Kinetic theory for non-equilibrium stationary states in long-range interacting systems

TL;DR

This paper develops a kinetic theory for long-range interacting systems under external stochastic forces, describing non-equilibrium stationary states with fluxes, and validates the theory through simulations, with potential applications to phase transitions.

Contribution

It generalizes kinetic theory to non-equilibrium states in long-range systems influenced by external stochastic fields, extending previous models for isolated systems.

Findings

The kinetic equation accurately predicts stationary states.

Numerical simulations confirm theoretical predictions.

Applicable to plasmas, gravitational systems, and more.

Abstract

We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic fields. The system reaches stationary states where external forces balance dissipation on average. These states do not respect detailed balance and support non-vanishing fluxes of conserved quantities. We generalize the kinetic theory of isolated long-range systems to describe the dynamics of this non-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 hold for homogeneous states, but may also be generalized to apply to inhomogeneous states. We obtain an excellent agreement between our theoretical predictions and numerical simulations. We discuss possible applications to describe non-equilibrium phase transitions.