Benford's Law in Statistical Physics
Benford's Law in Statistical Physics
Benford's law is the observation that for many datasets, the distribution of their first significant digit follows a non-uniform law; the probability that is the leading digit is .
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The Boltzmann–Gibbs (BG) and the Fermi–Dirac (FD) distributions are two frequently occurring statistical laws. This Demonstration shows that BG and FD distributions both fluctuate slightly in a periodic manner around the Benford distribution with the temperature of the system. The red points in the figure present Benford's law, while the blue ones present the first digit distributions of BG (or FD) statistics.