Replica wormhole geometries justify the replica trick computation of the Page curve in holographic black hole models and support entanglement wedge reconstruction via the Petz map.
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Average Entropy of a Subsystem
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If a quantum system of Hilbert space dimension $mn$ is in a random pure state, the average entropy of a subsystem of dimension $m\leq n$ is conjectured to be $S_{m,n}=\sum_{k=n+1}^{mn}\frac{1}{k}-\frac{m-1}{2n}$ and is shown to be $\simeq \ln m - \frac{m}{2n}$ for $1\ll m\leq n$. Thus there is less than one-half unit of information, on average, in the smaller subsystem of a total system in a random pure state.
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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 mechanics, random matrices, and Chern-Simons theory.
Modular flow in SYK models coupled to a bath reveals singularities allowing reconstruction of bulk flow past the horizon in two-sided AdS2 black holes.
In a 2d evaporating black hole model, large boosts create O(1/G_N) gradients in bulk entropy that move the quantum extremal surface, causing the generalized entropy to follow unitary expectations with information disappearing after a scrambling time and a phase transition at the Page time.
Families of complex tensor trace-invariants with tree-like dominant pairings factorize at large N, allowing computation of typical multipartite Rényi entropies for uniform random states.
A quantum Maxwell demon near a black hole horizon loses some work extraction ability for external observers due to information inaccessibility but obeys local thermodynamics and preserves the equivalence principle for internal observers.
Typical entanglement entropy with fixed global charge is given by the local thermal entropy at fixed charge density for both U(1) and SU(2) symmetries in the thermodynamic limit.
In a JT gravity model with an EoW brane, black hole interior complexity grows linearly until the Page time then decays exponentially, with fluctuations growing large afterward and signaling loss of self-averaging.
Nucleated black holes in de Sitter space evaporate via standard Hawking radiation back to the empty vacuum, rendering nucleation a temporary fluctuation.
Hawking radiation terminates around the scrambling time due to trans-Planckian stringy effects in GUP and string-field-theory-inspired toy models, yielding negligible evaporation and a mostly classical black hole.
The authors extend tensorial free cumulants to arbitrary orders, connect prior frameworks, and compute non-trivial examples for Gaussian tensors with structured covariances.
The volume-law coefficient of eigenstate entanglement entropy in Bose-Hubbard models remains unchanged by on-site disorder, while the O(1) contribution depends on particle density and bosonic cutoff in conserving cases and may become universal without conservation.
Review of random matrix theory application to quantum chaos, covering symmetry classes, eigenvalue statistics, unfolding, and correlation functions.
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Typical entanglement entropy with charge conservation
Typical entanglement entropy with fixed global charge is given by the local thermal entropy at fixed charge density for both U(1) and SU(2) symmetries in the thermodynamic limit.
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