crime and the Bright Side of Subversion of Law," CSEF Working Papers 446, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    4. 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.
    5. Quoc-Anh Do & Trang Van Nguyen & Anh N. Tran, 2013. "Do People Pay Higher Bribes for Urgent Services ?: Evidence from Informal Payements to Doctors in Vietnam," Sciences Po publications info:hdl:2441/3tk4fhvbi18, Sciences Po.

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