Abstract

These three lectures will give an introduction of the macroscopic fluctuation theory, which allow to describe large scale properties of out-of-equilibrium diffusive systems.  They will present a few examples of models for which the large deviation functions of the density or of the current can be computed with or/and without this theory.Some references: Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., & Landim, C. (2002). Macroscopic fluctuation theory for stationary non-equilibrium states. Journal of Statistical Physics, 107, 635-675. Derrida, B. (2007). Non-equilibrium steady states: fluctuations and large deviations of the density and of the current. Journal of Statistical Mechanics: Theory and Experiment, 2007(07), P07023 .The main review:Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., & Landim, C. (2015). Macroscopic fluctuation theory. Reviews of Modern Physics, 87(2), 593.