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- L. Bertini, A. De Sole, D. Gabrielli, G. Jona–Lasinio, C. Landim
- 2001

We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager–Machlup theory in the SNS; a general… (More)

- L. Bertini, A. De Sole, D. Gabrielli, G. Jona–Lasinio, C. Landim
- 2003

The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in non–equilibrium, namely for non reversible systems. In this paper we consider a simple example of a non–equilibrium situation, the symmetric simple exclusion process in which we let the system exchange particles with… (More)

We consider the weakly asymmetric exclusion process on the one dimensional lattice. It has been proven that, in the diiusive scaling limit, the density eld evolves according to the Burgers equation 8, 19, 14] and the uctuation eld converges to a generalized Ornstein-Uhlenbeck process 8, 10]. We analyze instead the density uctuations beyond the… (More)

- L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, C. Landim
- 2005

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation j of the empirical current with a rate functional I(j). We then estimate the probability of a fluctuation of the… (More)

We investigate a one dimensional chain of 2N harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites −N and N are in contact with thermal reservoirs at different temperature τ − and τ +. Kipnis, Marchioro, and Presutti [18] proved that this model satisfies Fourier's law and that in the hydrodynamical scaling… (More)

- L Bertini, A De Sole, D Gabrielli, G Jona-Lasinio, C Landim
- 2006

We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide… (More)

- L. Bertini, A. De Sole, D. Gabrielli, G. Jona–Lasinio, C. Landim
- 2007

This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a unified picture is emerging at the macroscopic level, applicable, in our view, to real phenomena where diffusion is the… (More)

- L Bertini, A De Sole, D Gabrielli, G Jona-Lasinio, C Landim
- 2005

We study current fluctuations in lattice gases in the hydrodynamic scaling limit. More precisely, we prove a large deviation principle for the empirical current in the symmetric simple exclusion process with rate functional I. We then estimate the asymptotic probability of a fluctuation of the average current over a large time interval and show that the… (More)

Stochastic lattice gases with degenerate rates, namely conservative particle systems where the exchange rates vanish for some configurations, have been introduced as simplified models for glassy dynamics. We introduce two particular models and consider them in a finite volume of size ℓ in contact with particle reservoirs at the boundary. We prove that, as… (More)

- L. Bertini, A. De Sole, D. Gabrielli, G. Jona–Lasinio, C. Landim
- 2008

In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide class of microscopic stochastic models where they are satisfied. The description however does not refer in any way to an… (More)