Large deviations in and out of equilibrium

The fluctuations of observables beyond their mean and variance is described in general by so-called large deviation functions (ldf).

Although they intrinsically describe rare or atypical events, we'll illustrate on specific examples how their atypical features can bring us information on the systems' dynamics. In the large system size limit, the ldf can e.g. develop singularities which correspond to a dynamical phase transition, due for example to dynamical phase coexistence in glass models. Some 1d transport models also present an intriguing duality between equilibrium and non-equilibrium that can be explicited through their ldf.