κ分布作为指数族系综的渐近边缘分布
Kappa distributions as asymptotic marginals of exponential family ensembles
AI总结：
该研究以受驱经典系统超统计行为的前期成果为基础，证明总动能服从逆伽马分布的N粒子系统在N→∞时单粒子速度服从κ分布，并提出了生成κ速度的实用模拟方法。
AI中文摘要：
近期研究（Physica A 660 130370, 2025）已证明，具有恒定微正则热容量的受驱经典系统会出现超统计行为。作为该结果的一项应用，本研究表明，总动能服从逆伽马分布的N粒子系统，在N→∞的极限下，其单粒子速度必服从κ分布。研究结果为非广延统计力学理论之外κ分布的本质提供了新见解，同时提出了一种在逆伽马系综中通过蒙特卡洛Metropolis模拟生成κ速度的实用方法。
英文摘要：
Recently (Physica A 660 130370, 2025), emergence of superstatistical behavior in driven classical systems has been shown for systems with constant microcanonical heat capacity. As an application of this result, in this work we show that a system of $N$ particles with inverse gamma distribution of total kinetic energies must have kappa-distributed single-particle velocities in the limit $N \rightarrow \infty$. Our results provide insight into the nature of kappa distributions outside the theory of nonextensive statistical mechanics, while also bringing forward a practical method for the generation of kappa velocities via Monte Carlo Metropolis simulation in the inverse gamma ensemble.
