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.

arXiv comment30 pages and 2 figures. V2: updated to match published version, new subsection 3.2

References in corpus (44)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The Black Hole in Three Dimensional Space Time
• Entanglement Entropy and Quantum Field Theory
• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Aspects of Holographic Entanglement Entropy
• Enthalpy and the Mechanics of AdS Black Holes
• Towards a derivation of holographic entanglement entropy
• Massive Gravity in Three Dimensions
• Black hole chemistry: thermodynamics with Lambda
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Surface Terms as Counterterms in the AdS/CFT Correspondence
• The cosmological constant and the black hole equation of state
• Holographic c-theorems in arbitrary dimensions
• Gravitation from Entanglement in Holographic CFTs
• Gravitational Dynamics From Entanglement "Thermodynamics"
• Relative Entropy and Holography
• More on Massive 3D Gravity
• Charged Rotating Black Hole in Three Spacetime Dimensions
• Holographic Heat Engines
• Entanglement entropy, conformal invariance and extrinsic geometry
• AdS2 Quantum Gravity and String Theory
• Entanglement Temperature and Entanglement Entropy of Excited States
• Entanglement hamiltonians in two-dimensional conformal field theory
• AdS/CFT Duals of Topological Black Holes and the Entropy of Zero-Energy States
• Equivalence of the Einstein and Jordan frames
• On the new massive gravity and AdS/CFT
• Asymptotic symmetries of AdS_2 and conformal group in d=1
• Markov property of the CFT vacuum and the a-theorem
• The $D\to 2$ Limit of General Relativity
• Lower-Dimensional Black Hole Chemistry
• Holographic Description of AdS_2 Black Holes
• Central Charge for AdS_2 Quantum Gravity
• Bose condensation and branes
• AdS${}_2$ Holographic Dictionary
• Chemical Potential in the First Law for Holographic Entanglement Entropy
• Holographic entanglement chemistry
• The F-Theorem and F-Maximization
• Central Charge for 2D Gravity on AdS(2) and AdS(2)/CFT(1) Correspondence
• The compressibility of rotating black holes in D-dimensions
• State-Dependent Divergences in the Entanglement Entropy
• On the first law of entanglement for Quasi-Topological gravity
• Localized thermal states and negative energy

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