Holographic Non-perturbative Thermodynamic Systems

The anti-de Sitter/conformal field theory (AdS/CFT) correspondence conjectures a duality between field theories and higher dimensional theories of gravitation. Recent results describing thermodynamic systems in the AdS/CFT context include an exact description of the efficiency of black hole heat engines, suggesting questions regarding the nature of heat engines within this formulation and the extent to which thermodynamic principles may be applied. We verify the Clausius statement and the maximum efficiency of the Carnot engine, and show that these follow from the thermodynamic definitions of the heat engine. In a related scope, we propose that, given the Ryu-Takayanagi prescription for holographic entanglement entropy, the null-energy condition for Poincaré invariant spaces implies the monotonicity of entanglement entropy with respect to the energy scale of the corresponding gauge theory. We examine the implications of this conjecture and describe our work toward its verification. Thesis Supervisor: Joshua Erlich Title: Associate Professor