First-Digit Law in Nonextensive Statistics

TL;DR

This paper investigates the first-digit distribution in nonextensive statistics, revealing it follows Benford's law and exhibits periodic fluctuations influenced by the nonextensive parameter q.

Contribution

It analytically and numerically demonstrates the connection between nonextensive statistics and Benford's law, highlighting how fluctuations depend on q and converge as q approaches 2.

Findings

First-digit distribution follows Benford's law.

Fluctuations are periodic with respect to the logarithm of temperature.

Fluctuations decrease as q increases, converging to Benford's law at q=2.

Abstract

Nonextensive statistics, characterized by a nonextensive parameter $q$, 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 $q$ increases, and the result converges to Benford's law exactly as $q$ approaches 2. The relevant regularities between nonextensive statistics and Benford's law are also presented and discussed.