Generalized Gibbs Ensembles and Generalized Hydrodynamics in quantum many-body systems.

In this talk we give a short review of the the recent theoretical progresses to explicitly construct non-thermal steady states in quantum systems as interacting bosons and spin chains. We show how the presence of multiple effective temperatures can be experimentally observed by means of a generalized fluctuation-dissipation theorem. Moreover we present an hydrodynamic description of such non-thermal steady states that allows to construct non-equilibrium steady states with persistent energy or spin currents and to predict time scales for local thermalization of inhomogeneous systems.