This dissertation contains the author's contributions to the study of non-equilibrium aspects of the correspondence between thermal states of quantum gauge field theories and black holes in string theory. This correspondence is contained in the larger holographic gauge/gravity duality, or AdS/CFT correspondence of string theory and M-theory. The work herein is divided into six fairly independent components. (1) We present results of a numerical simulation of the classical evolution of the plane-wave matrix model, which is dual to M-theory in a plane-wave background. We find evidence for rapid thermalization of the matrix model, related by the duality to the formation of a black hole. (2) We relate classical entropy production to the growth of entanglement entropy in a simple closed quantum system, in agreement with previous results for open quantum systems, and briefly investigate the dependence on the choice of coarse-graining. (3) We study the dynamics of a simple quantum system of two coupled degrees of freedom, one of which is undergoing non-adiabatic evolution. We study the resulting velocity dependent forces and quantum back-reaction. (4) We study the evolution of entanglement entropy due to local quenches in the D1--D5 conformal field theory (CFT), deformed away from the orbifold point, and discuss how this is one stage in a thermalization process, dual to the formation of a stringy black hole. (5) We investigate the holographic dual of a local quench of a CFT, and argue that it should be interpreted as a superposition of geometries. (6) We propose a quantum field theory state dual to a small anti-de Sitter (AdS) black hole. Finally, we discuss how all these various investigations fit into the larger context of black hole physics and non-equilibrium dynamics.
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