# On the Stochastic Dynamics for the Regularized Kappa-Distributed Plasmas

## TL;DR

This paper explores the dynamics of plasmas using regularized Kappa distributions and Fokker–Planck equations.

## Contribution

The study establishes generalized fluctuation–dissipation relations for regularized Kappa distributions and proves detailed balance.

## Key findings

- Regularized Kappa distributions are stationary solutions under generalized fluctuation–dissipation relations.
- The principle of detailed balance holds for all derived stationary solutions.
- Fokker–Planck equations are analyzed in different physical limits.

## Abstract

The generalized fluctuation–dissipation relations that produce the regularized Kappa distributions are studied. The two-variable Fokker–Planck equation, as well as its reductions in the absence of potential and in the overdamped limit, are considered. All these Fokker–Planck equations have the regularized Kappa distributions as the stationary solutions if the friction and diffusion coefficients satisfy the generalized fluctuation–dissipation relations. In addition, we prove that the principle of detailed balance holds for all the stationary solutions derived in this work.