On the Stochastic Dynamics for the Regularized Kappa-Distributed Plasmas

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.