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First-Digit Law in Nonextensive Statistics
Nonextensive statistics, characterized by a nonextensive parameter , is a
promising and practically useful generalization of the Boltzmann statistics to
describe power-law behaviors from physical and social observations. We here
explore the unevenness of the first digit distribution of nonextensive
statistics analytically and numerically. We find that the first-digit
distribution follows Benford's law and fluctuates slightly in a periodical
manner with respect to the logarithm of the temperature. The fluctuation
decreases when increases, and the result converges to Benford's law exactly
as approaches 2. The relevant regularities between nonextensive statistics
and Benford's law are also presented and discussed.Comment: 11 pages, 3 figures, published in Phys. Rev.