Pith. sign in

REVIEW 3 major objections 5 minor 72 references

CausalSent: Interpretable Sentiment Classification with RieszNet

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read The paper demonstrates that the quantum Mpemba effect—faster relaxation from a farther-from-equilibrium initial state—occurs in parity-time-symmetric qubit systems coupled to a thermal bath, and only while the Hamiltonian is genuinely…

desk verdict The record is internally mismatched—cs.CL abstract versus quant-ph full text—but the physics text underneath is a careful, novel demonstration of QMPE in intrinsic PT-symmetric qubits, with one load-bearing master equation that the authors assume rather than derive. read the letter →

arxiv 2508.17576 v2 pith:444CWL6O submitted 2025-08-25 cs.CL cs.LG

Daniel Frees , Martin Pollack This is my paper · ORCID
classification cs.CLcs.LG
keywords quantumMpembaeffectparity-timesymmetrynon-HermitiansystemsopenLindbladmasterequationtracedistanceexceptionalpointsrelaxationdynamics
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

The paper claims that the quantum Mpemba effect—the counterintuitive speeding-up of relaxation from a state that starts farther from equilibrium—occurs in a parity-time-symmetric qubit coupled to a bosonic thermal bath, as long as the system's Hamiltonian is genuinely non-Hermitian. The effect shows up in three standard dynamical quantifiers (trace distance, Frobenius distance, quantum relative entropy), persists both near and far from Hamiltonian and Liouvillian exceptional points, and disappears completely when the Hamiltonian is restored to Hermiticity. A long-time approximation turns the occurrence of a crossing between two relaxation trajectories into a solvable quadratic condition, and the paper uses it to separate genuine single-crossing quantum Mpemba regimes from multiple-crossing regimes that are not true Mpemba behavior. The result matters because it moves the effect from closed and open Hermitian systems into intrinsic non-Hermitian quantum systems, where it had not been established.

What carries the argument

The central object is an open parity-time-symmetric qubit with a non-Hermitian Hamiltonian, coupled to a bosonic bath through excitation and de-excitation jump operators, with dynamics governed by a Lindblad-type master equation for the normalized density matrix. The argument is carried by three pieces: the automatic suppression of the slowest relaxation mode for incoherent initial states or those with purely imaginary off-diagonal elements; a long-time approximation of the normalized density matrix that keeps only the remaining relaxation modes; and the resulting quadratic equation for a damped periodic function whose solutions must satisfy either $|X(\tau)_\pm|\le 1$ (left of the Liouvillian exceptional point) or $[X(\tau)]_\pm\ge 0$ (right of it) to give a physical crossing time. These constraints turn the question "does the quantum Mpemba effect occur?" into a parameter-regime calculation.

What would settle it

Prepare a PT-symmetric qubit in the two initial states $\hat\rho_I(0)=(\hat\sigma_z+\hat I)/2$ and $\hat\rho_{II}(0)=\hat I/2$, coupled to a bosonic bath with rates in the paper's predicted single-crossing regime (for example $a=1.3$, $\gamma_1=0.4$, $\gamma_2=1$), and measure the trace distance $D(t)=\frac12\|\hat\rho(t)-\hat\rho_{\rm ss}\|_1$ for both states; the claim requires exactly one early crossing between the two curves and no later crossings, and zero crossings in the Hermitian limit $a=0$.

Watch

Extended reading notes

Core claim

The paper asserts an unequivocal demonstration of the quantum Mpemba effect in experimentally realizable parity-time-symmetric qubit systems immersed in a bosonic bath. For a PT-symmetric Hamiltonian and Lindblad-type dynamics of the normalized density matrix, two initial states—one farther from the steady state than the other—can have quantifier trajectories that cross, so the initially farther state reaches stationarity sooner. The effect persists both near and far from Hamiltonian and Liouvillian exceptional points, and vanishes entirely when the Hermitian Hamiltonian is restored. For a wide family of initial states, the slowest relaxation mode is completely suppressed without engineered unitary transformations, so the remaining relaxation modes cooperate to produce the crossing; the paper derives analytical expressions for the number of intersections and verifies robustness against dephasing and against increasing qubit count.

Load-bearing premise

The whole analysis rests on the unproven (here) master equation for the normalized density matrix of an open PT-symmetric qubit, taken from the authors' earlier paper; if that equation misdescribes the bath coupling, the predicted quantum-Mpemba regimes are model artifacts.

Editorial extensions

If this is right

  • The quantum Mpemba effect is a real feature of intrinsic non-Hermitian dynamics, not an artifact of Hermitian open-system descriptions.
  • Exceptional points should not be used as a universal predictor for the quantum Mpemba effect: in this model the effect's regime is bounded by neither Hamiltonian nor Liouvillian exceptional points.
  • The Hermitian limit is a sharp diagnostic: restoring Hermiticity to the Hamiltonian eliminates the effect, so non-Hermiticity is the operative ingredient.
  • The analytical long-time conditions provide parameter regimes with exactly one crossing, so experiments can choose parameters guaranteed to show genuine quantum Mpemba behavior rather than multiple crossings.
  • The effect survives dephasing noise and tensor-product multi-qubit extensions, so currently available PT-symmetric qubit platforms should be able to observe it.

Reading between the lines

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

  • If the suppression of the slowest relaxation mode is as generic as the paper suggests, engineered initial-state preparation may be unnecessary for observing Mpemba-type speed-ups in any PT-symmetric open system, which would simplify experimental protocols.
  • The quantifier dependence visible in the relative-entropy results—a broader single-intersection regime than for trace distance—implies that the verdict "quantum Mpemba yes or no" can depend on which distance measure is chosen; fixing a canonical quantifier would tighten the definition.
  • The analytical constraints could be turned into a predictive diagnostic: scan the Liouvillian spectrum of a candidate non-Hermitian system and check the $|X_\pm|\le 1$ or $X_\pm\ge 0$ conditions before simulating relaxation, identifying new platforms for the effect.
  • Extending the tensor-product multiqubit result to genuinely interacting or disordered non-Hermitian chains would test whether the effect survives when the slowest mode is no longer automatically suppressed.
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

3 major / 5 minor

Summary. The manuscript studies the quantum Mpemba effect (QMPE) in a PT-symmetric qubit coupled to a bosonic thermal bath. It uses a Lindblad-type master equation for a normalized density matrix (Eq. (2)), identifies initial states for which the slowest relaxation mode is suppressed, and searches for trajectory crossings using three quantifiers: trace distance, Frobenius distance, and quantum relative entropy. A long-time approximation (Eq. (8)) leads to analytic conditions, Eqs. (12)-(13) and (21)-(22), that delineate multiple-intersection regimes; single-intersection regimes are identified as genuine QMPE. The authors report that the QMPE regime is not bounded by Hamiltonian or Liouvillian exceptional points, that QMPE disappears in the Hermitian limit, and that it persists under dephasing and in multiqubit extensions.

Significance. If the central claim holds, this is a substantial extension of the QMPE to intrinsic non-Hermitian systems, with a testable experimental prediction and a tractable analytic framework. The paper has clear strengths: the analytical boundaries are computed from the Liouvillian spectrum rather than fitted, and the numerical contour maps agree with those boundaries for three different quantifiers. The authors also carefully exclude overlap regions where finite-time counting misses periodic crossings, which is methodologically sound. However, the significance is conditional on the validity of the imported master equation, Eq. (2), and on the control of the long-time approximation. The word 'unequivocally' in the abstract is therefore stronger than what the manuscript currently supports.

major comments (3)
  1. [Sec. II, Eq. (2)] The master equation (2) is the foundation of every spectral and dynamical result in the paper, but it is not derived here; the text says 'For derivation details that lead to Eq. (2), we refer readers to Ref. [48]', a prior paper by the same authors. This matters because the standard weak-coupling derivation of a Lindblad equation assumes a Hermitian system Hamiltonian, and the trace-restoring last term in Eq. (2) is not an innocent addition: it modifies the Liouvillian spectrum (Fig. 2) that underlies Eqs. (4), (8), and (11)-(13). Unless the authors provide a derivation from a system-bath Hamiltonian, or at least a detailed justification of the normalization scheme including complete positivity, the central claim that QMPE 'unequivocally' occurs in this system is conditional on an uncontrolled model. I request an appendix or a clear statement of the model's status as phenomenological, with the abstract's 'unequivocally' weakened accordingly.
  2. [Sec. III.A, Eq. (8) and text after Fig. 3(c)] The long-time approximation (8) is used to rule out additional late-time intersections: the text states that 'Using Eq. (9), we confirm that no additional intersections occur at large times,' and this confirmation is what separates genuine-QMPE single-intersection regimes from multiple-intersection regimes. However, no uniform error bound for Eq. (8) is supplied; the approximation is checked only for selected parameters and finite times up to t=20. A late-time intersection not captured by Eq. (8) would change the parity of the crossing count and therefore invalidate the QMPE classification. Please provide an estimate of the neglected terms that is valid uniformly in the parameter regimes labeled genuine QMPE, or prove monotonicity of the exact difference D^I(t)-D^II(t) beyond the numerically checked window.
  3. [Sec. II, Eq. (5) and Appendix B] The indexing of the expansion coefficients is inconsistent in a way that affects the derivation of Eq. (8). Section II states that 'we have c1=0' for diagonal or imaginary-off-diagonal initial states and calls this a suppression of the slowest relaxation mode, but in Eq. (4) c1 is the coefficient of the steady-state eigenvector ρ1, and Appendix B explicitly uses c1=1 and c2=0 under the same initial conditions. Either the vanishing coefficient is c2, or the ordering of modes in Eq. (4) is different from what the text describes. Please clarify the notation and ensure that Eq. (8) is derived with the correct suppressed mode.
minor comments (5)
  1. [Section IV.A, Fig. 9] The robustness claim against dephasing is based on a single value γ3=0.2 at one parameter point; a parameter scan or an analytic argument would be needed to support 'moderate dephasing strengths' as a general statement.
  2. [Section IV.B, Fig. 10] The multiqubit claim is supported by three examples (N=2,3,4) with different non-Hermiticity values; the statement that QMPE is a 'generic phenomenon' in PT-symmetric multiqubit systems is stronger than the evidence presented.
  3. [References] There is a duplicated reference: Ref. [46] and Ref. [68] are the same paper (Fang et al., Phys. Rev. Res. 4, 033022 (2022)).
  4. [Figure 7 caption] The caption of Fig. 7 repeats 'Insets: Insets:'; please fix the typo.
  5. [Eq. (11) and surrounding text] The symbols C1, C3, C4 and τ are introduced inline in a dense paragraph; a short table of definitions, or a separate display equation for each, would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the QMPE boundaries are computed from the stated Liouvillian spectrum and initial conditions, not fitted or defined into existence.

full rationale

The claimed derivation is self-contained once the Lindblad-type master equation Eq. (2) is accepted as the dynamical model. All downstream results—the eigendecomposition Eq. (4), the long-time approximation Eq. (8), the intersection-time solutions Eqs. (11) and (20), and the physical-admissibility constraints Eqs. (12), (13), (21), and (22)—are obtained by algebra from the spectrum of L0 and the chosen initial states; no parameter is fitted to the target crossing numbers, and the genuine-QMPE criterion (odd number of intersections) and the distance/entropy quantifiers are imported from the external literature (Refs. 28, 33, 56, 57, 71). I flag explicitly the one omitted in-paper derivation, namely Eq. (2), whose derivation details are deferred to the authors' own Ref. [48]; this is a model-assumption citation with additional external support (Refs. 65–67), not a reduction of the QMPE prediction to an input, and it does not feed back into the identification of intersection regimes. The long-time approximation Eq. (8) is tested against the full numerical evolution rather than assumed circularly, and the theoretical boundaries are validated by independent contour counts. Accordingly there is no step in which a claimed prediction reduces by construction to a fitted parameter, a renamed input, or to the authors' prior conclusion.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper introduces no fitted constants and no invented entities: the parameters a, gamma1, gamma2, gamma3 are scanned and fixed by hand, and the initial states are chosen to make the slowest relaxation mode vanish (Eq. 5). The only nonstandard input is the master equation Eq. (2), imported from the authors' own Ref. [48] with its derivation deferred, and the long-time approximation Eq. (8) whose validity is checked numerically for specific parameter sets rather than proven uniformly. The QMPE criterion itself is an external convention from Ref. [28].

free parameters (5)
  • a (non-Hermiticity strength in H = sigma_x + i a sigma_z) = scanned over ranges, e.g., 0 <= a <= 1.5; stars at a = 1.0, 1.2, 1.3
    Degree of non-Hermiticity; controls PT-broken/unbroken phases and the Hermitian limit a=0. Scanned to map the QMPE regime rather than fitted to data.
  • gamma1 (bath excitation rate) = scanned, e.g., 0.1-1.0; gamma1 = 0.4 and 0.5 used in figures
    Sets the bath excitation strength; the QMPE regime is identified across ranges of gamma1, so no single fitted value is load-bearing.
  • gamma2 (bath relaxation rate) = gamma2 = 1 (fixed); gamma2 = 0.5 in Fig. 5
    Sets the time scale; ratio gamma1/gamma2 kept as in the Hermitian detailed-balance condition per Sec. II.
  • gamma3 (pure dephasing strength) = gamma3 = 0 and 0.2 in Fig. 9
    Robustness probe; only two values tested, showing persistence for moderate dephasing.
  • Initial states rho_I(0), rho_II(0) = rho_I(0) = (sigma_z + I)/2, rho_II(0) = I/2; Fig. 5 variant rho_I(0) = I/2 - 0.3 sigma_z - 0.2 sigma_y
    Chosen so that both satisfy the c1=0 suppression (Eq. 5) with different steady-state distances; the multiqubit case uses tensor products of these. The QMPE signature is specific to these initial conditions.
assumptions (5)
  • domain assumption The normalized-density-matrix Lindblad-type master equation Eq. (2), with the probability-conservation correction term, governs the open PT-symmetric qubit.
    Stated in Sec. II with derivation deferred to the authors' own Ref. [48]. All numerical and analytical results inherit this assumption.
  • domain assumption H = sigma_x + i a sigma_z (Eq. 1) is a PT-symmetric, experimentally realizable qubit Hamiltonian.
    Sec. II; PT symmetry checked in the text, experimental realizations cited (Refs. 42, 44, 63, 64).
  • domain assumption An odd number of crossings between two quantifier trajectories signals a genuine QMPE; periodic multiple crossings do not.
    Sec. III; standard convention from the QMPE literature (Ref. 28), used to classify all regimes.
  • domain assumption The long-time approximation Eq. (8) (slowest surviving mode only) correctly determines late-time intersection behavior.
    Appendix B; validated numerically for selected parameters (insets of Figs. 3, 7, 8) but without a uniform error bound; load-bearing for excluding late-time crossings in the left-of-LEP single-crossing regime.
  • domain assumption The bath rate ratio gamma1/gamma2 is maintained as in the Hermitian detailed-balance limit to make a=0 a physical Hermitian limit.
    Sec. II, paragraph 'To enable a physical Hermitian limit of Eq. (2)'; a modeling constraint on the dissipation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of CausalSent: Interpretable Sentiment Classification with RieszNet." pith.science (2026). https://pith.science/paper/444CWL6O

@misc{pith2026250817576,
  author       = {Pith},
  title        = {Pith review of: CausalSent: Interpretable Sentiment Classification with RieszNet},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/444CWL6O}},
  note         = {Machine review of arXiv:2508.17576}
}
read the original abstract

Despite the overwhelming performance improvements offered by recent natural language processing (NLP) models, the decisions made by these models are largely a black box. Towards closing this gap, the field of causal NLP combines causal inference literature with modern NLP models to elucidate causal effects of text features. We replicate and extend Bansal et al's work on regularizing text classifiers to adhere to estimated effects, focusing instead on model interpretability. Specifically, we focus on developing a two-headed RieszNet-based neural network architecture which achieves better treatment effect estimation accuracy. Our framework, CausalSent, accurately predicts treatment effects in semi-synthetic IMDB movie reviews, reducing MAE of effect estimates by 2-3x compared to Bansal et al's MAE on synthetic Civil Comments data. With an ensemble of validated models, we perform an observational case study on the causal effect of the word "love" in IMDB movie reviews, finding that the presence of the word "love" causes a +2.9% increase in the probability of a positive sentiment.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

72 extracted references · 43 canonical work pages

  1. [48]

    W. Ma, H. Zhang, and J. Liu, Dynamical non-Hermitian sys- tems: Fingerprints and pure-dephasing-induced protection ef- fect, Phys. Rev. A112, 012204 (2025)

    work page 2025

  2. [1]

    Mpemba and D

    E. Mpemba and D. Osborne, Cool?, Phys. Educ.4, 172 (1969)

    work page 1969

  3. [2]

    Carollo, A

    F. Carollo, A. Lasanta, and I. Lesanovsky, Exponentially accel- erated approach to stationarity in markovian open quantum sys- tems through the Mpemba effect, Phys. Rev. Lett.127, 060401 (2021)

    work page 2021

  4. [3]

    Kochsiek, F

    S. Kochsiek, F. Carollo, and I. Lesanovsky, Accelerating the ap- proach of dissipative quantum spin systems towards stationarity through global spin rotations, Phys. Rev. A106, 012207 (2022)

    2022

  5. [4]

    Ivander, N

    F. Ivander, N. Anto-Sztrikacs, and D. Segal, Hyperacceleration of quantum thermalization dynamics by bypassing long-lived coherences: An analytical treatment, Phys. Rev. E108, 014130 (2023)

    work page 2023

  6. [5]

    Moroder, O

    M. Moroder, O. Culhane, K. Zawadzki, and J. Goold, Thermo- dynamics of the quantum Mpemba effect, Phys. Rev. Lett.133, 140404 (2024)

    work page 2024

  7. [6]

    Strachan, A

    D. Strachan, A. Purkayastha, and S. R. Clark, Non-markovian quantum Mpemba effect, Phys. Rev. Lett.134, 220403 (2025)

    work page 2025

  8. [7]

    Van Vu and H

    T. Van Vu and H. Hayakawa, Thermomajorization Mpemba ef- fect, Phys. Rev. Lett.134, 107101 (2025)

    work page 2025

Show all 72 references
  1. [8]

    Longhi, Laser Mpemba effect, Opt

    S. Longhi, Laser Mpemba effect, Opt. Lett.50, 2069 (2025)

    2025

  2. [9]

    Longhi, Photonic Mpemba effect, Opt

    S. Longhi, Photonic Mpemba effect, Opt. Lett.49, 5188 (2024)

    2024

  3. [10]

    Medina, O

    I. Medina, O. Culhane, F. Binder, G. Landi, and J. Goold, Anomalous discharging of quantum batteries: The ergotropic Mpemba effect, Phys. Rev. Lett.134, 220402 (2025)

    2025

  4. [11]

    J. Lin, K. Li, J. He, J. Ren, and J. Wang, Power statistics of otto heat engines with the Mpemba effect, Phys. Rev. E105, 014104 (2022)

    2022

  5. [12]

    D. Liu, J. Yuan, H. Ruan, Y . Xu, S. Luo, J. He, X. He, Y . Ma, and J. Wang, Speeding up quantum heat engines by the Mpemba effect, Phys. Rev. A110, 042218 (2024)

    2024

  6. [13]

    F. Ares, S. Murciano, and P. Calabrese, Entanglement asymme- try as a probe of symmetry breaking, Nat. Commun.14, 2036 (2023)

    2023

  7. [14]

    S. Liu, H. Zhang, S. Yin, and S.-X. Zhang, Symmetry restora- tion and quantum Mpemba effect in symmetric random circuits, Phys. Rev. Lett.133, 140405 (2024)

    2024

  8. [15]

    Turkeshi, P

    X. Turkeshi, P. Calabrese, and A. De Luca, Quantum Mpemba effect in random circuits, Phys. Rev. Lett.135, 040403 (2025)

    2025

  9. [16]

    B. Khor, D. K ¨urkc ¸¨uoglu, T. Hobbs, G. Perdue, and I. Klich, Confinement and Kink Entanglement Asymmetry on a Quan- tum Ising Chain, Quantum8, 1462 (2024)

    2024

  10. [17]

    Rylands, E

    C. Rylands, E. Vernier, and P. Calabrese, Dynamical symmetry restoration in the heisenberg spin chain, J. Stat. Mech.2024, 123102 (2024)

    2024

  11. [18]

    Murciano, F

    S. Murciano, F. Ares, I. Klich, and P. Calabrese, Entanglement asymmetry and quantum Mpemba effect in the xy spin chain, J. Stat. Mech.2024, 013103 (2024)

    2024

  12. [19]

    Ferro, F

    F. Ferro, F. Ares, and P. Calabrese, Non-equilibrium entangle- ment asymmetry for discrete groups: the example of the xy spin chain, J. Stat. Mech.2024, 023101 (2024)

    2024

  13. [20]

    Liu, H.-K

    S. Liu, H.-K. Zhang, S. Yin, S.-X. Zhang, and H. Yao, Quantum Mpemba effects in many-body localization systems, arXiv:2408.07750

  14. [21]

    Klobas, C

    K. Klobas, C. Rylands, and B. Bertini, Translation symmetry restoration under random unitary dynamics, Phys. Rev. B111, L140304 (2025)

    2025

  15. [22]

    Yamashika, F

    S. Yamashika, F. Ares, and P. Calabrese, Entanglement asym- metry and quantum Mpemba effect in two-dimensional free- fermion systems, Phys. Rev. B110, 085126 (2024)

    2024

  16. [23]

    Zhang, G

    J. Zhang, G. Xia, C. Wu, T. Chen, Q. Zhang, Y . Xie, W. Su, W. Wu, C. Qiu, P. Chen, W. Li, H. Jing, and Y .-L. Zhou, Ob- servation of quantum strong Mpemba effect, Nat. Commun.16, 301 (2025)

    2025

  17. [24]

    Joshi, J

    L. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese, C. Roos, and M. Joshi, Observing the quantum Mpemba effect in quantum simulations, Phys. Rev. Lett.133, 010402 (2024)

    2024

  18. [25]

    Aharony Shapira, Y

    S. Aharony Shapira, Y . Shapira, J. Markov, G. Teza, N. Ak- erman, O. Raz, and R. Ozeri, Inverse Mpemba effect demon- strated on a single trapped ion qubit, Phys. Rev. Lett.133, 010403 (2024)

    2024

  19. [26]

    Y . Xu, C. Fang, B. Chen, M. Wang, Z. Ge, Y . Shi, Y . Liu, C. Deng, K. Zhao, Z. Liu, and et. al., Observation and mod- ulation of the quantum Mpemba effect on a superconducting quantum processor, arXiv:2508.07707

    arXiv

  20. [27]

    Nava and M

    A. Nava and M. Fabrizio, Lindblad dissipative dynamics in the presence of phase coexistence, Phys. Rev. B100, 125102 (2019)

    2019

  21. [28]

    F. Ares, P. Calabrese, and S. Murciano, The quantum Mpemba effects, Nat. Rev. Phys.7, 451 (2025)

    2025

  22. [29]

    H. Yu, S. Liu, and S.-X. Zhang, Quantum Mpemba effects from symmetry perspectives, AAPPS Bulletin35, 17 (2025)

    2025

  23. [30]

    J. Dong, H. Mu, M. Qin, and H. Cui, Quantum Mpemba effect of localization in the dissipative mosaic model, Phys. Rev. A 111, 022215 (2025)

    2025

  24. [31]

    D. Qian, H. Wang, and J. Wang, Intrinsic quantum Mpemba effect in markovian systems and quantum circuits, Phys. Rev. B 111, L220304 (2025)

    2025

  25. [32]

    Wang and J

    X. Wang and J. Wang, Mpemba effects in nonequilibrium open quantum systems, Phys. Rev. Res.6, 033330 (2024)

    2024

  26. [33]

    Nava and R

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

    2024

  27. [34]

    Furtado and A

    J. Furtado and A. C. Santos, Enhanced quantum Mpemba ef- fect with squeezed thermal reservoirs, Ann. Phys.480, 170135 (2025)

    2025

  28. [35]

    Kheirandish, N

    F. Kheirandish, N. Cheraghpour, and A. Moradian, The Mpemba effect in quantum oscillating and two-level systems, arXiv:2412.03943

    arXiv

  29. [36]

    X. Wang, J. Su, and J. Wang, Mpemba meets quantum chaos: Anomalous relaxation and Mpemba crossings in dissipative Sachdev-Ye-Kitaev models, arXiv:2410.06669

  30. [37]

    Rylands, K

    C. Rylands, K. Klobas, F. Ares, P. Calabrese, S. Murciano, and B. Bertini, Microscopic origin of the quantum mpemba effect in integrable systems, Phys. Rev. Lett.133, 010401 (2024)

    2024

  31. [38]

    F. Ares, V . Vitale, and S. Murciano, Quantum Mpemba effect in free-fermionic mixed states, Phys. Rev. B111, 104312 (2025)

    2025

  32. [39]

    Zatsarynna, A

    K. Zatsarynna, A. Nava, R. Egger, and A. Zazunov, Green’s function approach to josephson dot dynamics and application to quantum Mpemba effects, Phys. Rev. B111, 104506 (2025)

    2025

  33. [40]

    Summer, M

    A. Summer, M. Moroder, L. Bettmann, X. Turkeshi, I. Marvian, and J. Goold, A resource theoretical unification of Mpemba ef- fects: classical and quantum, arXiv:2507.16976 . 12

    arXiv

  34. [41]

    Kawabata, Y

    K. Kawabata, Y . Ashida, and M. Ueda, Information retrieval and criticality in parity-time-symmetric systems, Phys. Rev. Lett.119, 190401 (2017)

    2017

  35. [42]

    L. Xiao, K. Wang, X. Zhan, Z. Bian, K. Kawabata, M. Ueda, W. Yi, and P. Xue, Observation of critical phenomena in parity-time-symmetric quantum dynamics, Phys. Rev. Lett. 123, 230401 (2019)

    2019

  36. [43]

    J. Wen, G. Qin, C. Zheng, S. Wei, X. Kong, T. Xin, and G. Long, Observation of information flow in the anti-PT- symmetric system with nuclear spins, npj Quantum Inf.6, 28 (2020)

    2020

  37. [44]

    Y . Fang, J. Zhao, Y . Zhang, D. Chen, Q. Wu, Y . Zhou, C. Yang, and F. Nori, Experimental demonstration of coherence flow in pt- and anti-pt-symmetric systems, Commun. Phys.4, 223 (2021)

    2021

  38. [45]

    L. Ding, K. Shi, Y . Wang, Q. Zhang, C. Zhu, L. Zhang, J. Yi, S. Zhang, X. Zhang, and W. Zhang, Information retrieval and eigenstate coalescence in a non-hermitian quantum system with anti-PTsymmetry, Phys. Rev. A105, L010204 (2022)

    2022

  39. [47]

    Akram and C

    J. Akram and C. Zheng, Theoretical investigation of dynamics and concurrence of entangledPTand anti-PTsymmetric po- larized photons, Sci. Rep.13, 8542 (2023)

    2023

  40. [49]

    S. Guo, S. Yin, S.-X. Zhang, and Z.-X. Li, Skin effect induced anomalous dynamics from charge-fluctuating initial states, arXiv:2504.21631

  41. [50]

    Di Giulio, X

    G. Di Giulio, X. Turkeshi, and S. Murciano, Measurement- induced symmetry restoration and quantum Mpemba effect, En- tropy27, 407 (2025)

    2025

  42. [51]

    Prosen, Spectral theorem for the Lindblad equation for quadratic open fermionic systems, J

    T. Prosen, Spectral theorem for the Lindblad equation for quadratic open fermionic systems, J. Stat. Mech.2010, P07020 (2010)

    2010

  43. [52]

    Albert and L

    V . Albert and L. Jiang, Symmetries and conserved quantities in Lindblad master equations, Phys. Rev. A89, 022118 (2014)

    2014

  44. [53]

    Minganti, A

    F. Minganti, A. Miranowicz, R. Chhajlany, and F. Nori, Quan- tum exceptional points of non-Hermitian Hamiltonians and Li- ouvillians: The effects of quantum jumps, Phys. Rev. A100, 062131 (2019)

    2019

  45. [54]

    Hatano, Exceptional points of the Lindblad operator of a two-level system, Mol

    N. Hatano, Exceptional points of the Lindblad operator of a two-level system, Mol. Phys.117, 2121 (2019)

    2019

  46. [55]

    Minganti, A

    F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Spectral theory of Liouvillians for dissipative phase transitions, Phys. Rev. A 98, 042118 (2018)

    2018

  47. [56]

    Chatterjee, S

    A. Chatterjee, S. Takada, and H. Hayakawa, Quantum Mpemba effect in a quantum dot with reservoirs, Phys. Rev. Lett.131, 080402 (2023)

    2023

  48. [57]

    Chatterjee, S

    A. Chatterjee, S. Takada, and H. Hayakawa, Multiple quantum Mpemba effect: Exceptional points and oscillations, Phys. Rev. A110, 022213 (2024)

    2024

  49. [58]

    Y . Zhou, X. Yu, C. Wu, X. Li, J. Zhang, W. Li, and P. Chen, Accelerating relaxation through Liouvillian exceptional point, Phys. Rev. Res.5, 043036 (2023)

    2023

  50. [59]

    Bender and S

    C. Bender and S. Boettcher, Real spectra in non-hermitian hamiltonians havingPTsymmetry, Phys. Rev. Lett.80, 5243 (1998)

    1998

  51. [60]

    Bender, Introduction toPT-symmetric quantum theory, Contemp

    C. Bender, Introduction toPT-symmetric quantum theory, Contemp. Phys.46, 277 (2005)

    2005

  52. [61]

    Bender and D

    C. Bender and D. Hook,PT-symmetric quantum mechanics, Rev. Mod. Phys.96, 045002 (2024)

    2024

  53. [62]

    ¨ozdemir, S

    S. ¨ozdemir, S. Rotter, F. Nori, and L. Yang, Parity-time sym- metry and exceptional points in photonics, Nat. Mater.18, 783 (2019)

    2019

  54. [63]

    W. Chen, M. Abbasi, Y . Joglekar, and K. Murch, Quantum jumps in the non-hermitian dynamics of a superconducting qubit, Phys. Rev. Lett.127, 140504 (2021)

    2021

  55. [64]

    W. Wang, Y . Zhou, H. Zhang, J. Zhang, M. Zhang, Y . Xie, C. Wu, T. Chen, B. Ou, W. Wu, H. Jing, and P.-X. Chen, Ob- servation ofPT-symmetric quantum coherence in a single-ion system, Phys. Rev. A103, L020201 (2021)

    2021

  56. [65]

    Brody and E.-M

    D. Brody and E.-M. Graefe, Mixed-state evolution in the pres- ence of gain and loss, Phys. Rev. Lett.109, 230405 (2012)

    2012

  57. [66]

    H. Yuan, P. Yan, S. Zheng, Q. He, K. Xia, and M. Yung, Steady bell state generation via magnon-photon coupling, Phys. Rev. Lett.124, 053602 (2020)

    2020

  58. [67]

    H. Xu, U. Deli ´c, G. Wang, C. Li, P. Cappellaro, and J. Li, Expo- nentially enhanced non-hermitian cooling, Phys. Rev. Lett.132, 110402 (2024)

    2024

  59. [68]

    Y . Fang, J. Zhao, D. Chen, Y . Zhou, Y . Zhang, Q. Wu, C. Yang, and F. Nori, Entanglement dynamics in anti-PT-symmetric systems, Phys. Rev. Res.4, 033022 (2022)

    2022

  60. [69]

    Breuer and F

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

    2002

  61. [70]

    Campaioli, J

    F. Campaioli, J. Cole, and H. Hapuarachchi, Quantum master equations: Tips and tricks for quantum optics, quantum com- puting, and beyond, PRX Quantum5, 020202 (2024)

    2024

  62. [71]

    Chalas, F

    K. Chalas, F. Ares, C. Rylands, and P. Calabrese, Multiple crossings during dynamical symmetry restoration and impli- cations for the quantum Mpemba effect, J. Stat. Mech.2024, 103101 (2024)

    2024

  63. [72]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information(Cambridge University Press, Cam- bridge, 2000)

    2000

  64. [73]

    With the solutions in Eq. (11), we findX +X− = T� ��R� � ��−�R�� � �� � T� ��R� � ��−�R�� � �� � = T� ��R� � ��−�R�� � �� � T � � ��R� � ��−�R�� � �� �� due to properties that C1 is strictly real andC 3,4 form a complex conjugate pair ir- respective of initial conditions (Appe...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.