Large Deviations for the Boundary Driven Symmetric Simple Exclusion Process

Springer Science and Business Media LLC - Tập 6 - Trang 231-267 - 2003
L. Bertini1, A. De Sole2, D. Gabrielli1, G. Jona-Lasinio3, C. Landim4,5
1Dipartimento di Matematica, Università di Roma La Sapienza, Rome, Italy
2Department of Mathematics, MIT, Cambridge, U.S.A
3Dipartimento di Fisica and INFN, Università di Roma La Sapienza, Rome, Italy
4IMPA, Rio de Janeiro, Brazil
5CNRS UMR 6085, Université de Rouen, Mont-Saint-Aignan Cedex, France

Tóm tắt

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.

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Springer Science and Business Media LLC

Tập 6

231-267

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