Large deviation approach to non equilibrium processes in stochastic lattice gases

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.

Extended version of the lectures given by G. Jona-Lasinio at the 9th Brazilian school of Probability, August 2005

Cited by in corpus (30)

• Macroscopic fluctuation theory
• Fluctuation theorems for stochastic dynamics
• Stochastic interacting particle systems out of equilibrium
• Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Duality for stochastic models of transport
• Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process
• Large deviations and dynamical phase transitions in stochastic chemical networks
• Dynamical fluctuations for semi-Markov processes
• Dynamical large deviations for the boundary driven weakly asymmetric exclusion process
• Harmonic Systems With Bulk Noises
• Optimal paths of non-equilibrium stochastic fields: the Kardar-Parisi-Zhang interface as a test case
• Large deviations for the current and tagged particle in 1D nearest-neighbor symmetric simple exclusion
• Exact equalities and thermodynamic relations for nonequilibrium steady states
• Duality relations in single-file diffusion
• Strong asymmetric limit of the quasi-potential of the boundary driven weakly asymmetric exclusion process
• Fluctuations of the heat flux of a one-dimensional hard particle gas
• Static large deviations of boundary driven exclusion processes
• Joint distribution of currents in the symmetric exclusion process
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
• Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations
• Large deviation generating function for energy transport in the Pauli-Fierz model
• Hydrodynamic limit for a boundary driven stochastic lattice gas model with many conserved quantities
• Lattice gas model in random medium and open boundaries: hydrodynamic and relaxation to the steady state
• Hydrostatics and dynamical large deviations of boundary driven gradient symmetric exclusion
• Miniatures on Open Quantum Systems
• Diffusion of energy in chains of oscillators with bulk noise
• Quasi-potentials of the entropy functionals for scalar conservation laws
• Dynamical large deviations for a boundary driven stochastic lattice gas model with many conserved quantities