From dynamic to static large deviations in boundary driven exclusion particle systems

We consider the large deviations for the stationary measures associated to a boundary driven symmetric simple exclusion process. Starting from the large deviations for the hydrodynamics and following the Freidlin and Wentzell's strategy, we prove that the rate function is given by the quasi-potential of the Freidlin and Wentzell theory.This result is motivated by the recent developments on the non-equilibrium stationary measures by Derrida et al. (J. Statist. Phys. 107 (2002) 599) and the more closely related dynamical approach by Bertini et al. (J. Statist. Phys. 107 (2002) 635).