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Cited by 16Black Holes and Theoretical PhysicsQuantum many-body systemsAdvanced Thermodynamics and Statistical Mechanics

Quantum Thermodynamics of Holographic Quenches and Bounds on the Growth of Entanglement from the Quantum Null Energy Condition

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Kibe, Tanay, Mukhopadhyay, Ayan, Roy, Pratik·2022·Physical Review Letters
DOI 10.1103/physrevlett.128.191602
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Abstract

The quantum null energy condition (QNEC) is a lower bound on the energy-momentum tensor in terms of the variation of the entanglement entropy of a subregion along a null direction. To gain insights into quantum thermodynamics of many-body systems, we study if the QNEC restricts irreversible entropy production in quenches driven by energy-momentum inflow from an infinite memoryless bath in two-dimensional holographic theories. We find that an increase in both entropy and temperature, as implied by the Clausius inequality of classical thermodynamics, is necessary but not sufficient to not violate QNEC in quenches leading to transitions between thermal states with momentums that are dual to Banados-Teitelboim-Zanelli geometries. For an arbitrary initial state, we can determine the lower and upper bounds on the increase of entropy (temperature) for a fixed increase in temperature (entropy). Our results provide explicit instances of quantum lower and upper bounds on irreversible entropy production whose existence has been established in literature. We also find monotonic behavior of the nonsaturation of the QNEC with time after a quench, and analytically determine their asymptotic values. Our study shows that the entanglement entropy of an interval of length l always thermalizes in time l/2 with an exponent 3/2. Furthermore, we determine the coefficient of initial quadratic growth of entanglement analytically for any l, and show that the slope of the asymptotic ballistic growth of entanglement for a semi-infinite interval is twice the difference of the entropy densities of the final and initial states. We determine explicit upper and lower bounds on these rates of growth of entanglement.

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  • The rates of growth of entanglement can be bounded from both above and below.

    “Similarly, the rates of growth of entanglement can also be bounded from both above and below.”

    From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [279]

  • For an instantaneous transition between thermal rotating states in holography, the quantum null energy condition of the boundary theory bounds the growth of thermodynamic entropy (temperature) for a fixed increase in temperature (entropy) from both above and below.

    “Recently, even within the classical approximation in the bulk (with classical bulk matter) and assuming an infinite memoryless bath, it has been shown in [279] that for an instantaneous transition between thermal rotating states in holography, the quantum null energy condition [36] of the boundary theory bounds the growth of thermodynamic entropy (temperature) for a fixed increase in temperature (”

    From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [279]

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Authors
Kibe, T., Mukhopadhyay, A., & Roy, P.
Affiliations
Indian Institute of Technology Madras (IN)
ORCID
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
2022-05-09
Volume
128
Issue
19
Pages
191602-191602
ISSN
  • 0031-9007 (ISSN-L)
  • 1079-7114
DOI
10.1103/physrevlett.128.191602
OpenAlex
W4229365778
Cited by
16
References
83
Citations by year
2026: 3 · 2025: 2 · 2024: 5 · 2023: 2 · 2022: 4
FWCI
0.41
Type
journal article
Language
en
Open access
Licence
Locations
  • Physical Review Letters (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University) (cc-by)
Funders
  • Department of Science and Technology, Ministry of Science and Technology, India
  • Indian Institute of Technology Madras
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
Keywords
quantum null energy condition, entanglement entropy growth, irreversible entropy production, Clausius inequality, thermalization, quantum thermodynamics

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