秩分布中$q$统计量的发生率
Incidence of $q$-statistics in rank distributions
摘要：
我们发现，在大量的情况下，在一个广泛的家庭的系统服从Tsallis统计的幂律衰减（往往只在有限的程度上）的大小秩分布。这些分布的理论框架类似于切分叉附近的非线性迭代映射，其中李雅普诺夫指数可以忽略不计或为零。与这些分布相关的物理力学表达式来自最大熵原理，使用两种不同的约束，由此产生的熵指数的二元性被认为是描绘物理相关的信息。当指数$α$的值固定分布的幂律指数时，对偶指数$2-α$的值确保变形熵的扩展性。
英文摘要：
We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions is analogous to that of a nonlinear iterated map near a tangent bifurcation for which the Lyapunov exponent is negligible or vanishes. The relevant statistical-mechanical expressions associated with these distributions are derived from a maximum entropy principle with the use of two different constraints, and the resulting duality of entropy indexes is seen to portray physically relevant information. While the value of the index $α$ fixes the distribution's power-law exponent, that for the dual index $2-α$ ensures the extensivity of the deformed entropy.
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。
