pith. sign in

arxiv: 2509.05756 · v2 · submitted 2025-09-06 · ✦ hep-th · quant-ph

Quantum Mpemba-like effect in Unruh thermalization

Zihao Wang , Wenjing Chen , Si-Wei Han , Xiaoshan Feng , Linmu Qiao , Zhichun Ouyang , Jun Feng This is my paper

Pith reviewed 2026-05-18 17:41 UTC · model grok-4.3

classification ✦ hep-th quant-ph
keywords Unruh effectMpemba effectUDW detectorquantum thermalizationUhlmann fidelityBloch sphere trajectoriesquantum thermodynamicsheating and cooling protocols
0
0 comments X

The pith

Maximum fidelity difference distinguishes Unruh thermalization from classical thermal bath-driven thermalization of an inertial detector.

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

The paper examines how a Unruh-deWitt detector reaches thermal equilibrium due to acceleration in flat spacetime. It finds that the path taken on the Bloch sphere depends on the field the detector couples to and on the number of spacetime dimensions. Tracking quantum coherence and heat flow shows that heating and cooling follow different rates, producing a Mpemba-like pattern in which fidelity changes occur faster during heating. The central result is that the largest gap in Uhlmann fidelity between these paths appears only for the quantum Unruh process and is absent when the same detector thermalizes in an ordinary classical heat bath. This gap supplies a concrete signature that could be checked in future experiments or quantum simulations to confirm the quantum character of the Unruh effect.

Core claim

For a Unruh-deWitt detector in n-dimensional Minkowski spacetime, its irreversible thermalization to a Gibbs equilibrium state follows distinct trajectories on the Bloch sphere, which depend on the types of fields the detector interacts with, as well as the spacetime dimensionality. Using thermodynamic process functions, particularly quantum coherence and heat that form the quantum First Law, we characterize the Unruh thermalization through a complementary time evolution between the trajectory-dependent rates of process functions. Grounded in information geometry, we further explore the kinematics of the detector state as it flows along the trajectory. We propose two heating/cooling protoc

What carries the argument

maximum fidelity difference between heating and cooling protocols, serving as a diagnostic that separates Unruh thermalization trajectories on the Bloch sphere from those of classical thermal baths

Load-bearing premise

The irreversible thermalization trajectories on the Bloch sphere must differ enough between quantum Unruh dynamics and ordinary classical baths to make the maximum fidelity gap a reliable and unique signal rather than a generic feature of any quantum thermal process.

What would settle it

Measure the peak difference in Uhlmann fidelity between heating and cooling for both an accelerated detector in vacuum and an inertial detector coupled to a classical thermal bath; the claim is supported if the gap is present only in the accelerated case.

read the original abstract

We revisit the thermal nature of the Unruh effect within a quantum thermodynamic framework. For a Unruh-deWitt (UDW) detector in $n$-dimensional Minkowski spacetime, we demonstrate that its irreversible thermalization to a Gibbs equilibrium state follows distinct trajectories on the Bloch sphere, which depend on the types of fields the detector interacts with, as well as the spacetime dimensionality. Using thermodynamic process functions, particularly quantum coherence and heat that form the quantum First Law, we characterize the Unruh thermalization through a complementary time evolution between the trajectory-dependent rates of process functions. Grounded in information geometry, we further explore the kinematics of the detector state as it "flows" along the trajectory. In particular, we propose two heating/cooling protocols for the UDW detector undergoing Unruh thermalization. We observe a quantum Mpemba-like effect, characterized by faster heating than cooling in terms of Uhlmann fidelity "distance" change. Most significantly, we establish the maximum fidelity difference as a novel diagnostic that essentially distinguishes between Unruh thermalization and its classical counterpart, i.e., classical thermal bath-driven thermalization of an inertial UDW detector. This compelling criterion may serve as a hallmark of the quantum origin of the Unruh effect in future experimental detection and quantum simulation. Finally, we conclude with a general analysis of Unruh thermalization, starting from equal-fidelity non-thermal states, and demonstrate that the detectors' fidelity and "speed" of quantum evolution still exhibit a Mpemba-like behavior.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper examines Unruh thermalization of a Unruh-DeWitt detector in n-dimensional Minkowski spacetime coupled to scalar or fermionic fields. It shows that the detector state follows field- and dimension-dependent trajectories on the Bloch sphere during irreversible evolution to the Gibbs state. Using the quantum First Law with coherence and heat, it characterizes the process via complementary rates of thermodynamic functions. Two heating/cooling protocols are introduced, revealing a Mpemba-like effect in which heating reaches the target state faster than cooling when measured by Uhlmann fidelity. The central result is that the maximum fidelity difference between the evolving state and the Gibbs state serves as a diagnostic that distinguishes Unruh thermalization from classical thermal-bath-driven thermalization of an inertial detector. A final section extends the analysis to equal-fidelity non-thermal initial states and again finds Mpemba-like behavior in fidelity and evolution speed.

Significance. If the central diagnostic holds, the work supplies a concrete, information-geometric signature that could help isolate the quantum origin of the Unruh effect in future analog simulations or detector experiments. The Mpemba-like observation in a relativistic open-system setting adds a new example to the literature on anomalous thermalization. The trajectory analysis and thermodynamic-process characterization are technically solid and may be useful for other detector models.

major comments (2)
  1. [§4] §4 (comparison with classical bath): the claim that the maximum Uhlmann-fidelity difference 'essentially distinguishes' Unruh thermalization from its classical counterpart is load-bearing, yet the classical model is implemented via a standard Lindblad master equation with thermal rates. No argument is given that the same maximum difference cannot be reproduced by tuning the classical spectral density or coupling strength to match the Unruh response function for the same temperature and field dimension.
  2. [§3.2] §3.2 (heating/cooling protocols): the Mpemba-like effect is reported for two specific protocols, but the paper does not show that the ordering of heating versus cooling times remains robust when the initial states are varied continuously along the equal-fidelity surface introduced in the final section.
minor comments (2)
  1. [§2] Notation for the Uhlmann fidelity is introduced without an explicit formula; adding the standard expression (or a reference to its definition) would improve readability.
  2. [Figure 3] Figure 3 (Bloch-sphere trajectories): the color scale for different field types and dimensions is not labeled in the caption; this makes it difficult to match curves to the text discussion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. Below we provide point-by-point responses to the major comments and indicate the revisions we intend to implement.

read point-by-point responses

  1. Referee: [§4] §4 (comparison with classical bath): the claim that the maximum Uhlmann-fidelity difference 'essentially distinguishes' Unruh thermalization from its classical counterpart is load-bearing, yet the classical model is implemented via a standard Lindblad master equation with thermal rates. No argument is given that the same maximum difference cannot be reproduced by tuning the classical spectral density or coupling strength to match the Unruh response function for the same temperature and field dimension.

    Authors: We appreciate the referee highlighting the need for a stronger justification of this diagnostic. The classical bath is modeled via a Lindblad equation whose rates are fixed by the Unruh temperature for the chosen field and dimension, but the Unruh dynamics are generated by the specific two-point correlations of the quantum field in Minkowski spacetime. These correlations produce Bloch-sphere trajectories whose curvature and coherence content are constrained by the relativistic structure and enter the quantum First Law through the process functions. Consequently, the maximum fidelity difference is tied to these quantum-relativistic features rather than to an arbitrary thermal spectrum. We will add a clarifying paragraph in §4 that explicitly contrasts the fixed Unruh response with a generic classical bath and explains why matching only the response function does not reproduce the same extremal fidelity difference. revision: partial

  2. Referee: [§3.2] §3.2 (heating/cooling protocols): the Mpemba-like effect is reported for two specific protocols, but the paper does not show that the ordering of heating versus cooling times remains robust when the initial states are varied continuously along the equal-fidelity surface introduced in the final section.

    Authors: We thank the referee for this suggestion. The final section already demonstrates Mpemba-like behavior for a family of equal-fidelity non-thermal initial states, both in fidelity evolution and in the speed of quantum evolution. While the main protocols of §3.2 are representative, we agree that explicit confirmation along the continuous equal-fidelity surface would strengthen the claim. We will therefore include a brief additional discussion together with representative numerical checks showing that the heating-versus-cooling time ordering persists under continuous variation along that surface. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on standard Unruh dynamics and explicit computations

full rationale

The paper derives Unruh thermalization trajectories on the Bloch sphere from the standard Unruh response function for UDW detectors coupled to fields in n-dimensional Minkowski spacetime. It then computes process functions (coherence, heat) via the quantum First Law, explores kinematics in information geometry, and defines heating/cooling protocols to observe Mpemba-like behavior in Uhlmann fidelity. The maximum fidelity difference diagnostic is obtained by direct comparison of these computed trajectories against a classical thermal bath model. None of these steps reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the central distinction follows from the explicit quantum field-theoretic two-point functions versus generic Lindblad rates. The analysis is self-contained against external benchmarks of Unruh effect calculations, with no renaming of known results or ansatzes smuggled via prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard assumptions of the Unruh effect and quantum thermodynamics; no new free parameters, invented entities, or ad-hoc axioms are identifiable from the abstract alone.

axioms (1)
  • domain assumption An accelerated Unruh-DeWitt detector thermalizes to a Gibbs state via interaction with quantum fields in Minkowski spacetime.
    This is the foundational premise of the Unruh effect invoked throughout the abstract.

pith-pipeline@v0.9.0 · 5816 in / 1385 out tokens · 43186 ms · 2026-05-18T17:41:17.848114+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

61 extracted references · 61 canonical work pages

  1. [1]

    W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D14, 870 (1976)

    work page 1976

  2. [2]

    S. A. Fulling, Nonuniqueness of canonical field quantization in Riemannian space-time, Phys. Rev. D7, 2850 (1973)

    work page 1973

  3. [3]

    P. C. W. Davies, Scalar production in Schwarzschild and Rindler metrics, J. Phys. A8, 609 (1975)

    work page 1975

  4. [4]

    S. W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys.43, 199 (1975)

    work page 1975

  5. [5]

    G. W. Gibbons and S. W. Hawking, Cosmological Event Horizons, Thermodynamics, and Particle Creation, Phys. Rev. D15, 2738 (1977)

    work page 1977

  6. [6]

    Chen and T

    P. Chen and T. Tajima, Testing Unruh Radiation with Ultraintense Lasers, Phys. Rev. Lett.83, 256 (1999)

    work page 1999

  7. [7]

    Sch¨ utzhold, G

    R. Sch¨ utzhold, G. Schaller, and D. Habs, Signatures of the Unruh Effect from Electrons Accelerated by Ultrastrong Laser Fields, Phys. Rev. Lett.97, 121302 (2006)

    work page 2006

  8. [8]

    Mart´ ın-Mart´ ınez, I

    E. Mart´ ın-Mart´ ınez, I. Fuentes, and R. B. Mann, Using Berry’s Phase to Detect the Unruh Effect at Lower Accelerations, Phys. Rev. Lett.107, 131301 (2011)

    work page 2011

  9. [9]

    Cozzella, A

    G. Cozzella, A. G. S. Landulfo, G. E. A. Matsas, and D. A. T. Vanzella, Proposal for Observing the Unruh Effect using Classical Electrodynamics, Phys. Rev. Lett.118, 161102 (2017)

    work page 2017

  10. [10]

    C. A. U. Lima, F. Brito, J. A. Hoyos, and D. A. Turolla Vanzella, Probing the Unruh effect with an accelerated extended system, Nature Commun.10, 3030 (2019)

    work page 2019

  11. [11]

    Barcel´ o, S

    C. Barcel´ o, S. Liberati, and M. Visser, Analogue Gravity, Living Rev. Relativity14, 3 (2011)

    work page 2011

  12. [12]

    W. G. Unruh, Experimental black hole evaporation, Phys. Rev. Lett.46, 1351, (1981)

    work page 1981

  13. [13]

    Retzker, J

    A. Retzker, J. I. Cirac, M. B. Plenio, and B. Reznik, Methods for Detecting Acceleration Radiation in a Bose-Einstein Condensate, Phys. Rev. Lett.101, 110402 (2008). – 22 –

    work page 2008

  14. [14]

    Steinhauer, Observation of quantum Hawking radiation and its entanglement in an analogue black hole, Nature Phys.12, 959 (2016)

    J. Steinhauer, Observation of quantum Hawking radiation and its entanglement in an analogue black hole, Nature Phys.12, 959 (2016)

    work page 2016

  15. [15]

    P. O. Fedichev and U. R. Fischer, Gibbons-Hawking Effect in the Sonic de Sitter Space-Time of an Expanding Bose-Einstein-Condensed Gas, Phys. Rev. Lett.91, 240407 (2003)

    work page 2003

  16. [16]

    J. Hu, L. Feng, Z. Zhang, and C. Chin, Quantum simulation of Unruh radiation, Nature Phys.15, 785 (2019)

    work page 2019

  17. [17]

    Gooding, S

    C. Gooding, S. Biermann, S. Erne, J. Louko, W. G. Unruh, J. Schmiedmayer, and S. Weinfurtner, Interferometric Unruh Detectors for Bose-Einstein Condensates, Phys. Rev. Lett.125, 213603 (2020)

    work page 2020

  18. [18]

    Sriramkumar, What do detectors detect, in: J.S

    L. Sriramkumar, What do detectors detect, in: J.S. Bagla, S. Engineer (Eds.),Gravity and the Quantum, Springer Publishing, 2017

    work page 2017

  19. [19]

    G. L. Sewell, Quantum fields on manifolds: PCT and gravitationally induced thermal states, Annals of Physics141, 201 (1982)

    work page 1982

  20. [20]

    Takagi, Vacuum Noise and Stress Induced by Uniform Acceleration, Prog

    S. Takagi, Vacuum Noise and Stress Induced by Uniform Acceleration, Prog. Theor. Phys. Suppl.88, 1 (1986)

    work page 1986

  21. [21]

    Takagi, On the response of a Rindler-particle detector, Prog

    S. Takagi, On the response of a Rindler-particle detector, Prog. Theor. Phys.72, 505 (1984)

    work page 1984

  22. [22]

    B. S. DeWitt, Quantum gravity: the new synthesis, in: S. W. Hawking, W. Israel (Eds.), General Relativity: An Einstein Centenary Survey(Cambridge University Press, Cambridge, 1979) p. 680

    work page 1979

  23. [23]

    W. G. Unruh, Accelerated monopole detector in odd spacetime dimensions, Phys. Rev. D 34, 1222 (1986)

    work page 1986

  24. [24]

    Ooguri, Spectrum of Hawking radiation and Huygens’ principle,Phys

    H. Ooguri, Spectrum of Hawking radiation and Huygens’ principle,Phys. Rev. D33, 3573 (1986)

    work page 1986

  25. [25]

    Ohya, Emergent anyon distribution in the Unruh effect, Phys

    S. Ohya, Emergent anyon distribution in the Unruh effect, Phys. Rev. D96, 045017 (2017)

    work page 2017

  26. [26]

    Arrechea, C

    J. Arrechea, C. Barcel´ o, L.J. Garay, G. Garc´ ıa-Moreno, Inversion of statistics and thermalization in the Unruh effect, Phys. Rev. D104, 065004 (2021)

    work page 2021

  27. [27]

    H. P. Breuer and F. Petruccione,The Theory of Open Quantum Systems(Oxford University Press, 2002)

    work page 2002

  28. [28]

    Feng and J.-J

    J. Feng and J.-J. Zhang, Quantum Fisher information as a probe for Unruh thermality, Phys. Lett. B827,136992 (2022)

    work page 2022

  29. [29]

    A. P. C. M Lima, G. Alencar, and R. R. Landim, Asymptotic states of accelerated qubits in nonzero background temperature, Phys. Rev. D101, 125008 (2020)

    work page 2020

  30. [30]

    Feng, J.-J

    J. Feng, J.-J. Zhang and Y. Zhou, Thermality of the Unruh effect with intermediate statistics, Europhys. Lett.137, 60001 (2022)

    work page 2022

  31. [31]

    Vinjanampathy and J

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

    work page 2016

  32. [32]

    Kosloff, Quantum thermodynamics: A dynamical viewpoint, Entropy15, 2100 (2013)

    R. Kosloff, Quantum thermodynamics: A dynamical viewpoint, Entropy15, 2100 (2013)

    work page 2013

  33. [33]

    Goold, M

    J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, The role of quantum information in thermodynamics - a topical review, J. Phys. A: Math. Theor.49, 143001 (2016) – 23 –

    work page 2016

  34. [35]

    Alipour, A

    S. Alipour, A. T. Rezakhani, A. Chenu, A. del Campo, and T. Ala-Nissila, Entropy-based formulation of thermodynamics in arbitrary quantum evolution, Phys. Rev. A105, L040201 (2022)

    work page 2022

  35. [36]

    Ib´ a˜ nez, C

    M. Ib´ a˜ nez, C. Dieball, A. Lasanta,et al., Heating and cooling are fundamentally asymmetric and evolve along distinct pathways, Nat. Phys.20, 135 (2024)

    work page 2024

  36. [37]

    Lu and O

    Z. Lu and O. Raz, Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse, Proc. Natl. Acad. Sci. USA114, 5083 (2017)

    work page 2017

  37. [38]

    Moroder, O

    M. Moroder, O. Culhane, K. Zawadzki, and J. Goold, Thermodynamics of the Quantum Mpemba Effect, Phys. Rev. Lett.133, 140404 (2024)

    work page 2024

  38. [39]

    Nava and R

    A. Nava and R. Egger, Mpemba effects in open nonequilibrium quantum systems, Phys. Rev. Lett.133, 136302 (2024)

    work page 2024

  39. [40]

    Lindblad, On the generators of quantum dynamical semigroups, Commun

    G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976)

    work page 1976

  40. [41]

    Gorini, A

    V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N-level systems, J. Math. Phys.17, 821 (1976)

    work page 1976

  41. [42]

    Kaplanek and C

    G. Kaplanek and C. P. Burgess, Hot accelerated qubits: decoherence, thermalization, secular growth and reliable late-time predictions, J. High Energy Phys.03, 008 (2020)

    work page 2020

  42. [43]

    Kaplanek and E

    G. Kaplanek and E. Tjoa, Effective master equations for two accelerated qubits, Phys. Rev. A107, 012208 (2023)

    work page 2023

  43. [44]

    S.-W. Han, W. Chen, L. Chen, Z. Ouyang, and J. Feng, The reliable quantum master equation of the Unruh-DeWitt detector, 2502.06411

    work page arXiv

  44. [45]

    W. Chen, Y. Ma, S.-W. Han, Z. Wang, and J. Feng, Quantum thermodynamics in a rotating BTZ black hole spacetime, arXiv:2507.16787

    work page arXiv

  45. [46]

    D. A. Lidar, Lecture Notes on the Theory of Open Quantum Systems, arXiv:1902.00967

    work page arXiv 1902

  46. [47]

    Juan-Delgado and A

    A. Juan-Delgado and A. Chenu, First law of quantum thermodynamics in a driven open two-level system, Phys. Rev. A104, 022219 (2021)

    work page 2021

  47. [48]

    B. d. L. Bernardo, Unraveling the role of coherence in the first law of quantum thermodynamics, Phys. Rev. E102, 062152 (2020)

    work page 2020

  48. [49]

    S.-W. Han, Z. Ouyang, Z. Hu, and J. Feng, Relative entropy formulation of thermalization process in a Schwarzschild spacetime, Phys. Lett. B861, 139235 (2025)

    work page 2025

  49. [50]

    G. Teza, J. Bechhoefer, A. Lasanta, O. Raz, and M. Vucelja, Speedups in nonequilibrium thermal relaxation: Mpemba and related effects, arXiv:2502.01758

    work page arXiv

  50. [51]

    Carollo, A

    F. Carollo, A. Lasanta, and I. Lesanovsky, Exponentially accelerated approach to stationarity in Markovian open quantum systems through the Mpemba effect, Phys. Rev. Lett.127, 060401 (2021)

    work page 2021

  51. [52]

    L. P. Bettmann and J. Goold, Information geometry approach to quantum stochastic thermodynamics, Phys. Rev. E111, 014133 (2025)

    work page 2025

  52. [53]

    J. Liu, H. Yuan, X.-M. Lu, and X. Wang, Quantum Fisher information matrix and multiparameter estimation, J. Phys. A: Math. Theor.53, 023001 (2020). – 24 –

    work page 2020

  53. [54]

    Bengtsson, K

    I. Bengtsson, K. ˙Zyczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd Edition (Cambridge University Press, 2017)

    work page 2017

  54. [55]

    Petz and C

    D. Petz and C. Ghinea, in Quantum Probability and Related Topics (World Scientific, Singapore, 2011)

    work page 2011

  55. [56]

    Marvian, Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics, Phys

    I. Marvian, Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics, Phys. Rev. Lett.129, 190502 (2022)

    work page 2022

  56. [57]

    L. P. Garc´ ıa-Pintos, S. B. Nicholson, J. R. Green, A. Del Campo, and A. V. Gorshkov, Unifying Quantum and Classical Speed Limits on Observables, Phys. Rev. X12, 011038 (2022)

    work page 2022

  57. [58]

    Yadin, S

    B. Yadin, S. Imai, and O. G¨ uhne,Quantum Speed Limit for States and Observables of Perturbed Open Systems, Phys. Rev. Lett.132, 230404 (2024)

    work page 2024

  58. [59]

    Tejero, R

    ´A. Tejero, R. S´ anchez, L. El Kaoutit, D. Manzano, and A. Lasanta, Asymmetries of thermal processes in open quantum systems, Phys. Rev. Research7, 023020 (2025)

    work page 2025

  59. [60]

    Adjei, K

    E. Adjei, K. J. Resch, and A. M. Bra´ nczyk, Quantum simulation of Unruh-DeWitt detectors with nonlinear optics, Phys. Rev. A102, 033506 (2020)

    work page 2020

  60. [61]

    L. K. Joshi, et. al., Observing the quantum Mpemba effect in quantum simulations, Phys. Rev. Lett.133, 010402 (2024)

    work page 2024

  61. [62]

    Observa- tion and modulation of the quantum Mpemba effect,

    Yueshan Xu, et. al., Observation and Modulation of the Quantum Mpemba Effect on a Superconducting Quantum Processor, arXiv:2508.07707. – 25 –

    work page arXiv