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2018

Energy is Entanglement

Leichenauer, Stefan, Levine, Adam, Shahbazi-Moghaddam, Arvin

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We compute the local second variation of the von Neumann entropy of a region in theories with a gravity dual.

For null variations our formula says that the diagonal part of the Quantum Null Energy Condition is saturated in every state, thus providing an equivalence between energy and entropy.
We prove that the formula holds at leading order in 1/N, and further argue that it will not be affected at higher orders.
We conjecture that the QNEC is saturated in all interacting theories.

Energy is Entanglement · Around

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Then

J. Koeller and S. Leichenauer, “Holographic Proof of the Quantum Null Energy Condition,” Phys. Rev. D
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2016
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D. Marolf and A. C. Wall, “State-Dependent Divergences in the Entanglement Entropy,” JHEP
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2016
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D. L. Jafferis, A. Lewkowycz, J. Maldacena, and S. J. Suh, “Relative entropy equals bulk relative entropy,” JHEP
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T. Faulkner, R. G. Leigh, and O. Parrikar, “Shape Dependence of Entanglement Entropy in Conformal Field Theories,” JHEP
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T. Jacobson, “Entanglement Equilibrium and the Einstein Equation,” Phys. Rev. Lett

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2014

Cited alongside, same era.

R. Bousso, H. Casini, Z. Fisher, and J. Maldacena, “Entropy on a null surface for interacting quantum field theories and the Bousso bound,” Phys. Rev. D

2015

Cited alongside, same era.

N. Engelhardt and A. C. Wall, “Quantum Extremal Surfaces: Holographic Entanglement Entropy Beyond the Classical Regime,” JHEP

2015

Cited alongside, same era.

J. Bhattacharya, V. E. Hubeny, M. Rangamani, and T. Takayanagi, “Entanglement Density and Gravitational Thermodynamics,” Phys. Rev

2015

Cited alongside, same era.

R. Bousso, Z. Fisher, J. Koeller, S. Leichenauer, and A. C. Wall, “Proof of the Quantum Null Energy Condition,” Phys. Rev. D

2016

Cited alongside, same era.

T. Faulkner, R. G. Leigh, O. Parrikar, and H. Wang, “Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition,” arXiv:1605.08072 [hep-th]

Cited in the paper.

T. Hartman, S. Kundu, and A. Tajdini, “Averaged Null Energy Condition from Causality,” arXiv:1610.05308 [hep-th]

Cited in the paper.

J. Koeller and S. Leichenauer, “Holographic Proof of the Quantum Null Energy Condition,” arXiv:1512.06109 [hep-th]

Cited in the paper.

2016

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A. C. Wall, “A Lower Bound on the Energy Density in Classical and Quantum Field Theories,” Phys. Rev. Lett

2017

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Z. Fu, J. Koeller, and D. Marolf, “Violating the Quantum Focusing Conjecture and Quantum Covariant Entropy Bound in d ≥ 5 d\geq 5 dimensions,” Class. Quantum Grav

2017

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S. Balakrishnan, V. Chandreskaran, T. Faulkner, A. Levine, and A. Shahbazi-Moghaddam To Appear

2018

Closest in time.