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hal-00634205, version 1

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

Mustapha Mourragui () 1, Enza Orlandi () 2

(2011-10-20)

Abstract: 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.

  • 1:  Laboratoire de Mathématiques Raphaël Salem (LMRS)
  • CNRS : UMR6085 – Université de Rouen
  • 2:  Dipartimento di Matematica [Roma TRE]
  • Università degli Studi Roma TRE
  • Domain : Mathematics/Probability
  • Keywords : Kawasaki process – Kac potential – Large deviations – Stationary nonequilibrium states
  • Available versions :  v1 (2011-10-20) v2 (2012-09-30)
 
  • hal-00634205, version 1
  • http://hal.archives-ouvertes.fr/hal-00634205
  • oai:hal.archives-ouvertes.fr:hal-00634205
  • From: Mustapha Mourragui <>
  • Submitted on: Thursday, 20 October 2011 16:04:57
  • Updated on: Thursday, 20 October 2011 22:47:52