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Entropy and Area
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The ground state density matrix for a massless free field is traced over the degrees of freedom residing inside an imaginary sphere; the resulting entropy is shown to be proportional to the area (and not the volume) of the sphere. Possible connections with the physics of black holes are discussed.
Forward citations
Cited by 39 Pith papers
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Quantum Penrose Inequality
A conjectured inequality, m ≥ sqrt(ℏ S_gen/(4πG)), replaces the surface area in the Penrose bound by the generalized entropy on a quantum lightsheet.
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Determination of thermodynamics from entanglement entropy in the finite-density O(N) model
The derivative of entanglement entropy with respect to subregion volume equals the thermal entropy density in the large-subregion limit, verified via lattice simulations of the finite-density O(4) model using dual wor...
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Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition
Generalized entanglement entropies are constructed via left-, right-, and bi-invariant unit-invariant singular value decompositions to ensure scale invariance for non-Hermitian and rectangular operators in quantum mec...
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Relational entanglement entropies and quantum reference frames in gauge theories
Quantum reference frames built from Wilson lines give lattice gauge theories gauge-invariant subsystem factorizations and a hierarchy of relational entanglement entropies.
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Entanglement Entropy of a Scalar Field in Anti-de Sitter Space
For a free massive scalar in AdS4, the UV-divergent entanglement entropy of centered spherical regions takes a fitted form whose logarithmic coefficient, -1/90 plus (-mu^2 a^2/6 - 1/3) times the proper area, matches c...
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Geometric modular flows in 2d CFT and beyond
In 2d CFTs, every suitably regular Unruh flow on the Rindler wedge is the modular flow of a state obtained by a conformal unitary acting on the vacuum or thermal state, and local entropy and stress-tensor formulas follow.
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A critical state under weak measurement is not critical
Weakly measured critical free fermions have a gapped and long-ranged entanglement Hamiltonian while preserving logarithmic entanglement entropy.
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Entanglement entropy of linearized gravitons in a sphere
A linearized graviton field in a sphere has entanglement entropy equal to that of two massless scalars with l=0 and l=1 modes removed, giving a logarithmic coefficient of -61/45.
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Boundary Conditions and Entanglement in Anti-de Sitter Space
For a conformally coupled scalar in AdS4, the UV-divergent entanglement entropy is independent of boundary conditions, while the UV-finite part acquires a boundary-condition dependent R^2/a^2 correction with coefficie...
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Cosmological consequences of scale-dependent Barrow-Tsallis entropy
A scale-dependent Barrow-Tsallis entropy cosmology fits cosmic data but is statistically disfavored versus ΛCDM, with only a modest and partially circular Hubble-tension 'alleviation'.
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The Entanglement Wedge Polygon
The paper defines the entanglement wedge polygon as the intersection of entanglement wedges external to individual homology regions and studies its topological and geometric properties in AdS examples.
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Numerical approach to the modular operator for fermionic systems
A position-space discretization on a cylinder approximates the modular operator for one and two double cones in the 1+1D massive Majorana field, showing nontrivial mass dependence and reduced bilocal terms at higher masses.
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Universality of pseudoentropy for deformed spheres in dS/CFT
The quadratic shape-deformation correction to pseudoentropy in dS/CFT is controlled by the analytically continued stress-tensor coefficient C_T, making the sphere a local extremum across Einstein and quadratic-curvatu...
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Entanglement Entropy of a Non-Minimally Coupled Self-Interacting Scalar across a Schwarzschild Horizon at $\mathcal{O}(\alpha)$
The O(α) correction to entanglement entropy of a non-minimally coupled self-interacting scalar across a Schwarzschild horizon is proportional to (1/6 - ξ), with divergences that renormalize Newton's constant while pre...
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From the Corner Proposal to the Area Law
For spherically symmetric gravity, the entanglement entropy of 'classical' quantum-corner coherent states scales with horizon area — but the Bekenstein–Hawking coefficient 1/4 is fixed by hand-picked central charges, ...
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Optimal symmetry operators
The Araki cone α=0 purification uniquely attains the Uhlmann fidelity, defining an 'optimal symmetry operator' with maximal expectation value.
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Entanglement Entropy of Quantum Corners
For a two-dimensional corner symmetry algebra, coherent corner states give an entanglement entropy that scales with the area when mapped to near-extremal Reissner-Nordström black holes.
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Entanglement on a Sphere
The entanglement entropy of a scalar field on the R×S^3 Einstein universe has an infrared contribution from the zero mode with coefficient c_IR = 1/6, distinct from the de Sitter value 1/3.
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Internal color contributions to flux tube entanglement entropy
Preliminary lattice data support the conjecture that the internal color entanglement entropy of a flux tube equals <F> log N_c, where <F> is the average number of boundary crossings.
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Localized Black Holes in AdS$_3$: What Happens Below c/12 Stays Below c/12
Localized black holes in AdS3 x S3 x T4 fill the low-energy spectrum, dominate the microcanonical ensemble below a small positive energy, and appear to have the same entanglement entropy as BTZ black holes.
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R\'enyi entropy of single-character CFTs on the torus
A Wronskian-based method gives explicit torus conformal blocks for the Z2 orbifold of E8,1, yielding a two-periodic twist two-point function and the second Rényi entropy with universal logarithmic divergence plus UV-f...
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Entanglement Harvesting and Quantum Discord of Alpha Vacua in de Sitter Space
The reduced states of static UDW detectors coupled to a scalar field in alpha-vacua are derived analytically, revealing distinct behaviors of entanglement harvesting for time-like versus space-like separations and sup...
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Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
Kounterterm renormalization is extended to even-dimensional holographic CFTs, yielding a universal entanglement entropy formula whose logarithmic coefficient reproduces the type A central charge.
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Multi-entropy in heavy local quenches
Genuine multi-entropy in heavy local quenches in 2D holographic CFTs is kinematically fixed to logarithms of rational functions of time, independent of heavy operator dimension, due to global saddle selection in the g...
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Thermal and chemical response from entanglement entropy
The derivative of entanglement entropy with respect to region size equals the thermal entropy density, and a generalized Maxwell relation connects it to charge density — tested nonperturbatively in the 3D O(4) model.
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Hubble Tension as an Effect of Horizon Entanglement Nonequilibrium
A phenomenological 'horizon entanglement deficit' with the form ρ ∝ H² is fit to low-z data under a forced H0=73 prior; the nonzero amplitude is a restatement of that prior.
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Effective density matrix for vacua in asymptotically flat gravity
The vacuum of a large causal diamond in asymptotically flat gravity is claimed to be a Gaussian in the supertranslation Goldstone mode, giving modular Hamiltonian variance A/epsilon squared.
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Entanglement Entropy and Thermodynamics of Dynamical Black Holes
In f(R) theories, the replica-method gravitational entropy computed on the apparent horizon matches the Hollands-Wald-Zhang dynamical black hole entropy and satisfies the first law, while the event horizon does not; t...
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Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State
Numerical MPS study of the Moore-Read state finds approximate equipartition of symmetry-resolved entanglement entropy and good agreement with the Li-Haldane conjecture for the entanglement spectrum despite distinct ne...
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R\'enyi Entanglement of Purification and Half R\'enyi Reflected Entropy in Free Scalar Theory
In a free scalar lattice model, numerical calculations show Rényi entanglement of purification is at least half the Rényi reflected entropy for 0 < n < 2 in the small subsystems tested.
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Thermal Pseudo-Entropy
Thermal pseudo-entropy is the analytic continuation S(β+it) of thermal entropy, equals the pseudo-entropy of a Thermofield Double transition matrix, and its averaged real part tracks the spectral form factor.
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Constraints on Kaniadakis Cosmology from Starobinsky Inflation and Primordial Tensor Perturbations
Kaniadakis entropic cosmology modifies early-universe dynamics and is constrained by its predictions for Starobinsky inflation and the primordial tensor spectrum using current CMB and gravitational-wave observations.
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Island of acoustic black hole in Schwarzschild spacetime
For a Schwarzschild-surrounded acoustic black hole, phonon entanglement entropy follows a Page curve in the non-extremal case but diverges (no Page time) in the extremal case, according to the island formula.
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Integrals of motion on extremals of the equation Euler-Lagrange
The paper claims that Wronskian determinants of closed first-order ODE systems serve as integrals of motion on Euler-Lagrange extremals, constructed via the Jacobi equation.
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Emergent Holographic Spacetime from Quantum Information
Takayanagi's essay outlines a research program in which holographic spacetime, including the time direction, may emerge from entanglement, complexity, and complex-valued pseudo-entropy, without presenting a new derivation.
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Emergent Gravity in a Holographic Universe
Causal diamonds in symmetric spacetimes obey a thermodynamic first law with negative temperature, and the Einstein equations can be recast as an entropy equilibrium condition, with a long-string CFT picture for non-Ad...
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Effect of Non-Extensive Parameter on Page Curve
The entanglement entropy of Hawking radiation in non-extensive entropy-corrected Schwarzschild black holes grows linearly until an island forms and later saturates, with the Page time depending on the entropy deformat...
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Introduction to Black Hole Thermodynamics
A pedagogical review by Edward Witten that derives and explains the standard results of black hole thermodynamics: black hole entropy and temperature, the Unruh effect, the Euclidean approach, and the Ryu-Takayanagi formula.
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Lectures on entanglement entropy in field theory and holography
Lecture notes surveying entanglement entropy in QFT and holography, emphasizing physical aspects and the Ryu-Takayanagi formula.
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