Tsallis statistics as a theoretical basis for the empirical Kappa distribution for systems in a stationary state out of thermal equilibrium
Abstract:
Kappa distributions, which enable effective modeling of observed particle distributions in cosmic and astrophysical plasma environments throughout the heliosphere, have now gained widespread use. This article discusses the physical foundations and theoretical justification of Kappa distributions, which naturally arise within the framework of Tsallis nonextensive statistical mechanics. Such distributions provide an adequate description of sparse plasma configurations in stationary states that are out of thermal equilibrium. Key formulas for theoretical Kappa distributions are presented, and a brief overview of their application in studies of decaying small-scale turbulence in cosmic plasma is given. It is shown that these distributions, resulting from the Tsallis entropy functional in nonextensive statistical mechanics, provide a missing link between the empirical Kappa distributions of Vasyliunas and the theoretical power-law models of suprathermal characteristics in astrophysical plasma environments.
