A stochastic model of long-range interacting particles

Shamik Gupta 1, Thierry Dauxois 2, Stefano Ruffo 2

Journal of Statistical Mechanics: Theory and Experiment (2013) P11003

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.

  • 1 : Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS)
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2 : Laboratoire de Physique de l'ENS Lyon (Phys-ENS)
    CNRS : UMR5672 – École Normale Supérieure (ENS) - Lyon