Entropy-area law and temperature of de Sitter horizons from modular theory

Abstract

We derive an entropy-area law for the future horizon of an observer in diamonds inside the static patch of de Sitter spacetime, taking into account the backreaction of quantum matter fields. We prove positivity and convexity of the relative entropy for coherent states using Tomita--Takesaki modular theory, from which the QNEC for diamonds follows. Furthermore, we show that the generalized entropy conjecture holds. Finally, we reveal that the local temperature which is measured by an observer at rest exhibits subleading quantum corrections with respect to the well-known cosmological horizon temperature $H/(2\pi )$.

arXiv comment11 pages, 3 figures. Accepted for publication in PTEP

References in corpus (49)

• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement entropy and conformal field theory
• Notes on Some Entanglement Properties of Quantum Field Theory
• Entanglement entropy of black holes
• Entanglement Equilibrium and the Einstein Equation
• An Algebra of Observables for de Sitter Space
• Partial and Complete Observables for Canonical General Relativity
• Relative entropy and the Bekenstein bound
• Positive vacuum energy and the N-bound
• Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in General Covariant Quantum Theories
• A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
• Proof of the Quantum Null Energy Condition
• Scalar Material Reference Systems and Loop Quantum Gravity
• De Sitter Holography and Entanglement Entropy
• A New Area Law in General Relativity
• Diamonds's Temperature: Unruh effect for bounded trajectories and thermal time hypothesis
• The Role of Type III Factors in Quantum Field Theory
• Entanglement measures and their properties in quantum field theory
• Light-sheets and Bekenstein's bound
• A global picture of quantum de Sitter space
• De Sitter Space and Entanglement
• The minus sign in the first law of de Sitter horizons
• Non-local Entanglement and Fast Scrambling in De-Sitter Holography
• Upper bound for entropy in asymptotically de Sitter space-time
• Entropy, Entanglement and Swampland Bounds in DS/dS
• On extremal surfaces and de Sitter entropy
• Geometric modular action for disjoint intervals and boundary conformal field theory
• Some Information Theoretic Aspects of De-Sitter Holography
• Cosmological perturbation theory and quantum gravity
• Modular Flow of Excited States
• A Lower Bound on the Energy Density in Classical and Quantum Field Theories
• Relative entropy for coherent states from Araki formula
• Comment on the Bekenstein bound
• Entropy of Coherent Excitations
• Temperature and entropy-area relation of quantum matter near spherically symmetric outer trapping horizons
• Relative entropy for coherent states in chiral CFT
• Logarithmic Corrections, Entanglement Entropy, and UV Cutoffs in de Sitter Spacetime
• News vs Information
• de Sitter entropy as entanglement
• De Sitter-invariant States from Holography
• Relative entropy of coherent states on general CCR algebras
• Entropy for spherically symmetric, dynamical black holes from the relative entropy between coherent states of a scalar quantum field
• Conformal bounds in three dimensions from entanglement entropy
• Relative Entropy of Fermion Excitation States on the CAR Algebra
• Modular Hamiltonian for de Sitter diamonds
• Relative Entropy in de Sitter is a Noether Charge
• Synchronous coordinates and gauge-invariant observables in cosmological spacetimes
• Modular Theory for Operator Algebra in Bounded Region of Space-Time and Quantum Entanglement

Cited by in corpus (7)

• Modular Hamiltonian for de Sitter diamonds
• From Quantum Relative Entropy to the Semiclassical Einstein Equations
• Quantum information and the C-theorem in de Sitter
• Modular Hamiltonian for fermions of small mass
• Notions of Fermionic Entropies of a Causal Fermion System
• A numerical analysis of Araki-Uhlmann relative entropy in Quantum Field Theory
• Petz-Rényi relative entropy in QFT from modular theory