Large deviations in non-equilibrium systems

Bernard Derrida, Collège de France

After an introduction on the way large deviation functions appear in non-equilibrium systems, I will try to explain how they can be calculated for general Markov processes. Based on the theory, it is easy to establish general properties of non-equilibrium systems such as the fluctuation theorem. Then the main part of these lectures will be to review the theoretical approaches, such as matrix products, the Bethe ansatz or the macroscopic fluctuation theory, allowing to obtain a series of exact expressions of large deviation functions for lattice gas models.