# 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.

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## References

SHOWING 1-10 OF 30 REFERENCES

### Current fluctuations in stochastic lattice gases.

- Physics, MathematicsPhysical review letters
- 2005

A large deviation theory is established for the space-time fluctuations of the empirical current for lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles.

### Large deviations of the empirical current in interacting particle systems

- Mathematics
- 2006

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…

### Lattice gas models in contact with stochastic reservoirs: Local equilibrium and relaxation to the steady state

- Mathematics
- 1991

Extending the results of a previous work, we consider a class of discrete lattice gas models in a finite interval whose bulk dynamics consists of stochastic exchanges which conserve the particle…

### Large Deviations for the Boundary Driven Symmetric Simple Exclusion Process

- Mathematics, Physics
- 2003

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…

### Non Equilibrium Current Fluctuations in Stochastic Lattice Gases

- Physics
- 2006

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…

### Fluctuations in stationary nonequilibrium states of irreversible processes.

- PhysicsPhysical review letters
- 2001

We formulate a dynamical fluctuation theory for stationary nonequilibrium states (SNS) which covers situations in a nonlinear hydrodynamic regime and is verified explicitly in stochastic models of…

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

- Mathematics
- 2004

### Fluctuations and Irreversible Processes

- Physics
- 1953

The probability of a given succession of (nonequilibrium) states of a spontaneously fluctuating thermodynamic system is calculated, on the assumption that the macroscopic variables defining a state…

### Distribution of current in nonequilibrium diffusive systems and phase transitions.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

This time dependent profile persists in the large drift limit and allows one to understand on physical grounds the results obtained earlier for the totally asymmetric exclusion process on a ring.

### Hydrodynamics of stationary non-equilibrium states for some stochastic lattice gas models

- Mathematics
- 1990

We consider discrete lattice gas models in a finite interval with stochastic jump dynamics in the interior, which conserve the particle number, and with stochastic dynamics at the boundaries chosen…