Kinetic theory for non-equilibrium stationary states in long-range interactingsystems

Abstract

We study long-range interacting systems perturbed by external stochastic forces. Unlike thecase of short-range systems, where stochastic forces usually act locally on each particle,here we consider perturbations by external stochastic fields. The system reaches stationarystates where the external forces balance the dissipation on average. These states do notrespect detailed balance and support non-vanishing fluxes of conserved quantities. Wegeneralize the kinetic theory of isolated long-range systems to describe the dynamics of thisnon-equilibrium problem. The kinetic equation that we obtain applies to plasmas,self-gravitating systems, and to a broad class of other systems. Our theoretical results holdfor homogeneous states, but may also be generalized to apply to inhomogeneous states. Weobtain an excellent agreement between our theoretical predictions and numericalsimulations. We discuss possible applications to describe non-equilibrium phasetransitions.