# Large deviation approach to non equilibrium processes in stochastic lattice gases

@article{Bertini2006LargeDA, title={Large deviation approach to non equilibrium processes in stochastic lattice gases}, author={Lorenzo Bertini and Alberto De Sole and Davide Gabrielli and Giovanni Jona-Lasinio and Claudio Landim}, journal={Bulletin of the Brazilian Mathematical Society}, year={2006}, volume={37}, pages={611-643} }

Abstract.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 validity have been obtained leading to interesting physical consequences.

## 52 Citations

### Dynamical Large Deviations for a Boundary Driven Stochastic Lattice Gas Model with Many Conserved Quantities

- Mathematics, Physics
- 2009

We prove the dynamical large deviations for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is…

### Macroscopic fluctuation theory

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- 2015

Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new…

### Hydrodynamic Limit for a Boundary Driven Stochastic Lattice Gas Model with Many Conserved Quantities

- Mathematics, Physics
- 2010

We prove the hydrodynamic limit for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the…

### Hydrodynamic behavior of boundary driven stochastic lattice gas models and interacting particle systems with conductances in random environments

- Mathematics, Physics
- 2010

We prove the hydrodynamic limit for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles on the boundary: this is the…

### Microscopic versus macroscopic approaches to non-equilibrium systems

- Physics
- 2010

The one-dimensional symmetric simple exclusion process (SSEP) is one of the very few exactly soluble models of non-equilibrium statistical physics. It describes a system of particles which diffuse…

### Fluctuation Relations in Stochastic Thermodynamics

- Physics
- 2013

Fluctuation relations are identities, holding in non-equilibrium systems, that have attracted a lot of interest in the last 20 years. This is a series of 4 lectures discussing various aspects of such…

### Dynamical large deviations for the boundary driven weakly asymmetric exclusion process

- Mathematics
- 2008

We consider the weakly asymmetric exclusion process on a bounded interval with particle reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive…

### Stochastic interacting particle systems out of equilibrium

- Physics
- 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…

### Large deviations of the empirical current for the boundary driven Kawasaki process with long range interaction

- Mathematics
- 2014

We consider a lattice gas evolving in a bounded cylinder of length 2N+1 and interacting via a Neuman Kac interaction of range N, in contact with particles reservoirs at dierent densities. We…

### Fluctuation theorems for stochastic dynamics

- Physics
- 2007

Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but…

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