Kappa distributions as asymptotic marginals of exponential family ensembles

Abstract

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.