The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in nonequilibrium, namely for nonreversible systems. In this paper we consider a simple example of a nonequilibrium situation, the symmetric simple exclusion process in which we let the system exchange particles with the boundaries at two different rates. We prove a dynamical large deviation principle for the empirical density which describes the probability of fluctuations from the solutions of the hydrodynamic equation. The so-called quasi potential, which measures the cost of a fluctuation from the stationary state, is then defined by a variational problem for the dynamical large deviation rate function. By characterizing the optimal path, we prove that the quasi potential can also be obtained from a static variational problem introduced by Derrida, Lebowitz, and Speer.
Large deviations for the boundary driven symmetric simple exclusion process / BERTINI MALGARINI, Lorenzo; DE SOLE, Alberto; D., Gabrielli; JONA LASINIO, Giovanni; C., Landim. - In: MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY. - ISSN 1385-0172. - STAMPA. - 6:3(2003), pp. 231-267. [10.1023/a:1024967818899]
Large deviations for the boundary driven symmetric simple exclusion process
BERTINI MALGARINI, Lorenzo;DE SOLE, ALBERTO;JONA LASINIO, Giovanni;
2003
Abstract
The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in nonequilibrium, namely for nonreversible systems. In this paper we consider a simple example of a nonequilibrium situation, the symmetric simple exclusion process in which we let the system exchange particles with the boundaries at two different rates. We prove a dynamical large deviation principle for the empirical density which describes the probability of fluctuations from the solutions of the hydrodynamic equation. The so-called quasi potential, which measures the cost of a fluctuation from the stationary state, is then defined by a variational problem for the dynamical large deviation rate function. By characterizing the optimal path, we prove that the quasi potential can also be obtained from a static variational problem introduced by Derrida, Lebowitz, and Speer.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.