The exclusion process: A paradigm for non-equilibrium behaviour

•Review of non-equilibrium processes (large-deviation, generalized detailed balance, Fluctuation Theorem).•Basic properties of the Asymmetric Exclusion Process.•Crash-course on the Bethe Ansatz.•Exact results for large deviations of the stationary current.•Towards a fluctuating hydrodynamics description.

In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us with a unified description of many physical situations. These functions are expected to play, for systems far from equilibrium, a role akin to that of the thermodynamic potentials. These concepts will be illustrated by exact solutions of the Asymmetric Exclusion Process, a paradigm for non-equilibrium statistical physics.