I'll 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. I'll show how the presence of multiple effective temperatures can be experimentally observed by means of a generalized fluctuation-dissipation theorem. Moreover I'll present the recently introduced hydrodynamic description of such non-thermal steady states that allows to construct non-equilibrium steady states with persistent energy or spin currents and to study transport properties of the XXZ chain and the fermionic Hubbard model.

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