Entanglement Thermodynamics

Abstract

We study entanglement entropy for an excited state by making use of the proposed holographic description of the entanglement entropy. For a sufficiently small entangling region and with reasonable identifications we find an equation between entanglement entropy and energy which is reminiscent of the first law of thermodynamics. We then suggest four statements which might be thought of as four laws of entanglement thermodynamics.

17 pages, no figures, typos fixed, journal version

References in corpus (6)

• Relative Entropy and Holography
• A holographic proof of the strong subadditivity of entanglement entropy
• Thermodynamical Property of Entanglement Entropy for Excited States
• Dynamics of Entanglement Entropy from Einstein Equation
• Note on Entanglement Temperature for Low Thermal Excited States in Higher Derivative Gravity
• Geometric Entropy and Hagedorn/Deconfinement Transition

Cited by in corpus (45)

• Entanglement Tsunami: Universal Scaling in Holographic Thermalization
• Gravitational Dynamics From Entanglement "Thermodynamics"
• Holographic Complexity
• Entanglement growth during thermalization in holographic systems
• Dynamics of Entanglement Entropy from Einstein Equation
• Entanglement entropy in higher derivative holography
• Thermalization in backgrounds with hyperscaling violating factor
• Entropic Counterpart of Perturbative Einstein Equation
• Thermodynamics and Entanglement Entropy with Weyl Corrections
• Note on Entanglement Temperature for Low Thermal Excited States in Higher Derivative Gravity
• Holographic entanglement chemistry
• Spread of entanglement for small subsystems in holographic CFTs
• Renormalization group flow of entanglement entropy on spheres
• Holographic entanglement entropy in the nonconformal medium
• Entanglement thermodynamics for charged black holes
• Entanglement thermodynamics for non-conformal D-branes
• RG flow of entanglement entropy to thermal entropy
• Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
• Thermodynamic law from the entanglement entropy bound
• Entanglement Entropy & Anomaly Inflow
• On Holographic Entanglement Entropy with Second Order Excitations
• AdS plane waves, entanglement and mutual information
• Holographic subregion complexity of boosted black brane and Fisher information
• Time-evolution of holographic entanglement entropy and metric perturbations
• A First Law of Entanglement Rates from Holography
• Holographic complexity for Lifshitz system
• Holographic entanglement entropy and generalized entanglement temperature
• Thermodynamical property of entanglement entropy and deconfinement phase transition
• Modular Hamiltonian for de Sitter diamonds
• Holographic Entanglement Entropy, Subregion Complexity and Fisher Information metric of `black' Non-SUSY D3 Brane
• Generalized geodesic deviation equations and an entanglement first law for rotating BTZ black holes
• On a lightlike limit of entanglement
• Holographic equivalence between the first law of entanglement entropy and the linearized gravitational equations
• Holographic entanglement entropy and entanglement thermodynamics of `black' non-susy D3 brane
• The multiple realizability of general relativity in quantum gravity
• Logarithmic Correction to BMSFT Entanglement Entropy
• Holographic entanglement entropy of the double Wick rotated BTZ black hole
• A perturbative study on the analytic continuation for generalized gravitational entropy
• Entanglement temperature for the excitation of SYM theory in (De)confinement phase
• Holographic entanglement entropy for $Li{f}_4^{(2)}\times S^1\times S^5$ spacetime with string excitations
• Entanglement rules for holographic Fermi surfaces
• Spread of Entanglement in Non-Relativistic Theories
• Entanglement Temperature and Perturbed AdS${}_3$ Geometry
• Entanglement entropy and its linear response following a global quench in holographic Gauss-Bonnet gravity
• Schwinger Type Pair Production in Non-SUSY AdS/CFT