What is the entropy in entropic gravity?

Carroll, Sean M.; Remmen, Grant N.

doi:10.1103/PhysRevD.93.124052

Title: What is the entropy in entropic gravity?

Abstract

We explore theories in which gravity arises as a consequence of entropy. We distinguish between two approaches to this idea: holographic gravity, in which Einstein’s equation arises from keeping entropy stationary in equilibrium under variations of the geometry and quantum state of a small region, and thermodynamic gravity, in which Einstein’s equation emerges as a local equation of state from constraints on the area of a dynamical light sheet in a fixed spacetime background. Examining holographic gravity, we argue that its underlying assumptions can be justified in part using recent results on the form of the modular energy in quantum field theory. For thermodynamic gravity, on the other hand, we find that it is difficult to formulate a self-consistent definition of the entropy, which represents an obstacle for this approach. Our investigation points the way forward in understanding the connections between gravity and entanglement.

Authors:

Carroll, Sean M. ^[1]; Remmen, Grant N. ^[1]

California Institute of Technology (CalTech), Pasadena, CA (United States)

Publication Date:: Tue Jun 21 00:00:00 EDT 2016

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); Gordon and Betty Moore Foundation

OSTI Identifier:: 1600671

Alternate Identifier(s):: OSTI ID: 1258721

Grant/Contract Number:: SC0011632; DGE-1144469

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 93; Journal Issue: 12; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS

Citation Formats


                    Carroll, Sean M., and Remmen, Grant N. What is the entropy in entropic gravity?.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevD.93.124052.

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                    Carroll, Sean M., & Remmen, Grant N. What is the entropy in entropic gravity?.  United States.  https://doi.org/10.1103/PhysRevD.93.124052

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                    Carroll, Sean M., and Remmen, Grant N. Tue .  
"What is the entropy in entropic gravity?".  United States.  https://doi.org/10.1103/PhysRevD.93.124052.  https://www.osti.gov/servlets/purl/1600671.

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@article{osti_1600671,

  title        = {What is the entropy in entropic gravity?},

  author       = {Carroll, Sean M. and Remmen, Grant N.},

  abstractNote = {We explore theories in which gravity arises as a consequence of entropy. We distinguish between two approaches to this idea: holographic gravity, in which Einstein’s equation arises from keeping entropy stationary in equilibrium under variations of the geometry and quantum state of a small region, and thermodynamic gravity, in which Einstein’s equation emerges as a local equation of state from constraints on the area of a dynamical light sheet in a fixed spacetime background. Examining holographic gravity, we argue that its underlying assumptions can be justified in part using recent results on the form of the modular energy in quantum field theory. For thermodynamic gravity, on the other hand, we find that it is difficult to formulate a self-consistent definition of the entropy, which represents an obstacle for this approach. Our investigation points the way forward in understanding the connections between gravity and entanglement.},

  doi          = {10.1103/PhysRevD.93.124052},

  journal      = {Physical Review D},

  number       = 12,

  volume       = 93,

  place        = {United States},

  year         = {Tue Jun 21 00:00:00 EDT 2016},

  month        = {Tue Jun 21 00:00:00 EDT 2016}

}

Copy to clipboard

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Works referencing / citing this record:

Cosmic equilibration: A holographic no-hair theorem from the generalized second law
journal, February 2018

Carroll, Sean M.; Chatwin-Davies, Aidan
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Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
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Cao, ChunJun; Carroll, Sean M.
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Similar Records

Title: What is the entropy in entropic gravity?

Abstract

Citation Formats

The four laws of black hole mechanics journal, June 1973

Entanglement Equilibrium and the Einstein Equation journal, May 2016

Entropy on a null surface for interacting quantum field theories and the Bousso bound journal, April 2015

Relative entropy and the Bekenstein bound journal, September 2008

Wormhole and entanglement (non-)detection in the ER=EPR correspondence journal, November 2015

Entanglement entropy and conformal field theory journal, December 2009

The stretched horizon and black hole complementarity journal, October 1993

The world as a hologram journal, November 1995

Towards a derivation of holographic entanglement entropy journal, May 2011

Gravitational dynamics from entanglement “thermodynamics” journal, April 2014

Cosmological event horizons, thermodynamics, and particle creation journal, May 1977

Relative entropy and holography journal, August 2013

Black holes: complementarity or firewalls? journal, February 2013

Cool horizons for entangled black holes journal, August 2013

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

Black holes and thermodynamics journal, January 1976

Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality: Splitting spacetime and cloning qubits journal, November 2015

Black Holes and Entropy journal, April 1973

Thermodynamical aspects of gravity: new insights journal, March 2010

Nonequilibrium Thermodynamics of Spacetime journal, March 2006

Quantum source of entropy for black holes journal, July 1986

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence journal, May 2006

On the origin of gravity and the laws of Newton journal, April 2011

The string landscape, black holes and gravity as the weakest force journal, June 2007

Anti de Sitter space and holography journal, January 1998

Comments on Jacobson’s “entanglement equilibrium and the Einstein equation” journal, March 2016

Microscopic origin of the Bekenstein-Hawking entropy journal, June 1996

Thermodynamics of Spacetime: The Einstein Equation of State journal, August 1995

Thermodynamics of black holes from equipartition of energy and holography journal, May 2010

Entropy and area journal, August 1993

On the duality condition for quantum fields journal, January 1976

Generalized gravitational entropy journal, August 2013

Large N field theories, string theory and gravity journal, January 2000

Momentum-space entanglement and renormalization in quantum field theory journal, August 2012

Notes on black-hole evaporation journal, August 1976

On geometric entropy journal, July 1994

Particle creation by black holes journal, August 1975

Black hole entropy in M-Theory journal, December 1997

Running of the gravitational constant journal, May 2012

First Law of Thermodynamics and Friedmann Equations of Friedmann–Robertson–Walker Universe journal, February 2005

Proof of a quantum Bousso bound journal, August 2014

Gravitation from entanglement in holographic CFTs journal, March 2014

Cosmic equilibration: A holographic no-hair theorem from the generalized second law journal, February 2018

Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem journal, September 2016

Entanglement entropy, scale-dependent dimensions and the origin of gravity journal, October 2017

Space from Hilbert Space: Recovering Geometry from Bulk Entanglement text, January 2016

Cosmic Equilibration: A Holographic No-Hair Theorem from the Generalized Second Law text, January 2017

Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space text, January 2017

The four laws of black hole mechanics
journal, June 1973

Entanglement Equilibrium and the Einstein Equation
journal, May 2016

Entropy on a null surface for interacting quantum field theories and the Bousso bound
journal, April 2015

Relative entropy and the Bekenstein bound
journal, September 2008

Wormhole and entanglement (non-)detection in the ER=EPR correspondence
journal, November 2015

Entanglement entropy and conformal field theory
journal, December 2009

The stretched horizon and black hole complementarity
journal, October 1993

The world as a hologram
journal, November 1995

Towards a derivation of holographic entanglement entropy
journal, May 2011

Gravitational dynamics from entanglement “thermodynamics”
journal, April 2014

Cosmological event horizons, thermodynamics, and particle creation
journal, May 1977

Relative entropy and holography
journal, August 2013

Black holes: complementarity or firewalls?
journal, February 2013

Cool horizons for entangled black holes
journal, August 2013

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Black holes and thermodynamics
journal, January 1976

Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality: Splitting spacetime and cloning qubits
journal, November 2015

Black Holes and Entropy
journal, April 1973

Thermodynamical aspects of gravity: new insights
journal, March 2010

Nonequilibrium Thermodynamics of Spacetime
journal, March 2006

Quantum source of entropy for black holes
journal, July 1986

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006

On the origin of gravity and the laws of Newton
journal, April 2011

The string landscape, black holes and gravity as the weakest force
journal, June 2007

Anti de Sitter space and holography
journal, January 1998

Comments on Jacobson’s “entanglement equilibrium and the Einstein equation”
journal, March 2016

Microscopic origin of the Bekenstein-Hawking entropy
journal, June 1996

Thermodynamics of Spacetime: The Einstein Equation of State
journal, August 1995

Thermodynamics of black holes from equipartition of energy and holography
journal, May 2010

Entropy and area
journal, August 1993

On the duality condition for quantum fields
journal, January 1976

Generalized gravitational entropy
journal, August 2013

Large N field theories, string theory and gravity
journal, January 2000

Momentum-space entanglement and renormalization in quantum field theory
journal, August 2012

Notes on black-hole evaporation
journal, August 1976

On geometric entropy
journal, July 1994

Particle creation by black holes
journal, August 1975

Black hole entropy in M-Theory
journal, December 1997

Running of the gravitational constant
journal, May 2012

First Law of Thermodynamics and Friedmann Equations of Friedmann–Robertson–Walker Universe
journal, February 2005

Proof of a quantum Bousso bound
journal, August 2014

Gravitation from entanglement in holographic CFTs
journal, March 2014

Cosmic equilibration: A holographic no-hair theorem from the generalized second law
journal, February 2018

Entropy theorems in classical mechanics, general relativity, and the gravitational two-body problem
journal, September 2016

Entanglement entropy, scale-dependent dimensions and the origin of gravity
journal, October 2017

Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
text, January 2016

Cosmic Equilibration: A Holographic No-Hair Theorem from the Generalized Second Law
text, January 2017

Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
text, January 2017