Bit threads and the membrane theory of entanglement dynamics

Abstract Recently, an effective membrane theory was proposed that describes the “hydrodynamic” regime of the entanglement dynamics for general chaotic systems. Motivated by the new bit threads formulation of holographic entanglement entropy, given in terms of a convex optimization problem based on flow maximization, or equivalently tight packing of bit threads, we reformulate the membrane theory as a max flow problem by proving a max flow-min cut theorem. In the context of holography, we explain the relation between the max flow program dual to the membrane theory and the max flow program dual to the holographic surface extremization prescription by providing an explicit map from the membrane to the bulk, and derive the former from the latter in the “hydrodynamic” regime without reference to minimal surfaces or membranes.

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A PASSIVITY APPROACH TO SYNCHRONIZATION FOR TIME-DELAYED CHAOTIC SYSTEMS

Modern Physics Letters B ◽

10.1142/s0217984909021594 ◽

2009 ◽

Vol 23 (29) ◽

pp. 3531-3541 ◽

Cited By ~ 6

Author(s):

CHOON KI AHN

Keyword(s):

Neural Networks ◽

Optimization Problem ◽

Chaotic Systems ◽

Linear Matrix ◽

Asymptotically Stable ◽

Matrix Inequality ◽

Lmi Approach ◽

Convex Optimization Problem ◽

Synchronization Problem ◽

Error System

In this letter, we propose a new passivity-based synchronization method for time-delayed chaotic systems. Based on Lyapunov–Krasovskii theory and linear matrix inequality (LMI) approach, the passivity-based controller is presented to make the synchronization error system for time-delayed chaotic systems not only passive but also asymptotically stable. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. As an application of the proposed method, the synchronization problem for chaotic delayed Hopfield neural networks is investigated.

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Inverse reinforcement learning in contextual MDPs

Machine Learning ◽

10.1007/s10994-021-05984-x ◽

2021 ◽

Author(s):

Stav Belogolovsky ◽

Philip Korsunsky ◽

Shie Mannor ◽

Chen Tessler ◽

Tom Zahavy

Keyword(s):

Reinforcement Learning ◽

Optimization Problem ◽

Decision Processes ◽

Inverse Reinforcement Learning ◽

Convex Optimization Problem ◽

Reward Function ◽

Dynamic Treatment Regime ◽

Markov Decision ◽

Dynamic Treatment ◽

Recorded Data

AbstractWe consider the task of Inverse Reinforcement Learning in Contextual Markov Decision Processes (MDPs). In this setting, contexts, which define the reward and transition kernel, are sampled from a distribution. In addition, although the reward is a function of the context, it is not provided to the agent. Instead, the agent observes demonstrations from an optimal policy. The goal is to learn the reward mapping, such that the agent will act optimally even when encountering previously unseen contexts, also known as zero-shot transfer. We formulate this problem as a non-differential convex optimization problem and propose a novel algorithm to compute its subgradients. Based on this scheme, we analyze several methods both theoretically, where we compare the sample complexity and scalability, and empirically. Most importantly, we show both theoretically and empirically that our algorithms perform zero-shot transfer (generalize to new and unseen contexts). Specifically, we present empirical experiments in a dynamic treatment regime, where the goal is to learn a reward function which explains the behavior of expert physicians based on recorded data of them treating patients diagnosed with sepsis.

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Chern-Simons gravity dual of BCFT

Journal of High Energy Physics ◽

10.1007/jhep04(2021)193 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Tadashi Takayanagi ◽

Takahiro Uetoko

Keyword(s):

Field Theory ◽

Conformal Field Theory ◽

Entanglement Entropy ◽

Einstein Gravity ◽

Conformal Field ◽

Holographic Entanglement Entropy ◽

The World ◽

Higher Spin ◽

End Of The World ◽

Chern Simons

Abstract In this paper we provide a Chern-Simons gravity dual of a two dimensional conformal field theory on a manifold with boundaries, so called boundary conformal field theory (BCFT). We determine the correct boundary action on the end of the world brane in the Chern-Simons gauge theory. This reproduces known results of the AdS/BCFT for the Einstein gravity. We also give a prescription of calculating holographic entanglement entropy by employing Wilson lines which extend from the AdS boundary to the end of the world brane. We also discuss a higher spin extension of our formulation.

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Entanglement entropy in cubic gravitational theories

Journal of High Energy Physics ◽

10.1007/jhep05(2021)186 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Elena Cáceres ◽

Rodrigo Castillo Vásquez ◽

Alejandro Vilar López

Keyword(s):

Entanglement Entropy ◽

Gravitational Theory ◽

Riemann Tensor ◽

Holographic Entanglement Entropy ◽

Gravitational Theories ◽

Entropy Functional ◽

Wide Range ◽

Splitting Problem ◽

Range Of Values

Abstract We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature — minimal and non-minimal — produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4- dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.

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Probing phase transitions of holographic entanglement entropy with fixed area states

Journal of High Energy Physics ◽

10.1007/jhep12(2020)084 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Donald Marolf ◽

Shannon Wang ◽

Zhencheng Wang

Keyword(s):

Phase Transitions ◽

Entanglement Entropy ◽

Many Body ◽

Btz Black Hole ◽

Holographic Entanglement Entropy ◽

Volume Limit ◽

Cutoff Dependence ◽

Diagonal Approximation ◽

Fixed Area ◽

Many Body Systems

Abstract Recent results suggest that new corrections to holographic entanglement entropy should arise near phase transitions of the associated Ryu-Takayanagi (RT) surface. We study such corrections by decomposing the bulk state into fixed-area states and conjecturing that a certain ‘diagonal approximation’ will hold. In terms of the bulk Newton constant G, this yields a correction of order O(G−1/2) near such transitions, which is in particular larger than generic corrections from the entanglement of bulk quantum fields. However, the correction becomes exponentially suppressed away from the transition. The net effect is to make the entanglement a smooth function of all parameters, turning the RT ‘phase transition’ into a crossover already at this level of analysis.We illustrate this effect with explicit calculations (again assuming our diagonal approximation) for boundary regions given by a pair of disconnected intervals on the boundary of the AdS3 vacuum and for a single interval on the boundary of the BTZ black hole. In a natural large-volume limit where our diagonal approximation clearly holds, this second example verifies that our results agree with general predictions made by Murthy and Srednicki in the context of chaotic many-body systems. As a further check on our conjectured diagonal approximation, we show that it also reproduces the O(G−1/2) correction found Penington et al. for an analogous quantum RT transition. Our explicit computations also illustrate the cutoff-dependence of fluctuations in RT-areas.

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Spread of Entanglement in Non-Relativistic Theories

Advances in High Energy Physics ◽

10.1155/2018/9151707 ◽

2018 ◽

Vol 2018 ◽

pp. 1-27

Author(s):

Sagar F. Lokhande

Keyword(s):

Broad Class ◽

Entanglement Entropy ◽

Time Dependent ◽

Quantum Field Theories ◽

Strongly Coupled ◽

Conformal Field ◽

Instantaneous Power ◽

Holographic Entanglement Entropy ◽

Quantum Quenches ◽

Good Order

We use a simple holographic toy model to study global quantum quenches in strongly coupled, hyperscaling-violating-Lifshitz quantum field theories using entanglement entropy as a probe. Generalizing our conformal field theory results, we show that the holographic entanglement entropy of small subsystems can be written as a simple linear response relation. We use this relation to derive a time-dependent first law of entanglement entropy. In general, this law has a time-dependent term resembling relative entropy which we propose as a good order parameter to characterize out-of-equilibrium states in the post-quench evolution. We use these tools to study a broad class of quantum quenches in detail: instantaneous, power law, and periodic.

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Corner contributions to holographic entanglement entropy

Journal of High Energy Physics ◽

10.1007/jhep08(2015)068 ◽

2015 ◽

Vol 2015 (8) ◽

Cited By ~ 63

Author(s):

Pablo Bueno ◽

Robert C. Myers

Keyword(s):

Entanglement Entropy ◽

Holographic Entanglement Entropy

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Entanglement entropy of AdS5 × S5 with massive flavors

Modern Physics Letters A ◽

10.1142/s0217732318500086 ◽

2018 ◽

Vol 33 (03) ◽

pp. 1850008

Author(s):

Sen Hu ◽

Guozhen Wu

Keyword(s):

Phase Transition ◽

Line Segment ◽

Entanglement Entropy ◽

Point Of View ◽

Nucl Phys ◽

Zero Temperature ◽

Holographic Entanglement Entropy ◽

Deconfinement Phase Transition

We consider backreacted [Formula: see text] coupled with [Formula: see text] massive flavors introduced by D7 branes. The backreacted geometry is in the Veneziano limit with fixed [Formula: see text]. By dividing one of the directions into a line segment with length l, we get two subspaces. Then we calculate the entanglement entropy between them. With the method of [I. R. Klebanov, D. Kutasov and A. Murugan, Nucl. Phys. B 796, 274 (2008)], we are able to find the cut-off independent part of the entanglement entropy and finally find that this geometry shows no confinement/deconfinement phase transition at zero temperature from the holographic entanglement entropy point of view similar to the case in pure [Formula: see text].

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