A First Law of Entanglement Rates from Holography

Abstract

For a perturbation of the state of a Conformal Field Theory (CFT), the response of the entanglement entropy is governed by the so-called "first law" of entanglement entropy, in which the change in entanglement entropy is proportional to the change in energy. Whether such a first law holds for other types of perturbations, such as a change to the CFT Lagrangian, remains an open question. We use holography to study the evolution in time $t$ of entanglement entropy for a CFT driven by a $t$-linear source for a conserved $U(1)$ current or marginal scalar operator. We find that although the usual first law of entanglement entropy may be violated, a first law for the rates of change of entanglement entropy and energy still holds. More generally, we prove that this first law for rates holds in holography for any asymptotically $(d+1)$-dimensional Anti-de Sitter metric perturbation whose $t$ dependence first appears at order $z^d$ in the Fefferman-Graham expansion about the boundary at $z=0$.

arXiv comment20 pages + 1 appendix, v2: version accepted to Phys. Rev. D

References in corpus (60)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Aspects of Holographic Entanglement Entropy
• A Covariant Holographic Entanglement Entropy Proposal
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Entanglement entropy and conformal field theory
• Charged AdS Black Holes and Catastrophic Holography
• Towards a derivation of holographic entanglement entropy
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Generalized gravitational entropy
• Adding flavor to AdS/CFT
• Embedding AdS Black Holes in Ten and Eleven Dimensions
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Relative entropy equals bulk relative entropy
• The Gravity Dual of a Density Matrix
• Causality & holographic entanglement entropy
• A simple holographic model of momentum relaxation
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Quantum quenches in 1+1 dimensional conformal field theories
• Entanglement Tsunami: Universal Scaling in Holographic Thermalization
• Gravitational Dynamics From Entanglement "Thermodynamics"
• Relative Entropy and Holography
• Metallic AdS/CFT
• Thermodynamical Property of Entanglement Entropy for Excited States
• Deriving covariant holographic entanglement
• Entanglement Temperature and Entanglement Entropy of Excited States
• Entanglement growth during thermalization in holographic systems
• Energy flow in non-equilibrium conformal field theory
• AdS/CFT with Flavour in Electric and Magnetic Kalb-Ramond Fields
• Dynamics of Entanglement Entropy from Einstein Equation
• On Exactly Marginal Deformations of N=4 SYM and Type IIB Supergravity on AdS_5 * S^5
• Holographic Schwinger Effect and the Geometry of Entanglement
• Spread of entanglement and causality
• Quarks in an External Electric Field in Finite Temperature Large N Gauge Theory
• Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT
• Chemical Potential in the First Law for Holographic Entanglement Entropy
• Hawking Radiation and Non-equilibrium Quantum Critical Current Noise
• Relative entropy and the RG flow
• The open string membrane paradigm with external electromagnetic fields
• Vacuum Instability in Electric Fields via AdS/CFT: Euler-Heisenberg Lagrangian and Planckian Thermalization
• The Stress-Energy Tensor of Flavor Fields from AdS/CFT
• Entanglement Thermodynamics
• Far from equilibrium energy flow in quantum critical systems
• Entanglement Entropy for Probe Branes
• Exactly Marginal Deformations of N=4 SYM and of its Supersymmetric Orbifold Descendants
• Out of Equilibrium Temperature from Holography
• A Simple Holographic Model of Nonlinear Conductivity
• Magnetic instability in AdS/CFT : Schwinger effect and Euler-Heisenberg Lagrangian of Supersymmetric QCD
• Generalized gravitational entropy of probe branes: flavor entanglement holographically
• Steady-state Physics, Effective Temperature Dynamics in Holography
• Relativistic Hydrodynamics and Non-Equilibrium Steady States
• Speed Limits for Entanglement
• Driven Holographic CFTs
• Flavor corrections to the entanglement entropy
• Universality in the Large N_c Dynamics of Flavour: Thermal Vs. Quantum Induced Phase Transitions
• Universal Bounds on the Time Evolution of Entanglement Entropy
• Adiabatic pumping solutions in global AdS
• Flavour Fields in Steady State: Stress Tensor and Free Energy
• Flavored N=4 SYM -- a highly entangled quantum liquid
• Emergent Horizons and Causal Structures in Holography

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• Thermodynamical property of entanglement entropy and deconfinement phase transition
• A falling magnetic monopole as a holographic local quench
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