Macroscopic properties and dynamical large deviations of the boundary driven Kawasaki process with long range interaction

Mustapha Mourragui (1) , Enza Orlandi (2)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 Dipartimento di Matematica [Roma TRE]

We consider a boundary driven exclusion process associated to particles evolving under Kawasaki (conservative) dynamics and long range interaction in a regime in which at equilibrium phase separation might occur. We show that the empirical density under the diffusive scaling solves a non linear integro differential evolution equation with Dirichlet boundary conditions and we prove the associated dynamical large deviations principle. Further, tuning suitable the intensity of the interaction, in the uniqueness phase regime, we show that under the stationary measure the empirical density solves a non local, stationary, transport equation.

Mots clés: Kawasaki process; Kac potential; Large deviations; Stationary nonequilibrium states

Domaines: Probabilités [math.PR]

Mustapha Mourragui, Enza Orlandi. Macroscopic properties and dynamical large deviations of the boundary driven Kawasaki process with long range interaction. 2011. ⟨hal-00634205v1⟩