Out-of-equilibrium dynamics of classical and quantum complex systems

Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied, its subsequent relaxation to equilibrium may be either impossible or take very long times. From the point of view of fundamental physics, no generic principle such as the ones of thermodynamics allows us to fully understand its behaviour. The alternative is to treat each case separately. It is illusionary to attempt to give, at least at this stage, a complete description of all non-equilibrium situations. Still, one can try to identify and characterise some concrete, but still general features of a class of out-of-equilibrium problems – yet to be identified – and search for a unified description of these. In this report, I briefly describe the behaviour and theory of a set of non-equilibrium systems and I try to highlight common features and some general laws that have emerged in recent years.