Kinetic theory of nonequilibrium stochastic long-range systems: Phase transition and bistability

TL;DR

This paper develops a kinetic theory for nonequilibrium long-range systems under stochastic forces, revealing phase transitions and bistability, with predictions validated by simulations and potential for describing inhomogeneous states.

Contribution

It introduces a generalized kinetic approach for stochastic long-range systems, extending existing methods and capturing phase transitions and bistability phenomena.

Findings

Good agreement between kinetic theory and simulations.

Identification of a first-order phase transition.

Observation of bistable behavior near the transition.

Abstract

We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems, two-dimensional turbulence, and also in a broad class of other systems. Under the effect of stochastic driving, the system reaches a stationary state where external forces balance dissipation on average. These states have the invariant probability that does not respect detailed balance, and are characterized by non-vanishing currents of conserved quantities. In order to analyze spatially homogeneous stationary states, we develop a kinetic approach that generalizes the one known for deterministic long-range systems; we obtain a very good agreement between predictions from kinetic theory and extensive numerical simulations. Our approach may also be generalized to describe spatially inhomogeneous stationary states. We also report on numerical simulations exhibiting a first-order nonequilibrium phase transition from homogeneous to inhomogeneous states. Close to the phase transition, the system shows bistable behavior between the two states, with a mean residence time that diverges as an exponential in the inverse of the strength of the external stochastic forces, in the limit of low values of such forces.