Pith. sign in

REVIEW 2 major objections 4 minor 111 references

Dissipation suppression for an Unruh-DeWitt battery with a reflecting boundary

T0 review · 2 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read An accelerating quantum battery placed extremely close to a reflecting boundary sees its relaxation and dephasing rates vanish, restoring closed-system energy storage.

desk verdict Workmanlike image-method application to an Unruh-DeWitt battery; the boundary-induced suppression of dissipation is probably right, but the thermal-bath equivalence claim is undercut by a dropped zero-frequency term. read the letter →

arxiv 2509.00875 v1 pith:5OWU2ZJA submitted 2025-08-31 hep-th gr-qcquant-ph

Xiaobao Liu , Zehua Tian , Jiliang Jing This is my paper · ORCID
classification hep-thgr-qcquant-ph PACS 04.62.+v03.70.+k42.50.Lc05.70.-a
keywords quantumbatteryUnruh-DeWittdetectorUnruheffectdissipationsuppressionreflectingboundaryergotropyopensystemsvacuumfluctuations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that an ideal reflecting boundary can almost completely shield a uniformly accelerated quantum battery from the decoherence and energy loss caused by vacuum fluctuations. The battery is modeled as a two-level Unruh-DeWitt detector driven by an external classical field, with a Dirichlet plate parallel to the acceleration. Using the method-of-images Wightman function, the authors compute the incoherent relaxation rate J and dephasing rate S, and show that both vanish as the battery-wall distance z goes to zero; the ergotropy then reduces to the undamped closed-system formula. The paper also identifies a characteristic acceleration length z_a = 1/a: for z much smaller than this scale, the suppression is near perfect and matches what a static battery in a thermal bath at the Unruh temperature would show, while for z much larger the suppression weakens and the accelerated and thermal cases differ. If true, this gives a practical positional handle for protecting relativistic quantum batteries against Unruh-induced dissipation.

What carries the argument

The load-bearing object is the Wightman function of the massless scalar field, modified by the reflecting boundary through the method of images. Substituting the uniformly accelerated trajectory into this two-point function and Fourier-transforming gives the Kossakowski coefficients A, B, C of the Born-Markov master equation; those coefficients fix the two rates that drive decoherence: the incoherent relaxation rate J = 4A and the dephasing rate S = 2(2A + C). The ergotropy formula then converts the Bloch-vector dynamics into maximum extractable work. The boundary enters only through the image term, so all suppression effects trace to interference between direct and reflected field modes.

What would settle it

Compute the exact detector response or solve the full non-Markovian dynamics for a uniformly accelerated Unruh-DeWitt detector at distance z from a Dirichlet boundary and check whether the relaxation and dephasing rates actually tend to zero as z → 0; a direct measurement of the transition rate of a detector-like system near a conducting or reflecting surface would also settle it. If the rates saturate at a nonzero floor due to finite-size effects, non-Markovian correlations, or higher-order coupling, the closed-system conclusion fails.

Watch

Extended reading notes

Core claim

The central claim is that the dissipative dynamics of an accelerated Unruh-DeWitt quantum battery are controlled by the distance z to a reflecting boundary: the boundary modifies the vacuum two-point function, and through it the Kossakowski coefficients of the master equation. In free space the battery equilibrates to a thermal state at the Unruh temperature T = a/2π, with relaxation rate J0 and dephasing rate S0. With a Dirichlet boundary at distance z, the rates become J = J0[1 - sin f(a,z)/(2z√(1+a²z²))] and S = J/2 + (ω²a/(Ω²π))[1 - f(a,z)/(2z√(1+a²z²))], where f(a,z) = (2/a) sinh⁻¹(az). In the limit z → 0, J → 0 and S → 0, and the ergotropy becomes W(τ) = (ω0/2)(ω²/Ω²)[1 - cos(Ωτ)], exa

Load-bearing premise

The paper assumes the weak-coupling, Markovian master equation remains valid all the way down to z → 0, where the boundary suppresses the field's local amplitude; if memory effects or higher-order correlations become important that close to the wall, the predicted vanishing of J and S would not describe the true dissipative dynamics.

Editorial extensions

If this is right

  • For battery-wall distances z much smaller than 1/a, the accelerated battery behaves as a closed system: relaxation and dephasing are suppressed and ergotropy oscillates without decay.
  • Boundary suppression erases the signature of the Unruh effect on energy storage in the near-boundary regime, since accelerated and static-thermal batteries have identical decay rates there.
  • The characteristic length z_a = 1/a separates a boundary-dominated regime from an acceleration-dominated regime, so tuning z gives a way to trade off charging behavior and storage lifetime.
  • Far from the boundary, the accelerated battery loses energy faster than its thermal analogue, meaning acceleration-induced non-thermal features become observable in the ergotropy.
  • The same image-method mechanism is expected to persist for multi-qubit batteries and in higher-dimensional spacetimes, with quantitative changes but the same qualitative suppression.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The z → 0 limit is derived inside the Born-Markov approximation; whether real detectors so close to a wall remain Markovian is an open question, and non-Markovian corrections could cap the achievable suppression at finite z.
  • Because the boundary suppresses the field amplitude at the detector, it also weakens the detector-field coupling, suggesting a general trade-off between protecting stored energy and being able to interrogate or discharge the battery.
  • The oscillatory dependence of J and S on z implies that not all small distances are equal: a protocol could choose a local minimum of dissipation at finite z rather than pushing all the way to contact with the boundary.
  • The predicted crossover at z ≈ 1/a could be used as a laboratory probe of the Unruh effect: measuring where boundary-dominated suppression gives way to acceleration-dominated behavior would test the local thermal approximation directly.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The manuscript studies an Unruh-DeWitt two-level quantum battery (QB) moving with uniform acceleration parallel to a reflecting Dirichlet boundary, driven by a classical charger. Working in the Born-Markov weak-coupling regime, the authors derive the Kossakowski coefficients, the relaxation rate J and dephasing rate S, and the resulting ergotropy. In free space the known Unruh thermal analogy is recovered. With the boundary, the rates acquire position-dependent suppression factors; as the QB-boundary distance z tends to zero, J and S vanish and the ergotropy reduces to the closed-system expression. The paper further claims that for z much smaller than the acceleration length z_a = 1/a, the accelerated QB is dissipatively equivalent to a static QB in a thermal bath at T = a/2π, and that z_a marks a crossover between boundary-dominated and acceleration-dominated regimes.

Significance. The central physical phenomenon — boundary-induced suppression of dissipation for a relativistic quantum battery, with a closed-system limit at z → 0 — is interesting and, if correct, provides a concrete environment-engineering tool for quantum energy storage in relativistic settings. The calculation is analytic, uses standard open-quantum-system machinery, and has no fitted parameters. However, the advertised equivalence between the accelerated QB and the static thermal QB for z ≪ z_a is not established as stated: the short-distance expansion of the dephasing rate drops a term that is not controlled by az ≪ 1, and there is a sign error in the thermal Wightman function. These issues are local and fixable, but they affect the paper's central comparative claim.

major comments (2)
  1. [Sec. III C, Eq. (50)] The sign between the free-space and image terms in Eq. (50) is inconsistent with the Dirichlet boundary condition. For a Dirichlet plane the Wightman function must vanish at z = 0; with the printed plus sign, G^+ at z = 0 is −(1/2π^2)Σ(Δτ − in/T − iϵ)^{-2}, which is not zero. The correct expression is G^+ = −(1/4π^2)Σ[1/(Δτ − in/T − iϵ)^2 − 1/((Δτ − in/T − iϵ)^2 − (2z)^2)]. Equation (51), with its [1 − sin(2z)/(2z)] factor, appears to have been derived from the minus sign, so Eq. (50) as printed cannot produce Eq. (51). Please correct the sign and re-verify the subsequent thermal-bath coefficients.
  2. [Sec. III B, Eqs. (44)–(47)] The short-distance equality 2S_{z≪z_a} = J_{z≪z_a} is not the limit of Eq. (44). Equation (44) gives S = J/2 + Δ, Δ = (ω²a/Ω²π)[1 − f/(2z√N)]. For az ≪ 1, Δ ≃ 2ω²a³z²/(3Ω²π), while J ≃ 2(ω0²/Ω²)coth(π/a)[1 − sin(2z)/(2z)]. The ratio Δ/J is not controlled by az ≪ 1 alone; for a ≳ ω0/ω it is O(1) even when az → 0. Since the static thermal bath has 2S_T = J_T exactly (Eq. (52)) — here the Dirichlet image term does cancel G(0), so C = −A is correct — the claimed equivalence J_{z≪z_a} = J_T and 2S_{z≪z_a} = S_T is not established. The authors should either prove a condition under which Δ is negligible (e.g., a²ω²/ω0² ≪ 1) or weaken the claim to the strict z → 0 limit.
minor comments (4)
  1. [Sec. III A, Eq. (34)] The notation coth^{-1}(π/a) is ambiguous. In context it means 1/coth(π/a) = tanh(π/a), not the inverse hyperbolic cotangent. Please clarify, e.g., use tanh(π/a) or [coth(π/a)]^{-1}.
  2. [Conclusions] The conclusion states that the static QB in a thermal bath has temperature T = a/π. This should be T = a/(2π) to match Sec. III C and the Unruh temperature used throughout.
  3. [Sec. III B and Fig. 5] The characteristic scale z_a = 1/a is introduced after Eq. (46), but Fig. 5 already uses 'za = 0.5'. Please introduce z_a earlier and define how the plotted dimensionless z and a relate to z_a.
  4. [Sec. II] The authors may wish to comment briefly on the validity of the Born-Markov master equation as z → 0, since the closed-system conclusion is obtained within this approximation. The vanishing rates make the result plausible, but a sentence on the spectral-density change near the boundary would strengthen the presentation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the rates, limits, and accelerated/thermal comparison follow from standard open-system machinery and external Wightman-function results, with no fitted parameters or load-bearing self-citations.

full rationale

The paper's central derivation is self-contained and does not reduce to its inputs. The master equation (Eq. 9) is the standard Kossakowski-Lindblad form from external references [24,80,81]; the Wightman functions for free space, the reflecting boundary, and the thermal bath are taken from Birrell-Davies [62], an external textbook result, not from the authors' own prior work. The relaxation and dephasing rates J, S in Eqs. (44) are computed by Fourier and Hilbert transforms of these Wightman functions, with no free parameters fitted to the results they later 'predict.' The claimed limits (z→0 giving a closed system, Eq. 46; z≪za matching the static thermal bath, Eqs. 47 and 52) are algebraic limits of those explicitly computed rates, not assumptions inserted to force the conclusion. The Unruh temperature T = a/2π is standard, and the comparison with the static thermal bath uses the independently stated thermal Wightman function (50). The paper cites several of its own prior works, but these appear as background in the introduction (e.g., [28-32], [45], [49], [75,76]) and are not load-bearing for the derivation of the suppression effect or the thermal equivalence. Concerns such as the validity of the Born-Markov approximation very close to the boundary, or whether the thermal-bath coefficient C = -A in Eq. (51) follows from the Wightman function, are potential correctness or assumption issues, not circularity: no equation is defined in terms of the quantity it is said to predict, and no fitted parameter is relabeled as a prediction. Therefore the circularity score is 0.

Assumptions & free parameters 0 free parameters · 7 assumptions · 0 invented entities

The paper introduces no new particles, forces, or entities. The central calculation rests on standard open-quantum-system axioms plus an idealized Dirichlet boundary. The main nonstandard assumptions are the unshown contour integrations and the treatment of the static thermal bath, which drops the zero-frequency dephasing term. No parameters are fitted to data: ω0, ω, μ, a and z are physical inputs.

assumptions (7)
  • domain assumption Born-Markov and weak-coupling approximations are used to derive the Kossakowski-Lindblad master equation.
    Section II A, Eq. (9); the coupling μ is assumed small and the field memory is neglected. This is standard but not proven for the near-boundary regime.
  • domain assumption The reflecting boundary is an ideal infinite plane with Dirichlet boundary conditions, so the method of images gives the Wightman function as a free term minus an image term.
    Section III B, Eq. (38); used to write Eq. (39). This is the standard idealization, with finite-size effects explicitly excluded.
  • domain assumption The accelerated trajectory is exactly hyperbolic and parallel to the boundary, with constant distance z.
    Section III B, Eq. (37). The physical scenario assumes the external force maintains this trajectory for all proper time.
  • ad hoc to paper The Fourier transforms of the modified Wightman function, especially the boundary correction in Eq. (40), are computed by contour integration and are correct.
    The integrals are not shown; the displayed G(0) in Eqs. (30) and (40) has a factor-π typo compared with the downstream C coefficients, so the correctness of these transforms is not fully transparent.
  • domain assumption The Lamb shift is neglected, with Omega' approximately Omega.
    Section II A, after Eq. (14). This is a standard weak-coupling simplification.
  • domain assumption The static thermal-bath Wightman function in the presence of the boundary is given by the image sum in Eq. (50).
    Section III C, Eq. (50). The displayed plus sign between free and image terms appears to be a typo: the subsequent coefficients use the cancellation that comes from a minus sign.
  • ad hoc to paper The zero-frequency thermal noise contribution G(0) from the σz coupling can be set to zero for the static thermal battery, leading to C=-A in Eq. (51).
    Section III C, Eq. (51). This is not derived and is inconsistent with a finite-temperature bosonic bath, where zero-frequency noise produces a pure-dephasing contribution. This assumption is load-bearing for the comparison in Section III C.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Dissipation suppression for an Unruh-DeWitt battery with a reflecting boundary." pith.science (2026). https://pith.science/paper/5OWU2ZJA

@misc{pith2026250900875,
  author       = {Pith},
  title        = {Pith review of: Dissipation suppression for an Unruh-DeWitt battery with a reflecting boundary},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5OWU2ZJA}},
  note         = {Machine review of arXiv:2509.00875}
}
read the original abstract

In the framework of open quantum systems, we study the dynamics of an accelerated quantum battery (QB), modeled as an Unruh-DeWitt detector interacting with a real massless scalar quantum field. The QB is driven by an external classical force acting as a charger. A major challenge in this setup is the environment-induced decoherence, which leads to energy dissipation of the QB. Accelerated motion exacerbates this dissipation, manifesting effects analogous to those experienced by a static QB in a thermal bath in free space, consistent with the Unruh effect. To overcome these challenges, we introduce a reflecting boundary in a space, which modifies the vacuum fluctuations of the field and leads to a position-dependent suppression of dissipation for the Unruh-DeWitt QB. Our analysis reveals that as the QB approaches the boundary, the relevant dissipation is significantly reduced. In particular, when the QB is placed extremely close to the boundary, the dissipation is nearly eliminated, as if the QB were a closed system. Furthermore, we identify a characteristic length scale associated with the acceleration of QB. When the distance between the QB and the boundary is much smaller than this scale, the boundary effectively suppresses dissipation, and this suppression effect becomes identical for both an accelerated QB and a static QB in a thermal bath. Conversely, when the distance is beyond this scale, the suppression effect weakens and manifests a significant difference between these two cases. Our findings demonstrate the potential of boundary-induced modifications in vacuum fluctuations to effectively suppress dissipation, offering valuable insights for optimizing QB performance. This work paves the way for the development of high-efficiency quantum energy storage systems in the relativistic framework.

Figures

Figures reproduced from arXiv: 2509.00875 by the authors.

Figure 1
Figure 1. FIG. 1: Ergotropy [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Uniformly accelerated QB is at a distance [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (a) The incoherent relaxation rate and the dephasing rate in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: The maximum ergotropy [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: (a) Ergotropy [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

111 extracted references · 72 canonical work pages

  1. [1]

    Esposito, U

    M. Esposito, U. Harbola, and S. Mukamel, Rev. Mod. Phys. 81, 1665 (2009)

    2009

  2. [2]

    Levy, and R

    A. Levy, and R. Kosloff, Phys. Rev. Lett. 108, 070604 (2012)

    2012

  3. [3]

    Pekola, Nat

    J. Pekola, Nat. Phys. 11, 118 (2015)

    2015

  4. [4]

    Vinjanampathy, and J

    S. Vinjanampathy, and J. Anders, Contemp. Phys. 57, 545 (2016)

    2016

  5. [5]

    Benenti, G, Casati, K, Saito, and R

    G. Benenti, G, Casati, K, Saito, and R. S. Whitney, Phys. Rep. 694, 1 (2017)

    2017

  6. [6]

    M. N. Bera, A. Riera, M. Lewenstein, Z. B. Khanian, and A. Winter, Quantum 3, 121 (2019)

    2019

  7. [7]

    Carrega, M

    M. Carrega, M. Sassetti, and U. Weiss, Phys. Rev. A 99, 062111 (2019)

    2019

  8. [8]

    Alicki, and M

    R. Alicki, and M. Fannes, Phys. Rev. E 87, 042123 (2013)

    2013

Show all 111 references
  1. [9]

    Campaioli, F

    F. Campaioli, F. A. Pollock, and S. Vinjanampathy, Quantum batteries, in F. Binder, L. A. Correa, C. Gogolin, J. Anders and G. Adesso eds.,Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions , (Springer Interna- tional Publishing, 2018), pp. 207-225

    2018

  2. [10]

    Campaioli, S

    F. Campaioli, S. Gherardini, J.Q. Quach, M. Polini, and G.M. Andolina, Rev. Mod. Phys. 96, 031001 (2024)

    2024

  3. [11]

    F. C. Binder, S. Vinjanampathy, K. Modi, and J. Goold, New J. Phys. 17, 075015 (2015)

    2015

  4. [12]

    G. M. Andolina, M. Keck, A. Mari, M. Campisi, V . Giovan- netti, and M. Polini, Phys. Rev. Lett. 122, 047702 (2019)

    2019

  5. [13]

    K. V . Hovhannisyan, M. Perarnau-Llobet, M. Huber, and A. A´ın, Phys. Rev. Lett. 111, 240401 (2013)

    2013

  6. [14]

    H. -L. Shi, S. Ding, Q. -K. Wan, X. -H. Wang, and W. -L. Yang, Phys. Rev. Lett. 129, 130602 (2022)

    2022

  7. [15]

    J. Y . Gyhm, and U. R. Fischer, A VS Quantum Sci. 6, 012001 (2024)

    2024

  8. [16]

    Ferraro, M

    D. Ferraro, M. Campisi, G. M. Andolina, V . Pellegrini, and M. Polini, Phys. Rev. Lett. 120, 117702 (2018)

    2018

  9. [17]

    Campaioli, F

    F. Campaioli, F. A. Pollock, F. C. Binder, L. C ´eleri, J. Goold, S. Vinjanampathy, and K. Modi, Phys. Rev. Lett. 118, 150601 (2017)

    2017

  10. [18]

    Grazi, D

    R. Grazi, D. S. Shaikh, M Sassetti, N. T. Ziani, and D. Ferraro, Phys. Rev. Lett. 133, 197001 (2024)

    2024

  11. [19]

    J. Q. Quach, K. E. McGhee, L. Ganzer, D. M. Rouse, B. W. Lovett, E. M. Gauger, J. Keeling, G. Cerullo, D. G. Lidzey, and T. Virgili, Sci. Adv. 8, eabk3160 (2022)

    2022

  12. [20]

    Gemme, M

    G. Gemme, M. Grossi, D. Ferraro, S. Vallecorsa, and M. Sas- setti, Batteries 8, 43 (2022)

    2022

  13. [21]

    C. -K. Hu, J. Qiu, P. J. P. Souza, J. Yuan, Y . Zhou, L. Zhang, J. Chu, X. Pan, L. Hu, J. Li, Y . Xu, Y . Zhong, S. Liu, F. Yan, 11 D. Tan, R. Bachelard, C. J. Villas-Boas, A. C. Santos, and D. Yu, Quantum Sci. Technol. 7, 045018 (2022)

    2022

  14. [22]

    Joshi, and T

    J. Joshi, and T. S. Mahesh, Phys. Rev. A 106, 042601 (2022)

    2022

  15. [23]

    Wenniger, S

    I. Wenniger, S. E. Thomas, M. Ma ffei, S. C. Wein, M. Pont, N. Belabas, S. Prasad, A. Harouri, A. Lema ˆıtre, I. Sagnes, N. Somaschi, A. Auff`eves, and P. Senellart, Phys. Rev. Lett. 131, 260401 (2023)

    2023

  16. [24]

    H. -P. Breuer, and F. Petruccione, The Theory of Open Quan- tum Systems, (Oxford University Press, USA, 2002)

    2002

  17. [25]

    Haroche, and J

    S. Haroche, and J. -M. Raimond, Exploring the Quantum. Atoms, Cavities and Photons, (Oxford University Press, USA, 2006)

    2006

  18. [26]

    Weiss, Quantum Dissipative Systems 4th edn, (World Sci- entific, Singapore, 2012)

    U. Weiss, Quantum Dissipative Systems 4th edn, (World Sci- entific, Singapore, 2012)

    2012

  19. [27]

    Wu, and H

    S. Wu, and H. Zeng, Eur. Phys. J. C 82, 4 (2022)

    2022

  20. [28]

    J. Jing, S. Chen, M. Sun, X. He, M. Wang, and J. Wang, Sci. China-Phys. Mech. Astron. 65, 260411 (2022), arXiv: 2112.09838

    2022 arXiv

  21. [29]

    J. Jing, S. Long, W. Deng, M. Wang, and J. Wang, Sci. China- Phys. Mech. Astron. 65, 100411 (2022), arXiv: 2208.02420

    2022 arXiv

  22. [30]

    J. Jing, W. Deng, S. Long, and J. Wang, Sci. China-Phys. Mech. Astron. 66, 270411 (2023), arXiv: 2305.03225

    2023 arXiv

  23. [31]

    Z. Tian, J. Jing, and J. Du, Sci. China-Phys. Mech. Astron. 66, 110412 (2023)

    2023

  24. [32]

    X. Liu, Z. Tian, and J. Jing, Sci. China-Phys. Mech. Astron. 67, 100411 (2024)

    2024

  25. [33]

    Pirmoradian, and K

    F. Pirmoradian, and K. Mølmer, Phys. Rev. A 100, 043833 (2019)

    2019

  26. [34]

    Farina, G

    D. Farina, G. M. Andolina, A. Mari, M. Polini, and V . Giovan- netti, Phys. Rev. B 99, 035421 (2019)

    2019

  27. [35]

    Carrega, A

    M. Carrega, A. Crescente, D. Ferraro, and M. Sassetti, New J. Phys. 22, 083085 (2020)

    2020

  28. [36]

    F. Zhao, F. -Q. Dou, and Q. Zhao, Phys. Rev. A 103, 033715 (2021)

    2021

  29. [37]

    Yao, and X

    Y . Yao, and X. Q. Shao, Phys. Rev. E 104, 044116 (2021)

    2021

  30. [38]

    E Bruschi, Ralph, T

    D. E Bruschi, Ralph, T. C. Ralph, I. Fuentes, T. Jennewein, and M. Razavi, Phys. Rev. D 90, 045041 (2014)

    2014

  31. [39]

    R. H. Jonsson, D. Q. Aruquipa, M. Casals, A. Kempf, and E. Mart´ın-Mart´ınez, Phys. Rev. D 101, 125005 (2020)

    2020

  32. [40]

    Ahmadi, D

    M. Ahmadi, D. E Bruschi, and I. Fuentes, Phys. Rev. D 89, 065028 (2014)

    2014

  33. [41]

    Z. Tian, J. Wang, J. Jing, and H. Fan, Sci. Rep. 5, 07946 (2015)

    2015

  34. [42]

    X. Liu, Z. Tian, J. Wang, and J. Jing, Eur. Phys. J. C 78, 665 (2018)

    2018

  35. [43]

    P. T. Grochowski, G. Rajchel, F. Kiałka, and A. Dragan, Phys. Rev. D 95, 105005 (2017)

    2017

  36. [44]

    W Barrett, and L

    J. W Barrett, and L. Crane, J. Math. Phys. 39, 3296 (1998)

    1998

  37. [45]

    Z. Tian, X. Liu, J. Jing, and J. Wang, J. High Energ. Phys. 04, 188 (2025)

    2025

  38. [46]

    X. Hao, K. Yan, J. Tan, and Q. -Y . Wu, Phys. Rev. A 107, 012207 (2023)

    2023

  39. [47]

    Y . Chen, W. Wei, X. Tian, and X. Hao, Phys. Rev. D 111, 065028 (2025)

    2025

  40. [48]

    Arnab Mukherjee, Sunandan Gangopadhyay, and A. S. Ma- jumdar, arXiv:2411.02849

  41. [49]

    X. Liu, J. Jing, Z. Tian, and W. Yao, Phys. Rev. D 103, 125025 (2021)

    2021

  42. [50]

    Abdolrahimi, Class

    S. Abdolrahimi, Class. Quantum Grav. 31, 135009 (2014)

    2014

  43. [51]

    Yao, and X

    Y . Yao, and X. Q. Shao, Phys. Rev. E 106, 014138 (2022)

    2022

  44. [52]

    J. Q. Quach, and W. J. Munro, Phys. Rev. Appl. 14, 024092 (2020)

    2020

  45. [53]

    S. -Y . Bai, and J. -H. An, Phys. Rev. A 102, 060201(R) (2020)

    2020

  46. [54]

    F. T. Tabesh, F. H. Kamin, and S. Salimi, Phys. Rev. A 102, 052223 (2020)

    2020

  47. [55]

    K. Xu, H. -J. Zhu, G. -F. Zhang, and W. -M. Liu, Phys. Rev. E 104, 064143 (2021)

    2021

  48. [56]

    Ghosh, T

    S. Ghosh, T. Chanda, S. Mal, and A. Sen(De), Phys. Rev. A 104, 032207 (2021)

    2021

  49. [57]

    Carrasco, J

    J. Carrasco, J. R. Maze, C. Hermann-Avigliano, and F. Barra, Phys. Rev. E 105, 064119 (2022)

    2022

  50. [58]

    Mayo, and A

    F. Mayo, and A. J. Roncaglia, Phys. Rev. A 105, 062203 (2022)

    2022

  51. [59]

    M. -L. Song, L. -J. Li, X. -K. Song, L. Ye, and D. Wang, Phys. Rev. E 106, 054107 (2022)

    2022

  52. [60]

    DeWitt, General Relativity: An Einstein Centenary Survey , (Cambridge University Press, Cambridge, U.K

    B. DeWitt, General Relativity: An Einstein Centenary Survey , (Cambridge University Press, Cambridge, U.K. 1979)

    1979

  53. [61]

    W. G. Unruh, and R. M. Wald, Phys. Rev. D 29, 1047 (1984)

    1984

  54. [62]

    N. D. Birrell, and P. Davies, Quantum Fields in Curved Space, (Cambridge University Press, Cambridge, England, 1984)

    1984

  55. [63]

    Takagi, Prog

    S. Takagi, Prog. Theor. Phys. Suppl. 88, 1 (1986)

    1986

  56. [64]

    L. C. B. Crispino, A. Higuchi, and G. E. A Matsas, Rev. Mod. Phys. 80, 787 (2008)

    2008

  57. [65]

    Louko, and A

    J. Louko, and A. Satz, Class. Quantum Grav. 25, 055012 (2008)

    2008

  58. [66]

    Conroy, Phys

    A. Conroy, Phys. Rev. D 105, 123513 (2022)

    2022

  59. [67]

    Pozas-Kerstjens, and E

    A. Pozas-Kerstjens, and E. Mart´ın-Mart´ınez, Phys. Rev. D 92, 064042 (2015)

    2015

  60. [68]

    Sriramkumar, and T

    L. Sriramkumar, and T. Padmanabhan, Class. Quantum Grav. 13, 2061 (1999)

  61. [69]

    S. Y . Lin, and B. L. Hu, Phys. Rev. D 73, 124018 (2006)

    2006

  62. [70]

    Doukas, and L

    J. Doukas, and L. C. L. Hollenberg, Phys. Rev. A 79, 052109 (2009)

    2009

  63. [71]

    Yu, and S

    H. Yu, and S. Lu, Phys. Rev. D 72, 064022 (2005)

    2005

  64. [72]

    Zhu, and H

    Z. Zhu, and H. Yu, Phys. Lett. B 645, 459 (2007)

    2007

  65. [73]

    Yu, and S

    H. Yu, and S. Lu, Phys. Rev. A 82, 042108 (2010)

    2010

  66. [74]

    Arias, J

    E. Arias, J. G. Due ˜nas, G. Menezes, and N. F. Svaiter, J. High Energ. Phys. 07, 147 (2016)

    2016

  67. [75]

    X. Liu, Z. Tian, J. Wang, and J. Jing, Ann. Phys. 366, 102 (2016)

    2016

  68. [76]

    X. Liu, Z. Tian, J. Wang, and J. Jing, Quantum Inf. Process. 15, 3677 (2016)

    2016

  69. [77]

    Y . Ye, H. Yu, and J. Hu, Commun. Theor. Phys. 73, 065104 (2021)

    2021

  70. [78]

    Ghosh, T

    S. Ghosh, T. Chanda, and A. Sen De, Phys. Rev. A 101, 032115 (2020)

    2020

  71. [79]

    X. J. Huang, K. K. Wang, L. Xiao, L. Gao, H. Q. Lin, and P. Xue, Phys. Rev. A 107, L030201 (2023)

    2023

  72. [80]

    Manzano, AIP Adv

    D. Manzano, AIP Adv. 10, 025106 (2020)

    2020

  73. [81]

    Benatti, R

    F. Benatti, R. Floreanini, and M. Piani, Phys. Rev. Lett. 91, 070402 (2003)

    2003

  74. [82]

    Alicki and K

    R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications, Lecture Notes in Physics V ol. 286 (SpringerVer- lag, Berlin, 1987)

    1987

  75. [83]

    Monsel, M

    J. Monsel, M. Fellous-Asiani, B. Huard, and A. Au ff`eves, Phys. Rev. Lett. 124, 130601 (2020)

    2020

  76. [84]

    A. E. Allahverdyan, R. Balian, and Th. M. Nieuwenhuizen, Europhys. Lett. 67, 565 (2004)

    2004

  77. [85]

    Francica, F

    G. Francica, F. C. Binder, G. Guarnieri, M. T. Mitchison, J. Goold, and F. Plastina, Phys. Rev. Lett. 125, 180603 (2020)

    2020

  78. [86]

    C ¸ akmak, Phys

    B. C ¸ akmak, Phys. Rev. E 102, 042111 (2020)

    2020

  79. [87]

    W. G. Unruh, Phys. Rev. D 14, 870 (1976)

    1976

  80. [88]

    S. A. Fulling, Phys. Rev. D 7, 2850 (1973)

    1973

  81. [89]

    P. C. W. Davies, J. Phys. A 8, 609 (1975)

    1975

  82. [90]

    H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)

    1948

  83. [91]

    Barton, J

    G. Barton, J. Phys. A 34, 4083 (2001)

    2001

  84. [92]

    Scheel, and S

    S. Scheel, and S. Y . Buhmann, Acta Phys. Slovaca 58, 675 (2008). 12

    2008

  85. [93]

    G. L. Klimchitskaya, and V . M. Mostepanenko, Contemp. Phys. 47, 131 (2006)

    2006

  86. [94]

    J. N. Munday, F. Capasso, and V . A. Parsegian, Nature 457, 170 (2009)

    2009

  87. [95]

    G. L. Klimchitskaya, U. Mohideen, and V . M. Mostepanenko, Rev. Mod. Phys. 81, 1827 (2009)

    2009

  88. [96]

    C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, (San Francisco: W. H. Freeman and Co., 1973)

    1973

  89. [97]

    Marino, A

    J. Marino, A. Noto, and R. Passante, Phys. Rev. Lett. 113, 020403 (2014)

    2014

  90. [98]

    Binder, L

    F. Binder, L. Correa, C. Gogolin, J. Anders, and G. Adesso, Thermodynamics in the Quantum Regime: Fundamental As- pects and New Directions , Fundamental Theories of Physics, (Springer International Publishing, 2018)

    2018

  91. [99]

    N. M. Myers, O. Abah, and S. De ffner, A VS Quantum Sci. 4, 027101 (2022)

    2022

  92. [100]

    M. T. Mitchison, Contemp. Phys. 60, 164 (2019)

    2019

  93. [101]

    Uzdin, A

    R. Uzdin, A. Levy, and R. Koslo ff, Phys. Rev. X 5, 031044 (2015)

    2015

  94. [102]

    Ghosh, W

    A. Ghosh, W. Niedenzu, V . Mukherjee, and G. Kurizki.Ther- modynamic principles and implementations of quantum ma- chines, in F. Binder, L. A. Correa, C. Gogolin, J. Anders and G. Adesso eds., Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions , (Spri...

    2018

  95. [103]

    Merkli, G

    M. Merkli, G. P. Berman, and I. M. Sigal, Ann. Phys. 323, 3091 (2008)

    2008

  96. [104]

    S. -Y . Lin, and B. L. Hu, Phys. Rev. D 79, 085020 (2009)

    2009

  97. [105]

    Braun, Phys

    D. Braun, Phys. Rev. Lett. 89, 277901 (2002)

    2002

  98. [106]

    Feng, and J

    J. Feng, and J. J. Zhang, Phys. Lett. B 827, 136992 (2022)

    2022

  99. [107]

    Yan, and B

    J. Yan, and B. Zhang, J. High Energ. Phys. 2022, 51 (2022)

    2022

  100. [108]

    Y . Zhou, H. Yu, and Z. Zhu, Commun. Theor. Phys. 57, 387 (2012)

    2012

  101. [109]

    Y . Zhou, J. Hu, and H. Yu, J. High Energ. Phys. 09, 088 (2021)

    2021

  102. [110]

    Huang, Eur

    Z. Huang, Eur. Phys. J. D 76, 67 (2022)

    2022

  103. [111]

    Y . Pan, J. Yan, S. Yang, and B. Zhang, Eur. Phys. J. C 84, 1111 (2024)

    2024

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.