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. As I will discuss, these ideas find applications in the context of high energy nuclear collisions, hadronization models, and in cosmology.

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