非广延统计中的一位数定律
First-Digit Law in Nonextensive Statistics
摘要：
非广延统计是玻尔兹曼统计的一种推广，它以非广延参数$q$为特征，可以用来描述物理和社会观测中的幂律行为。我们在这里探索的第一位数分布的非广延统计的不均匀性分析和数值。我们发现，第一位数的分布遵循本福德定律，并略有波动，在一个周期性的方式相对于对数的温度。当$q$增加时，波动减小，并且当$q$接近2时，结果完全收敛于本福德定律。本文还讨论了非广延统计量与本福特定律之间的关系。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
