Novel Aspects of the Extended First Law of Entanglement

Abstract

Using AdS/CFT an extended first law of entanglement has been previously derived for the vacuum reduced to a ball in Minkowski. The statement not only includes perturbations of the state but also of the conformal field theory (CFT), via variations of the generalized central charge. We clarify some subtleties previously overlooked and use simple arguments to generalize prior derivations to arbitrary gravity theories in the bulk as well as new regions in the boundary CFT. Our construction also applies to two-dimensional bulk theories and admits an interesting extension for a three-dimensional bulk, providing a curious result regarding the thermodynamic volume in extended black hole thermodynamics. We discuss future prospects regarding the extended first law of entanglement.

30 pages and 2 figures. V2: updated to match published version, new subsection 3.2

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• Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity
• Holographic Complexity and Thermodynamic Volume
• Bit threads, Einstein's equations and bulk locality
• $D\to 4$ Einstein-Gauss-Bonnet Gravity and Beyond
• Quantum information probes of charge fractionalization in large-$N$ gauge theories
• Quantum bit threads and holographic entanglement
• The first law of differential entropy and holographic complexity
• Universality for Black Hole Heat Engines Near Critical Points
• The Stringy Origins of Galileons and their Novel Limit
• Holographic complexity of rotating black holes