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The Significant Digit Law in Statistical Physics
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The Significant Digit Law in Statistical Physics
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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.
Forward citations
Cited by 1 Pith paper
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Digit anomalies in the hadronic mass spectrum, classical and quantum information entropies, and the dynamical QCD scale
The first digits of PDG hadron masses deviate strongly from Benford's law, and the paper reads the resulting Shannon-entropy deficit as a signature of Lambda_QCD.
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