Most many-particle systems occurring in nature are so complex that one has to rely on statistical methods. Systems in thermodynamic equilibrium, which can be characterised by a few macroscopic parameters such as temperature, are very well understood. The situation is different for systems that are either externally driven or are strongly perturbed to begin with. Such so-called non-equilibrium systems exhibit a wide variety of new phenomena, including unusual phase transitions and non-trivial fluctuations, which can be described using methods from statistical physics, computer simulations and field theory. Such processes usually produce entropy and are therefore irreversible in time. But how does this apparent irreversibility harmonise with the fundamental laws of quantum mechanics, which are reversible in time? Such and similar questions in the area of tension between statistical physics and quantum information theory are of increasing interest and are being investigated at our chair using various methods.