Stochastic interacting particle systems out of equilibrium

By Lorenzo Bertini, A. Sole, D. Gabrielli, Giovanni Jona-Lasinio, Claudio Landim. 2007

171 citations recorded by the source corpus.

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 dominating physical mechanism. We rely mainly on an approach developed by the authors based on the study of dynamical large fluctuations in stationary states of open systems. The outcome of this approach is a theory connecting the non-equilibrium thermodynamics to the transport coefficients via a variational principle. This leads ultimately to a functional derivative equation of Hamilton–Jacobi type for the non-equilibrium free energy in which local thermodynamic variables are the independent arguments. In the first part of the paper we give a detailed introduction to the microscopic dynamics considered, while the second part, devoted to the macroscopic properties, illustrates many consequences of the Hamilton–Jacobi equation. In both parts several novelties are included.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/14fd951d986e6c26c634b27a820d5b3b5535cd7a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

The large deviation approach to statistical mechanics (2008, background): “Two excellent review papers [113,215] have appeared recently on interacting particle models and their large deviations, so we will not review this subject in detail here.”
Nonequilibrium Markov Processes Conditioned on Large Deviations (2014, background): “modeling systems driven in nonequilibrium steady states by noise and external forces [52–54], such as interacting particle systems coupled to different particle and energy reservoirs, which have been studied actively in the mathematics and physics literature recently [75–79].”
Metric viscosity solutions of Hamilton–Jacobi equations depending on local slopes (2015, background): “Such equations arise for instance in statistical mechanics and large deviations [9, 10, 11, 12, 13, 14, 32, 33, 34], fluid mechanics [30, 33, 34, 35, 36, 38, 39, 40], Mean Field Games [16, 51, 52], optimal control [31, 33, 34], study of functional inequalities [6, 42, 43, 53] and other related areas”
A pedestrian's view on interacting particle systems, KPZ universality and random matrices (2008, background): “An important goal in the study of stochastic interacting particle systems is to understand how deterministic evolution equations emerge from the stochastic microscopic dynamics on large scales [18, 66, 124].”
Macroscopic fluctuation theory (2014, background): “Here we just show, in a specific example, how the basic principles of the MFT need to be modified to cover these processes.”