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The significant digit law in statistical physics

Author

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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:hal:spmain:info:hdl:2441/3tk4fhvbi18ndq2n4gs2e9pp6j is not listed on IDEAS
    2. Villas-Boas, Sofia B. & Fu, Qiuzi & Judge, George, 2017. "Benford’s law and the FSD distribution of economic behavioral micro data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 711-719.
    3. Sofia B. Villas-Boas & Qiuzi Fu & George Judge, 2015. "Is Benford’s Law a Universal Behavioral Theory?," Econometrics, MDPI, vol. 3(4), pages 1-11, October.
    4. Gamermann, Daniel & Antunes, Felipe Leite, 2018. "Statistical analysis of Brazilian electoral campaigns via Benford’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 171-188.
    5. Pavol Farkašovský & Lubomíra Regeciová, 2019. "Magnetization plateaus and phase diagrams of the extended Ising model on the Shastry-Sutherland lattice: effects of long-range interactions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(2), pages 1-6, February.
    6. Gamba, Astrid & Immordino, Giovanni & Piccolo, Salvatore, 2018. "Corruption, organized crime and the bright side of subversion of law," Journal of Public Economics, Elsevier, vol. 159(C), pages 79-88.
    7. 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.
    8. repec:spo:wpmain:info:hdl:2441/3tk4fhvbi18ndq2n4gs2e9pp6j is not listed on IDEAS

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