Pith. sign in

REVIEW 2 major objections 5 minor 47 references

Pareto-optimal work extraction and the thermodynamic cost of precision in quantum information engines

T0 review · 2 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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

Pith's one-line read A measurement-driven quantum engine's work fluctuations have a thermal floor set by the qubit's own temperature.

desk verdict Solid analytic bound for the cold-meter limit, but the open-system assumption needs a quantitative check before the device claims stick. read the letter →

arxiv 2607.14973 v1 pith:UYVJTD45 submitted 2026-07-16 quant-ph

Jonas Berx , Ted Olander , Henning Kirchberg This is my paper · ORCID
classification quant-ph
keywords quantuminformationengineworkfluctuationsParetofrontergotropyFishertwo-levelsystemharmonicoscillatormeternoise-to-signalratio
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 studies a finite-time quantum information engine in which a two-level system (the qubit) is measured by a harmonic-oscillator meter, and work is extracted only when the measurement outcome indicates population inversion. The paper establishes that average work and cycle-to-cycle work fluctuations are genuinely competing objectives, and it maps the full trade-off as a Pareto front (the set of designs where neither objective can improve without worsening the other). In the cold-meter regime the engine's work statistics reduce to a Bernoulli process — each cycle either yields one quantum of work or none — and the noise-to-signal ratio is (1-p)/p, bounded below by e^{ΔE/k_B T_S}. The bound is purely thermal, set by the qubit's own excited-state population, so even a perfectly accurate meter cannot make the output quieter. Reducing fluctuations therefore costs: more information acquisition, more cycles, longer measurement times, and lower average output.

What carries the argument

The load-bearing object is the conditional ergotropy for a two-level system, W_ext(t_m|n)=ΔE Π_n(t_m)Θ(Π_n(t_m)), where Π_n is the conditional population inversion after projecting the oscillator onto energy eigenstate n. In the cold-meter limit the joint probabilities become P(0,n)=a δ_{n,0} and P(1,n)=b λ^n e^{-λ}/n!, which collapses the entire work statistics to a Bernoulli trial with success probability p=b(1-e^{-λ}). The Pareto front is then parametrised by two dimensionless combinations — the qubit gap ΔE/k_B T_S and the measurement strength λ=g²_eff(1-cos ωt_m)/(ℏω) — and the Fisher information matrix has rank at most two, so the four control parameters (temperature gap, oscillator fr

What would settle it

Measure the per-cycle work statistics of a qubit-oscillator information engine in the cold-meter limit with high statistics. If the noise-to-signal ratio drops below e^{ΔE/k_B T_S}, or if the work distribution deviates from a Bernoulli distribution (for instance, by showing partial work values or a success probability p different from b(1-e^{-λ})), then the central claim fails. This can be done by counting successful cycles over many runs and comparing q to b(1-e^{-λ}).

Watch

Extended reading notes

Core claim

Working in the limit of a cold meter (ℏω/k_B T_M ≫ 1), the paper obtains the exact work distribution analytically: P(W_ext=ΔE)=p=b(1-e^{-λ}) and P(W_ext=0)=1-p, where b=(1+e^{-ΔE/k_B T_S})^{-1} is the qubit's thermal excited-state population and λ is the effective measurement strength set by coupling, oscillator frequency, and measurement time. From this Bernoulli distribution the noise-to-signal ratio follows as ΔW²_ext/⟨W_ext⟩²=(1-p)/p, and because p≤b it is never smaller than (1-b)/b=e^{ΔE/k_B T_S}. The paper's central claim is that this lower bound is a thermodynamic precision floor: it comes from the single bath that supplies the energy, not from measurement imperfection, and it cannot

Load-bearing premise

The argument assumes that during the measurement step the qubit and oscillator are perfectly isolated from their baths and evolve unitarily; if decoherence or relaxation acts during t_m, the conditional probabilities, the ergotropy, and the entire Pareto front would move.

Editorial extensions

If this is right

  • If the bound holds, no improvement in meter accuracy can push the noise-to-signal ratio of this engine below e^{ΔE/k_B T_S}; output precision is fundamentally limited by the thermal bath from which work is drawn.
  • Precision has a price: along the Pareto front, lower fluctuations require larger mutual information gain, higher measurement cost, more engine cycles, and a smaller average work output.
  • The engine is fundamentally an intermittent converter, not a steady work source: its noise-to-signal ratio is always at least 1, and at the maximal-work point the success probability is around p≈0.218.
  • Finite-sample resolution of the front needs N≳2p(1-p)/ε² ln(1/δ) cycles, giving a parameter-free overhead ratio N_0/N_*≈1.467 between the low-work and maximum-work regimes.
  • The effective two-parameter control space means a shorter measurement time can be compensated by stronger coupling (and vice versa) without leaving the Pareto front.

Reading between the lines

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

  • A direct experimental test: in a qubit-waveguide device operated in the cold-meter limit, the measured work distribution should be exactly two-valued with P(W=ΔE)=b(1-e^{-λ}); any partial-work events or deviations in the success fraction would reveal bath coupling during the measurement stage.
  • If the precision floor is generic, similar Bernoulli-type bounds should appear for any information engine whose feedback is binary and whose success probability is bounded by a thermal occupation; examining other meters (e.g., a qubit meter) would show whether e^{ΔE/k_B T_S} is universal.
  • The Fisher-information sloppiness result suggests a practical design principle: since only two parameter combinations matter, experimentalists can choose the most convenient hardware settings (coupling, frequency, time) as long as they preserve λ and a; this may generalise to other quantum control problems.
  • The Cramér-Rao-type power bound ⟨W_ext⟩/t_m ≤ sqrt(⟨ΔW²_ext⟩⟨I⟩) implies that any attempt to boost output power must either accept larger fluctuations or increase the meter's sensitivity; this could be used to compare different feedback protocols beyond this specific engine.
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 / 5 minor

Summary. The paper studies a finite-time quantum information engine consisting of a two-level system (system) and a quantum harmonic oscillator (meter), initially thermalized at temperatures T_S and T_M. After a unitary interaction of duration t_m, the meter is projectively measured; conditional on the outcome, work is extracted from the system by ergotropy. The authors use NSGA-II multi-objective optimization to map the trade-off between squared mean extractable work and its variance. In the cold-meter limit ℏω/k_B T_M ≫ 1 they derive an exact Bernoulli work distribution with success probability p = b(1−e^{−λ}), where b is the initial excited-state population and λ is the effective measurement strength. This yields the noise-to-signal ratio ΔW²/⟨W⟩² = (1−p)/p and the lower bound e^{ΔE/k_B T_S} in the perfect-measurement limit. They also derive information-theoretic quantities (mutual information, Fisher information) and finite-sample bounds on the number of cycles.

Significance. Under the model's stated unitary-measurement assumption, the central derivation is internally consistent and elegant: the work distribution in the cold-meter limit is exactly Bernoulli, and the bound (26) is parameter-free and independent of the meter. The paper gives a compact analytical result in a setting that is usually treated numerically. Reproducibility is supported by the Zenodo code, and the numerical collapse in Fig. 3 is a useful consistency check. If the underlying closed-system idealization is quantitatively justified, the result is a clean addition to the thermodynamics of information engines.

major comments (2)
  1. [Sec. III, Eq. (11); Sec. II, step b] The central Bernoulli result, Eqs. (22)–(26), assumes that system and meter are decoupled from their baths during 0 < t < t_m and evolve unitarily. The paper justifies this by stating that control is fast compared with relaxation and decoherence times, citing Ref. [40], but no quantitative condition is given. The cold-meter regime producing the analytic front requires large λ = g_eff²/(ℏω)(1−cos ωt_m); for fixed coupling this means t_m near π/ω, which must also satisfy the fast-control condition. A finite bath coupling during t_m will modify P(i,n,t_m), and the derivation of Eq. (22), the moments (23)–(24), and the bound (26) no longer applies. Please provide a quantitative validity criterion (e.g., explicit comparison of t_m with relaxation/decoherence times for the quoted qubit-waveguide platforms) or state clearly that the bound is for the idealized closed model. As written, the abstr
  2. [Sec. IV, Figs. 2–3] The global Pareto front is computed with NSGA-II, but the paper gives no information on the optimization setup: parameter ranges, population size, number of generations, crossover/mutation rates, or stopping criterion. The caption of Fig. 2 asserts that “all sub-optimal engine configurations lie above the front,” which is a global statement that cannot be verified from the presented data. Since the analytic cold-meter line Eq. (25) is the rigorous content, the numerical front is not strictly necessary for the lower bound, but the multi-objective claims and the finite-λ fronts in Fig. 4 depend on convergence. Please add the missing optimization details and a convergence check, or explicitly frame the numerical fronts as heuristic.
minor comments (5)
  1. [Eq. (15)] The typesetting of Eq. (15) is ambiguous: “α = g_eff√ 2ℏω [...]” should read α = g_eff/(√(2ℏω)) [...] to be consistent with λ = |α|² in Eq. (21).
  2. [Appendix B, Eq. (B4)] The Cauchy–Schwarz inequality should be applied to the difference d_tm⟨W⟩ − ⟨d_tm W⟩; the printed equation is only valid after the cold-meter argument. Please clarify the intermediate step.
  3. [Sec. V, Eq. (5)] The quantity I is an entropy reduction after projective measurement, not the standard quantum mutual information I(S:M). Since the paper calls it “mutual information,” a clarifying sentence would help.
  4. [Fig. 5] The text says mutual information is plotted “in nats,” but Eq. (31) includes k_B; if k_B = 1 is assumed, please state this explicitly.
  5. [Sec. IV, finite-sample analysis] Equation (28) is derived from the quadratic large-deviation expansion; stating that it is asymptotic or providing the exact Chernoff form would make the bound more precise. The numerical agreement N0 = 920, N* = 626 with Eq. (28) is reassuring.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: analytic work statistics are derived from the stated model; self-citation [24] is context, not load-bearing.

full rationale

The paper's central analytic results (Eqs. 22-26) are obtained by evaluating the model's joint probabilities (Eqs. 13-14) in the cold-meter limit (ℏω/kBTM≫1, m=0), giving P(0,n)=aδ_{n,0} and P(1,n)=b λ^n e^{-λ}/n!. Because a>1/2>b, the n=0 conditional polarization is always negative, so only n≥1 outcomes yield work ΔE, with total probability p=b(1-e^{-λ}). The Bernoulli distribution (Eq. 22) and the moments (Eqs. 23-24) are direct consequences, not fits; Eq. (25) and the bound Eq. (26) follow algebraically. The numerical Pareto-front collapse in Fig. 3 is a consistency check of the same model's asymptotic limit, not a construction. The self-citation [24] is used only for the average-work information bound and as context; the new fluctuation result does not rest on it. No fitted parameter is relabeled as a prediction, and no uniqueness or ansatz is imported via self-citation. The only caveat is the unquantified unitary-evolution assumption during the measurement stage, but that is a physical approximation, not circular reasoning.

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

No free parameters are fitted to data; Delta E/k_B T_S and lambda are physical model inputs/combinations. The main load-bearing assumptions are the isolated unitary measurement step and the cold-meter limit. The NSGA-II convergence is an unproven practical assumption. No new particles, forces, or entities are introduced.

assumptions (7)
  • domain assumption Initial system and meter states are thermal and uncorrelated; during measurement they are decoupled from their baths and evolve unitarily under H_S + H_M + V_I(t).
    Sec. II steps a-b and Sec. III. Justified for qubit-waveguide setups by short measurement times relative to relaxation/decoherence times, but not quantified.
  • domain assumption The meter is projectively measured in energy eigenstates by a classical device (Heisenberg cut), and the Landauer erasure cost of resetting the classical readout is negligible at low temperature.
    Sec. II steps c-e. This is a modeling choice that affects the thermodynamic cost accounting.
  • standard math Work extraction is captured by ergotropy via outcome-conditioned unitaries, giving W_ext = Delta E * Pi_n * Theta(Pi_n) for a two-level system.
    Sec. II d, Eq. (6)-(16). Established result from Allahverdyan et al. [34].
  • domain assumption Cold-meter limit hbar omega >> k_B T_M, so the meter initially occupies only its ground state, P(0,n)=a delta_{n,0}, and the work distribution is Bernoulli with p=b(1-e^{-lambda}).
    Sec. IV, Eq. (21). All analytic Pareto-front results rely on this limit. The numerical optimization is claimed to always find this limit.
  • ad hoc to paper NSGA-II genetic algorithm converges to the global Pareto front of the full model.
    Sec. IV. No convergence certificate, exhaustive comparison, or multi-start verification is provided.
  • standard math Large-deviation approximation for finite cycles uses Stirling's approximation and a quadratic rate function near q=p.
    Appendix A, Eqs. (A1)-(A10). Standard asymptotic method; the resulting N estimates are approximate.
  • standard math Cramer-Rao bound is applied to the derivative of mean work and then time-averaged.
    Appendix B, Eqs. (B1)-(B6). Uses Cauchy-Schwarz and known time-averaging result [47].

how reviews work

0 comments
Cite this review

Pith. "Pith review of Pareto-optimal work extraction and the thermodynamic cost of precision in quantum information engines." pith.science (2026). https://pith.science/paper/UYVJTD45

@misc{pith2026260714973,
  author       = {Pith},
  title        = {Pith review of: Pareto-optimal work extraction and the thermodynamic cost of precision in quantum information engines},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UYVJTD45}},
  note         = {Machine review of arXiv:2607.14973}
}
read the original abstract

We study a finite-time quantum information engine in which a two-level system is measured by a quantum harmonic oscillator acting as a meter and where useful work is extracted conditionally on the measurement outcome. Using multi-objective optimisation, we find a Pareto-optimal trade-off between extractable work and its fluctuations and show that reducing fluctuations entails higher thermodynamic costs: greater information consumption, more engine cycles, longer operation time, and reduced average work output. In the limit of a highly accurate meter, we obtain the work distribution, its moments, and the Pareto front analytically. In this regime, the work statistics of the engine reduce to those of a qubit in contact with a single thermal bath. We further analyse the associated information flows by examining the mutual information and Fisher information, and show that the Pareto-optimal engine designs lie very close to local maxima of the latter with respect to the operation time of the device. Our results provide a compact description of the trade-offs between work, its fluctuations, and thermodynamic costs in quantum information engines.

Figures

Figures reproduced from arXiv: 2607.14973 by the authors.

Figure 1
Figure 1. (a) Schematic of a single information-engine cycle, showing a concrete model in which the system is a two-level system (TLS) and the meter is a quantum harmonic oscilla￾tor (QHO). Coupling them via the time-dependent interac￾tion VˆI costs the measurement work Wmeas and goes along with information transfer I. In the k-th cycle, the QHO is projectively measured in its energy eigenstate nk with a clas￾sical measuremen… view at source ↗
Figure 2
Figure 2. Pareto front (thick, colour gradient curve, starting [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 2
Figure 2. Interestingly, Eq. (26) reduces to the relative en [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Pareto front (thick, colour gradient curve) for simul [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Moreover, we find that Eq. (31) is upper bounded by Iopt ≤ Ibin = −kB [p ln p + (1 − p) ln (1 − p)] , (32) with the bound being saturated in the limit λ → ∞, as shown in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: The speed vF (tm), measured in units of kBTS/ℏ, as a function of the unconstrained measurement time for the three selected points on the Pareto front of [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

47 extracted references

  1. [24]

    Hagman, J

    R. Hagman, J. Berx, J. Splettstoesser, and H. Kirchberg, New J. Phys.27, 114507 (2025)

    2025

  2. [40]

    I. Yang, T. Agrenius, V. Usova, O. Romero-Isart, and G. Kirchmair, Sci. Adv.11, eadr4492 (2025)

    2025

  3. [1]

    H. E. D. Scovil and E. O. Schulz-DuBois, Phys. Rev. Lett. 2, 262 (1959)

    1959

  4. [2]

    Alicki, Journal of Physics A: Mathematical and Gen- eral12, L103 (1979)

    R. Alicki, Journal of Physics A: Mathematical and Gen- eral12, L103 (1979)

    1979

  5. [3]

    Kosloff, The Journal of Chemical Physics80, 1625 (1984)

    R. Kosloff, The Journal of Chemical Physics80, 1625 (1984)

    1984

  6. [4]

    Jarzynski, Phys

    C. Jarzynski, Phys. Rev. Lett.78, 2690 (1997)

    1997

  7. [5]

    Campisi, P

    M. Campisi, P. Talkner, and P. H¨ anggi, Phys. Rev. Lett. 102, 210401 (2009)

    2009

  8. [6]

    Szilard, Z

    L. Szilard, Z. Phys.53, 840 (1929)

    1929

Show all 47 references
  1. [7]

    Maruyama, F

    K. Maruyama, F. Nori, and V. Vedral, Rev. Mod. Phys. 81, 1 (2009)

    2009

  2. [8]

    A. d. O. Junior, J. B. Brask, and R. Chaves, PRX Quan- tum6, 030201 (2025)

    2025

  3. [9]

    Sagawa and M

    T. Sagawa and M. Ueda, Phys. Rev. Lett.100, 080403 (2008)

    2008

  4. [10]

    Toyabe, T

    S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, Nat. Phys.6, 988 (2010)

    2010

  5. [11]

    J. V. Koski, V. F. Maisi, J. P. Pekola, and D. V. Averin, PNAS111, 13786 (2014)

    2014

  6. [12]

    Monsel, M

    J. Monsel, M. Acciai, R. S´ anchez, and J. Splettstoesser, Phys. Rev. B111, 045419 (2025)

    2025

  7. [13]

    Kirchberg and A

    H. Kirchberg and A. Nitzan, Phys. Rev. A112, 032201 (2025)

    2025

  8. [14]

    H. J. D. Miller, M. Scandi, J. Anders, and M. Perarnau- Llobet, Phys. Rev. Lett.123, 230603 (2019)

    2019

  9. [15]

    Kirchberg and A

    H. Kirchberg and A. Nitzan, The Journal of Chemical Physics157, 184304 (2022)

    2022

  10. [16]

    Tesser and J

    L. Tesser and J. Splettstoesser, Phys. Rev. Lett.132, 186304 (2024)

    2024

  11. [17]

    G. E. Crooks, Phys. Rev. E60, 2721 (1999)

    1999

  12. [18]

    H¨ anggi and P

    P. H¨ anggi and P. Talkner, Nature Physics11, 108 (2015)

    2015

  13. [19]

    Spiecker, P

    M. Spiecker, P. Paluch, N. Gosling, N. Drucker, S. Matityahu, D. Gusenkova, S. G¨ unzler, D. Rieger, I. Takmakov, F. Valenti, P. Winkel, R. Gebauer, O. Sander, G. Catelani, A. Shnirman, A. V. Ustinov, W. Wernsdorfer, Y. Cohen, and I. M. Pop, Nature Physics19, 1320 (2023)

    2023

  14. [20]

    Zhang, P

    J. Zhang, P. Wang, W. Chen, Z. Cai, M. Qiao, R. Li, Y. Huang, H. Tian, C. Luan, H. Tu, K. Cui, L. Yan, J. Zhang, J. Zhang, M. Yung, and K. Kim, Phys. Rev. Lett.135, 140403 (2025)

    2025

  15. [21]

    Cottet, S

    N. Cottet, S. Jezouin, L. Bretheau, P. Campagne-Ibarcq, Q. Ficheux, J. Anders, A. Auff` eves, R. Azouit, P. Rou- chon, and B. Huard, PNAS114, 7561 (2017)

    2017

  16. [22]

    Masuyama, K

    Y. Masuyama, K. Funo, Y. Murashita, A. Noguchi, S. Kono, Y. Tabuchi, R. Yamazaki, M. Ueda, and Y. Nakamura, Nature Communications9, 1291 (2018)

    2018

  17. [23]

    Dassonneville, C

    R. Dassonneville, C. Elouard, R. Cazali, R. Assouly, A. Bienfait, A. Auff` eves, and B. Huard, Phys. Rev. Res. 8, 013228 (2026)

    2026

  18. [25]

    Deb,Multi-Objective Optimization using Evolution- ary Algorithms, Wiley Interscience Series in Systems and Optimization (Wiley-Blackwell, Hoboken, NJ, 2008)

    K. Deb,Multi-Objective Optimization using Evolution- ary Algorithms, Wiley Interscience Series in Systems and Optimization (Wiley-Blackwell, Hoboken, NJ, 2008)

    2008

  19. [26]

    Berx and K

    J. Berx and K. Proesmans, EPL145, 51001 (2024)

    2024

  20. [27]

    G. A. L. For˜ ao, J. Berx, and C. E. Fiore, New J. Phys. 27, 074605 (2025)

    2025

  21. [28]

    J. Berx, P. Singh, and K. Proesmans, New J. Phys.27, 023034 (2025)

    2025

  22. [29]

    P. A. Erdman, A. Rolandi, P. Abiuso, M. Perarnau- Llobet, and F. No´ e, Phys. Rev. Res.5, L022017 (2023)

    2023

  23. [30]

    Taranto, F

    P. Taranto, F. Bakhshinezhad, A. Bluhm, R. Silva, N. Friis, M. P. Lock, G. Vitagliano, F. C. Binder, T. De- barba, E. Schwarzhans, F. Clivaz, and M. Huber, PRX Quantum4, 010332 (2023)

    2023

  24. [31]

    Heisenberg,The physical principles of the quantum theory / by Werner Heisenberg ; transl

    W. Heisenberg,The physical principles of the quantum theory / by Werner Heisenberg ; transl. by Carl Eckart and Frank C. Hoyt.(Dover, 1949)

    1949

  25. [32]

    Von Neumann,Mathematical Foundations of Quantum Mechanics(Princeton Univ

    J. Von Neumann,Mathematical Foundations of Quantum Mechanics(Princeton Univ. Press., Princeton, NJ, 1955)

    1955

  26. [33]

    Atmanspacher, World Futures49, 333 (1997)

    H. Atmanspacher, World Futures49, 333 (1997)

    1997

  27. [34]

    A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, EPL67, 565 (2004)

    2004

  28. [35]

    Francica, J

    G. Francica, J. Goold, F. Plastina, and M. Paternostro, npj Quantum Inf.3, 1 (2017)

    2017

  29. [36]

    Landauer, IBM J

    R. Landauer, IBM J. Res. Dev.5, 183 (1961)

    1961

  30. [37]

    Elouard, D

    C. Elouard, D. Herrera-Mart ´ ı, B. Huard, and A. Auff` eves, Phys. Rev. Lett.118, 260603 (2017)

    2017

  31. [38]

    Jordan, C

    A. Jordan, C. Elouard, and A. Auff` eves, Quantum Stud- ies: Mathematics and Foundations7, 203 (2020)

    2020

  32. [39]

    Janzen, X

    N. Janzen, X. Dai, S. Ren, J. Shi, and A. Lupascu, Phys. Rev. Res.5, 033155 (2023)

    2023

  33. [41]

    Magnus, F

    W. Magnus, F. Oberhettinger, and R. P. Soni,Formu- las and theorems for the special functions of mathemati- cal physics, 1966th ed., Grundlehren der mathematischen Wissenschaften (Springer, Berlin, Germany, 2013)

    2013

  34. [42]

    Seifert, Physica A504, 176 (2018)

    U. Seifert, Physica A504, 176 (2018)

    2018

  35. [43]

    M. F. Anka, T. R. de Oliveira, and D. Jonathan, Phys. Rev. E109, 064129 (2024)

    2024

  36. [44]

    Bouton, J

    Q. Bouton, J. Nettersheim, S. Burgardt, D. Adam, E. Lutz, and A. Widera, Nat. Commun.12, 2063 (2021)

  37. [45]

    Chitambar and G

    E. Chitambar and G. Gour, Reviews of modern physics 91, 025001 (2019)

    2019

  38. [46]

    Touchette, Phys

    H. Touchette, Phys. Rep.478, 1 (2009)

    2009

  39. [47]

    Juli` a-Farr´ e, T

    S. Juli` a-Farr´ e, T. Salamon, A. Riera, M. N. Bera, and M. Lewenstein, Phys. Rev. Res.2, 023113 (2020)

    2020

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.