Anisotropic kappa distributions I: Formulation based on particle correlations

TL;DR

This paper establishes a theoretical framework linking anisotropic kappa distributions to particle velocity correlations, generalizing these distributions within nonextensive statistical mechanics and exploring their dependence on correlations and anisotropy parameters.

Contribution

It introduces a novel correlation-based formulation of anisotropic kappa distributions and extends them within nonextensive statistical mechanics, considering different correlation scenarios.

Findings

Derived correlation coefficients among particle energies.

Connected anisotropy to effective dimensionality and polytropic index.

Generalized distributions for various correlation types.

Abstract

We develop the theoretical basis for the connection of the variety of anisotropic distributions with the statistical correlations among particles velocity components. By examining the most common anisotropic distribution, we derive the correlation coefficient among particle energies, show how this correlation is connected to the effective dimensionality of the velocity distribution, and derive the connection between anisotropy and adiabatic polytropic index. Having established the importance of correlation among particles in the formulation of anisotropic kappa distributions, we generalize these distributions within the framework of nonextensive statistical mechanics and based on the types of homogeneous or heterogeneous correlations among the particles velocity components. The formulation of the developed generalized distributions mediates the main two types of anisotropic kappa distributions, considering (a) equal correlations, or (b) zero correlations, among different velocity components. Finally, the developed anisotropic kappa distributions are expressed in terms of the energy and pitch angle in arbitrary reference frames.