| Summary: | This thesis explores applications of gauge/gravity duality to strongly coupled quantum field theories out of equilibrium. Within the framework of holography, it addresses both small deviations from equilibrium accessible via the effective theory of hydrodynamics, as well as far-from-equilibrium dynamics, which are studied using a first-principles approach. After an introduction into the duality and a presentation of the two approaches to out-of-equilibrium physics, we present our results on holographic fluids in the first part of the thesis. We derive new Kubo formulae for five second-order transport coefficients of relativistic non-conformal fluids and apply them to a class of non-conformal holographic field theories at infinite coupling. We find strong evidence that the Haack-Yarom identity, which is known to hold for conformal holographic fluids at infinite coupling, is universally satisfied by strongly coupled fluids regardless of conformal symmetry. We prove analytically that the identity is obeyed when taking into account leading non-conformal corrections and provide numerical evidence that the result holds beyond these leading corrections. In the second part of the thesis, we examine two proposals for the holographic dictionary for correlation functions in out-of-equilibrium states. We show that these proposals are equivalent on the level of two-point functions of operators dual to free scalar bulk fields. We then use one of the two non-equilibrium dictionaries to study the thermalisation of two-point functions of scalar operators and effective occupation numbers in a holographic model of quantum quenches. We find that both thermalise with a rate set by the lowest quasinormal mode of the final-state black hole in the gravitational dual.
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