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There is a fascinating relation between the dynamics of quantum fields and information theory formulated in terms of entropy. While this is well known and understood in thermal equilibrium, the extension to non-equilibrium dynamics is a topic of current research. I will discuss how in quantum field theory entropy results from entanglement between different regions and how local production of entropy is related to dissipation. A local form of the second law of thermodynamics emerges and is the starting point of an effective low energy description in terms of relativistic fluid dynamics. These ideas find applications in the context of high energy collisions and in cosmology and can be tested further with ultra-cold atoms.