A stochastic model of long-range interacting particles

TL;DR

This paper introduces a stochastic model for long-range interacting particles, analyzing both equilibrium and nonequilibrium steady states, and deriving exact phase space distributions for the nonequilibrium case.

Contribution

It presents a novel stochastic Monte Carlo model for long-range interactions and provides exact solutions for the nonequilibrium steady state distributions.

Findings

System reaches Gibbs equilibrium with symmetric updates.

Out-of-equilibrium steady states occur with asymmetric updates.

Exact phase space distribution derived for the nonequilibrium case.

Abstract

We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For symmetric increments, the system at long times settles to the Gibbs equilibrium state, while for asymmetric updates, the steady state is out of equilibrium. For the associated Fokker-Planck dynamics in the thermodynamic limit, we compute exactly the phase space distribution in the nonequilibrium steady state, and find that it has a nontrivial form that reduces to the familiar Gibbsian measure in the equilibrium limit.