Title: Large deviation approach to nonequilibrium systems

Abstract: The theory of large deviations has been applied with great
success in the last 30 years or so to study the properties of
equilibrium systems and, ultimately, to put the foundations of
equilibrium statistical mechanics on a clearer and more rigorous
footing. A similar approach has been followed more recently for
nonequilibrium systems, especially in the context of interacting
particle systems, such as the exclusion process, the zero-range
process, and their many variants. We review here the basis of this
approach, emphasizing the similarities and differences that exist
between the application of large deviation theory for studying
equilibrium systems on the one hand and nonequilibrium systems on the
other. Of particular importance in this review are the notions of
macroscopic, hydrodynamic, and long-time limits, which are analogues
of the equilibrium thermodynamic limit, and the notion of statistical
ensembles which can be generalized to nonequilibrium systems. For the
purpose of illustrating our discussion, we focus on applications to
Markov processes evolving continuously in time.

Keywords: Large deviations, nonequilibrium systems, typical states,