Pith. sign in

REVIEW 1 major objections 4 minor 1 cited by

Thermodynamics of precision in quantum nano-machines

T0 review · 1 major / 4 minor · reviewed 2026-08-27 · deepseek-v4-flash

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

Pith's one-line read A three-qubit quantum heat engine can beat the classical thermodynamic-precision limit.

desk verdict A solid, clearly written paper that derives exact TUR ratios for three few-qubit engines and gives a concrete three-qubit model beating the classical Markovian bound; the central claim holds within the stated fast-thermalisation regime, though a few sign/typo fixes and an optional numerical check would make it tighter. read the letter →

arxiv 2009.11303 v3 pith:EETBPURS submitted 2020-09-23 quant-ph cond-mat.mes-hallcond-mat.stat-mech

Antoine Rignon-Bret , Giacomo Guarnieri , John Goold , Mark T. Mitchison This is my paper · ORCID
classification quant-phcond-mat.mes-hallcond-mat.stat-mech
keywords thermodynamicuncertaintyrelationquantumheatenginepowerfluctuationsentropyproductioncoherenceautonomousthree-qubitvirtualqubitOtto
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 derives exact relations connecting average power, power fluctuations, and entropy production rate for small quantum heat engines that deposit work into a quantized load. It shows that quantum coherence is a double-edged resource: coherent transport inside the engine reduces power fluctuations at fixed entropy production, while coherent states of the load itself increase them. The headline result is an autonomous three-qubit engine whose thermodynamic-uncertainty ratio can fall as low as 1.245, below the bound of 2 that applies to every classical Markovian engine. If the derivation holds, the work supplies a concrete design rule: insert an extra coherent stage between engine and load to make nanoscale machines steadier without extra dissipation.

What carries the argument

The central object is the TUR ratio $\dot{\Delta W}\,\dot{\Sigma}/\dot{W}^2$, the product of relative power fluctuations and entropy production rate. For the autonomous engines the argument runs through the virtual qubit, the effective two-level system formed by one excitation shared between two machine qubits, whose population inversion drives a coherent current to the load. The three-qubit engine modifies this machinery by making the load couple to a physical qubit that is itself thermalised to the virtual temperature, so the coherent current is shielded from the fast bath-induced decoherence of the two engine qubits. The exact steady-state solutions express power, entropy production, and power fluctuations in terms of the virtual or physical qubit bias $\langle\hat{Z}\rangle_{\mathrm{eq}}$ or $\langle\hat{\sigma}_3^z\rangle_{\mathrm{eq}}$, which converts the classical biased-random-walk bound into the parameter-dependent quantum TUR ratios.

What would settle it

Build the three-qubit engine with tunable qubit-bath and coherent couplings, measure steady-state power $\dot{W}$, power-variance growth $\dot{\Delta W}$, and heat currents to obtain $\dot{\Sigma}$, and check whether $\dot{\Delta W}\,\dot{\Sigma}/\dot{W}^2$ falls below 2 and approaches 1.245 near the optimal coupling ratio. A simpler test of the model's scope is to integrate the full three-qubit-plus-load master equation without the fast-thermalisation elimination and see whether any parameter choice within the claimed regime violates the bound.

Watch

Extended reading notes

Core claim

The paper claims that few-qubit quantum heat engines are not constrained by the same precision-dissipation trade-off as classical stochastic machines. For the minimal two-qubit absorption engine the TUR ratio $\dot{\Delta W}\,\dot{\Sigma}/\dot{W}^2$ satisfies an inequality of the classical form $\ge 2$. Adding a third qubit to intermediate the energy flow changes the ratio to $\chi\coth(\chi/2)\bigl[1 - 6\Gamma_3 p/(p^2+8g^2)\tanh^2(\chi/2)\bigr]$, whose minimum over the coupling ratio is $1.245\ldots$. The authors thus establish a concrete example of an autonomous engine that is steadier, per unit of entropy produced, than any classical Markovian engine. They also show the opposite for a cyclic Otto engine with a harmonic-oscillator load: coherent states of the flywheel carry intrinsic energy uncertainty, inflating the ratio by a factor of three relative to a random walk over Fock states.

Load-bearing premise

The three-qubit result rests on the assumption that qubits 1 and 2 thermalise much faster than the coherent couplings ($p'\gg g,k$), so that the Born-Markov master equation (28) is valid; if that separation of timescales fails, the predicted bound 1.245 is not guaranteed to hold.

Editorial extensions

If this is right

  • The three-qubit design can reduce relative power fluctuations to roughly 62% of the level a classical Markovian engine would need for the same entropy production.
  • The classical bound of 2 is not universal: coherent transport inside a few-qubit machine gives an autonomous steady-state engine a TUR floor of about 1.245.
  • Regardless of quantum effects, approaching Carnot efficiency at finite power still requires power fluctuations to diverge.
  • Coherence in the machine's transport pathway helps precision, whereas coherence in the load's energy basis hurts it, so the geometry of the engine and the nature of the load decide whether quantum effects reduce or amplify fluctuations.
  • A general design principle follows: reduce bath-induced decoherence of the coherent current, for example by inserting additional stages between engine and load, to lower fluctuations at fixed entropy production.

Reading between the lines

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

  • A direct experimental test is within reach in platforms where qubit reset rates and coherent couplings are separately tunable: measuring the steady-state TUR ratio below 2 would certify non-classical operation purely from fluctuation statistics.
  • The same intermediate-stage mechanism that steadies engines should apply to autonomous clocks and thermoelectric generators that operate with coherent currents, since their precision is also limited by a TUR; the paper cites neighbouring work but does not develop this transfer.
  • A natural formal extension is to solve the full three-qubit-plus-load dynamics without the fast-thermalisation elimination; if the sub-classical floor survives strong coupling, the design could combine high power with quantum-enhanced precision.
  • Replacing the load's bare energy statistics by ergotropy would change the definition of useful output and could remove the factor-of-three penalty found for coherent-state flywheels; the paper flags ergotropy as future work, so this is an extrapolation.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Request a human review

A listed scientist reviews the paper for a fee and the review publishes here regardless of verdict. See the reviewers or get listed.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 4 minor

Summary. The paper studies thermodynamic uncertainty relations (TURs) for few-qubit quantum heat engines whose work is deposited in a quantized load. It derives TUR ratios, i.e. explicit relations between power, power fluctuations, and entropy production rate, for three settings: a two-qubit autonomous engine under reset and local-Lindblad dissipation models, a proposed three-qubit autonomous engine whose effective dynamics gives a TUR ratio with a lower bound of 1.245, and a single-qubit Otto engine with a harmonic-oscillator flywheel modelled as a discrete-time random walk over coherent states. The derivations are presented as exact solutions of the relevant Heisenberg equations, with analytic bounds collected in Appendices A and B and the three-qubit effective master equation derived in Appendix C.

Significance. If fully supported, the central result is of clear interest: a concrete autonomous quantum heat engine whose power fluctuations for a given entropy production can lie below the universal classical Markovian TUR bound of 2, with a physically transparent design principle (moving the coherent coupling away from the decohering baths). The paper also provides useful exact TUR ratios for established two-qubit engine models and a clean explanation of the factor-of-three noise enhancement for coherent-state flywheels. The analytical derivations are detailed and self-contained, the relations are parameter-free rather than fitted, and the authors are explicit about the main approximation behind the three-qubit engine. The significance is tempered by the fact that the headline three-qubit advantage is established only within an effective master equation, with no direct check of the variance rate against the full microscopic model.

major comments (1)
  1. [Sec. III B and Appendix C, Eqs. (28), (32), (C8)-(C17)] The three-qubit TUR ratio (32) is derived from the effective master equation (28), obtained by adiabatically eliminating qubits 1 and 2 under the assumption p' >> k,g. The dissipative kernel is computed only to lowest order in the interaction terms, while the coherent coupling H_int is then included non-perturbatively in the equations for C and Omega (C11)-(C16). Since the claimed advantage is the reduction of the TUR ratio from the classical bound 2 to 1.245, uncontrolled relative corrections of order k/p' or g/p' could in principle restore a ratio above 2. The authors explicitly flag the fast-thermalisation restriction and defer the strong-coupling regime, but they do not provide a numerical or analytical check of the long-time variance slope against the full reset model at finite p'. I request such a check: for example, simulating the full three-qubit-plus-load master equation over a range of p'/k, p'/g, and chi, and comparing the asymptotic slope of Var(W) with Eq. (31). If a benchmark is not feasible, the abstract and Section III should be reworded so that the claim is explicitly stated as conditional on the validity of the effective model rather than as a property of the original microscopic engine.
minor comments (4)
  1. [Appendix C, Eq. (C15)] The term 2g(2Omega - E_v) in Eq. (C15) should read 2g(2Omega + E_v) to be consistent with the driving term in Eq. (C17) and with the final result Eq. (31). This appears to be a typographical sign error that does not affect the final bounds.
  2. [Appendix B, text before Eq. (B1)] The sentence states <Z>_eq >= (1/2) tanh(chi/2), but from Eqs. (9) and (10) the correct inequality is <Z>_eq <= (1/2) tanh(chi/2). The subsequent bound in Eq. (B1) uses the correct direction, so the final inequality is unaffected.
  3. [Abstract and Sec. III A] The abstract describes the results as exact relations. For the two-qubit models this is appropriate, but for the three-qubit engine the TUR ratio (32) is obtained from the approximate effective master equation (28) under the fast-thermalisation condition p' >> k,g. The abstract and the discussion in Section III should qualify this point so that the status of the three-qubit result is unambiguous.
  4. [Fig. 3 caption and Sec. III] The horizontal axis g/p is not directly comparable across the models shown in Fig. 3: for the two-qubit engine p is the microscopic reset rate, while for the three-qubit engine p is the effective rate gamma_+ + gamma_- of the reduced model. A sentence in the caption defining p in each case would improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the TUR ratios are exact algebraic consequences of the stated master equations, with no fitted parameters or definitional identities.

full rationale

The paper's central TUR ratios are obtained by solving, not assuming, the stated master equations. For the two-qubit reset model, Eqs. (12)-(14) are derived in Appendix A from Eq. (4) via closed Heisenberg equations, and Eq. (16) is an algebraic rewrite of those solutions. For the three-qubit engine, Eq. (32) follows directly by inserting Eq. (27) into Eqs. (29)-(31), which in turn come from solving the effective master equation (28) in Appendix C. No parameter is fitted to the quantity being predicted, and no definition of a TUR ratio smuggles the bound into the model. The self-citations are background or consistency checks rather than load-bearing premises: for example, Ref. [47] is used only to state that Eq. (32) satisfies an existing quantum TUR, and Refs. [21,22] are invoked to identify the weak-coupling random-walk limit after the exact solution is already in hand. The effective-master-equation derivation in Appendix C invokes an approximation (rapid thermalisation, p' >> g,k), but an approximation with stated validity conditions is not a circular reduction; the authors explicitly defer strong coupling to future work. The transcription issues noted by a careful reader, namely the sign before E_v in Eq. (C15) and the inequality direction before Eq. (B1), are typos in intermediate steps and do not make any result equivalent to its input by construction.

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

The central results are exact consequences of the specified master equations and random-walk model. There are no fitted free parameters; all model inputs (energies, temperatures, coupling rates) are stated as part of the model. The load-bearing premises are the master equation formulations and the fast-thermalisation approximation for the three-qubit engine, all explicitly identified in the text.

assumptions (5)
  • domain assumption The reset master equation (4) faithfully describes thermalisation of the qubits, with local dissipation that is thermodynamically consistent because [H0, Hint] = 0.
    The entire two-qubit analysis rests on this master equation; the authors note it assumes g is not much larger than other energy or frequency scales.
  • domain assumption For the three-qubit engine, the Born-Markov approximation and fast thermalisation (p' >> g, k) justify eliminating qubits 1 and 2 to obtain the effective master equation (28).
    This is the load-bearing approximation for the claimed quantum advantage; the authors acknowledge it limits the result to the weak-coupling regime.
  • domain assumption The entropy production rate is quantified by heat fluxes only, ignoring the load's growing von Neumann entropy.
    Explicitly stated in Sec. II B after Eq. (6); this choice affects the numerical value of the TUR ratio.
  • domain assumption For the Otto engine, a mean-field approximation for the qubit energy and neglect of corrections to the Boltzmann factors are valid, with the random-walk mapping reproducing the flywheel dynamics.
    Used in Eqs. (34)-(36) and the discrete-time random walk derivation in Sec. IV.
  • standard math Standard tools of open quantum systems: Lindblad master equation formalism, ladder operator algebra, and generating function techniques.
    Invoked throughout without proof, as is standard in this literature.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Thermodynamics of precision in quantum nano-machines." pith.science (2026). https://pith.science/paper/EETBPURS

@misc{pith2026200911303,
  author       = {Pith},
  title        = {Pith review of: Thermodynamics of precision in quantum nano-machines},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EETBPURS}},
  note         = {Machine review of arXiv:2009.11303}
}
read the original abstract

Fluctuations strongly affect the dynamics and functionality of nanoscale thermal machines. Recent developments in stochastic thermodynamics have shown that fluctuations in many far-from-equilibrium systems are constrained by the rate of entropy production via so-called thermodynamic uncertainty relations. These relations imply that increasing the reliability or precision of an engine's power output comes at a greater thermodynamic cost. Here we study the thermodynamics of precision for small thermal machines in the quantum regime. In particular, we derive exact relations between the power, power fluctuations, and entropy production rate for several models of few-qubit engines (both autonomous and cyclic) that perform work on a quantised load. Depending on the context, we find that quantum coherence can either help or hinder where power fluctuations are concerned. We discuss design principles for reducing such fluctuations in quantum nano-machines, and propose an autonomous three-qubit engine whose power output for a given entropy production is more reliable than would be allowed by any classical Markovian model.

Figures

Figures reproduced from arXiv: 2009.11303 by the authors.

Figure 1
Figure 1. FIG. 1. Illustration of an autonomous two-qubit engine coupled to an [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The virtual qubit is the pair of states [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Thermodynamics of precision for autonomous few-qubit en [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Schematic of the autonomous three-qubit engine. The energy [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Schematic depiction of an Otto cycle where a qubit working [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The flywheel dynamics can be modelled as a discrete-time [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Thermodynamics of precision for random walks. The TUR [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Black hole thermodynamics at null infinity. Part 2: Open systems, Markovian dynamics and work extraction from non-rotating black holes

    hep-th 2026-01 conditional novelty 6.0 of 10

    Null-infinity black hole thermodynamics is recast as Markovian open-system thermodynamics, with chemical-potential terms identified as extractable work and used to formulate generalized grand-potential laws for Schwar...

Reference graph

Works this paper leans on

100 extracted references · 58 canonical work pages · cited by 1 Pith paper

  1. [1]

    The results are equivalent to those already obtained by Brun- ner et al

    Reset model For completeness, in this Appendix we detail the solution of the two-qubit engine modelled by the reset master equation. The results are equivalent to those already obtained by Brun- ner et al. [61], but it is convenient to recast them here in our notation. Starting from the master equation [Eq. (4)] written as dˆρ/dt =−i[ ˆH, ˆρ] + ∑ j=1,2D j...

  2. [2]

    anti-virtual qubit

    (equivalent to the bias of an “anti-virtual qubit” [61]). Together with the current, these quantities obey the coupled equations d ˆC dt = 2g ˆZ− 2p ˆC, (A1) d ˆZ dt = p ( ⟨ ˆZ⟩eq− ˆZ ) − 2g ˆC, (A2) d ˆN dt = p ( 1− 2 ˆN +⟨ ˆZ⟩eq ˆZ−⟨ ˆS⟩eq ˆS ) , (A3) d ˆS dt = p ( ⟨ ˆS⟩eq− ˆS ) , (A4) where the equilibrium averages denoted by, for example, ⟨ ˆZ⟩eq = Tr...

  3. [3]

    (19), which differs from the reset model of Eq

    Local Lindblad equation We now carry out the same calculation for the local Lind- blad dissipation model defined by Eq. (19), which differs from the reset model of Eq. (4) by the absence of the dephasing terms proportional toγz. These terms affect only off-diagonal operators in the computational basis. Therefore, only the equations of motion for ˆC and ˆK are...

  4. [4]

    (B7) Appendix C: Solution for the three-qubit engine

    As a result, we obtain the bound ˙∆W ˙W2 ˙Σ≥χ coth(χ/2) [ 1− 3 4 tanh2(χ/2) ] ≥ 1.245... . (B7) Appendix C: Solution for the three-qubit engine

  5. [5]

    weak co- herent coupling)

    Master equation derivation In this Appendix, we detail the solution of the three-qubit engine model in the limit of fast thermalisation (i.e. weak co- herent coupling). We begin by sketching the derivation of the effective master equation. Let ˆR(t) denote the total density matrix of the three qubits and the load. We consider a reset thermalisation model f...

  6. [6]

    The mean energy of the load follows from the equation of motion d ˆW/dt = gEv⟨ ˆC⟩, with the cur- rent operator now given by ˆC = ig ( ˆσ+ 3 ˆA− ˆσ− 3 ˆA†)

    Asymptotic solution The solution proceeds straightforwardly according to the methods of Appendix A. The mean energy of the load follows from the equation of motion d ˆW/dt = gEv⟨ ˆC⟩, with the cur- rent operator now given by ˆC = ig ( ˆσ+ 3 ˆA− ˆσ− 3 ˆA†) . (C10) The current and qubit bias obey the coupled differential equa- tions d ˆC dt = 2g ˆσz 3− p 2 ˆ...

  7. [7]

    Einstein, Annalen der Physik 322, 549 (1905)

    A. Einstein, Annalen der Physik 322, 549 (1905)

    1905

  8. [8]

    Rold ´an and J

    E. Rold ´an and J. M. R. Parrondo, Phys. Rev. Lett. 105, 150607 (2010)

    2010

Show all 100 references
  1. [9]

    Ribezzi-Crivellari and F

    M. Ribezzi-Crivellari and F. Ritort, Proc. Nat. Acad. Sci. 111, E3386 (2014)

    2014

  2. [10]

    Rossnagel, S

    J. Rossnagel, S. T. Dawkins, K. N. Tolazzi, O. Abah, E. Lutz, F. Schmidt-Kaler, and K. Singer, Science 352, 325 (2016)

    2016

  3. [11]

    von Lindenfels, O

    D. von Lindenfels, O. Gr ¨ab, C. T. Schmiegelow, V . Kaushal, J. Schulz, M. T. Mitchison, J. Goold, F. Schmidt-Kaler, and U. G. Poschinger, Phys. Rev. Lett.123, 080602 (2019)

    2019

  4. [12]

    N. V . Horne, D. Yum, T. Dutta, P. H¨anggi, J. Gong, D. Poletti, and M. Mukherjee, npj Quantum Info. 6, 37 (2020). 12

    2020

  5. [13]

    A. B. Kolomeisky and M. E. Fisher, Annu. Rev. Phys. Chem. 58, 675 (2007)

    2007

  6. [14]

    H. B. Callen and T. A. Welton, Phys. Rev. 83, 34 (1951)

    1951

  7. [15]

    Esposito, U

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

    2009

  8. [16]

    Campisi, P

    M. Campisi, P. H ¨anggi, and P. Talkner, Rev. Mod. Phys. 83, 771 (2011)

    2011

  9. [17]

    Seifert, Rep

    U. Seifert, Rep. Prog. Phys. 75, 126001 (2012)

    2012

  10. [18]

    H ¨anggi and P

    P. H ¨anggi and P. Talkner, Nature Phys.11, 108 (2015)

    2015

  11. [19]

    G. T. Landi and M. Paternostro, arXiv:2009.07668 [quant-ph] (2020)

    2020 arXiv

  12. [20]

    A. C. Barato and U. Seifert, Phys. Rev. Lett. 114, 158101 (2015)

    2015

  13. [21]

    T. R. Gingrich, J. M. Horowitz, N. Perunov, and J. L. England, Phys. Rev. Lett. 116, 120601 (2016)

    2016

  14. [22]

    J. M. Horowitz and T. R. Gingrich, Nature Phys. 16, 15 (2019)

    2019

  15. [23]

    Campisi and R

    M. Campisi and R. Fazio, Nature Commun. 7, 11895 (2016)

    2016

  16. [24]

    Holubec and A

    V . Holubec and A. Ryabov, Phys. Rev. E96, 030102 (2017)

    2017

  17. [25]

    Pietzonka and U

    P. Pietzonka and U. Seifert, Phys. Rev. Lett. 120, 190602 (2018)

    2018

  18. [26]

    A. C. Barato and U. Seifert, Phys. Rev. X 6, 041053 (2016)

    2016

  19. [27]

    Erker, M

    P. Erker, M. T. Mitchison, R. Silva, M. P. Woods, N. Brunner, and M. Huber, Phys. Rev. X7, 031022 (2017)

    2017

  20. [28]

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

    2019

  21. [29]

    A. N. Pearson, Y . Guryanova, P. Erker, E. A. Laird, G. A. D. Briggs, M. Huber, and N. Ares, arXiv:2006.08670 [cond- mat.mes-hall] (2020)

    2020 arXiv

  22. [30]

    Schwarzhans, M

    E. Schwarzhans, M. P. E. Lock, P. Erker, N. Friis, and M. Hu- ber, arXiv:2007.01307 [quant-ph] (2020)

    2020 arXiv

  23. [31]

    G. J. Milburn, arXiv:2007.02217 [quant-ph] (2020)

    2020 arXiv

  24. [32]

    M. P. Woods, arXiv:2005.04628 [quant-ph] (2020)

    2020 arXiv

  25. [33]

    S. E. Harvey, S. Lahiri, and S. Ganguli, arXiv:2002.10567 [physics.bio-ph] (2020)

    2020 arXiv

  26. [34]

    Pietzonka, A

    P. Pietzonka, A. C. Barato, and U. Seifert, J. Stat. Mech.: Theor. Exp. 2016, 124004 (2016)

    2016

  27. [35]

    Seifert, Annu

    U. Seifert, Annu. Rev. Cond. Matt. Phys. 10, 171 (2019)

    2019

  28. [36]

    Pietzonka, F

    P. Pietzonka, F. Ritort, and U. Seifert, Phys. Rev. E 96, 012101 (2017)

    2017

  29. [37]

    J. M. Horowitz and T. R. Gingrich, Phys. Rev. E 96, 020103 (2017)

    2017

  30. [38]

    Proesmans and C

    K. Proesmans and C. V . den Broeck, Europhys. Lett.119, 20001 (2017)

    2017

  31. [39]

    Chiuchi `u and S

    D. Chiuchi `u and S. Pigolotti, Phys. Rev. E 97, 032109 (2018)

    2018

  32. [40]

    J. P. Garrahan, Phys. Rev. E 95, 032134 (2017)

    2017

  33. [41]

    P. P. Potts and P. Samuelsson, Phys. Rev. E100, 052137 (2019)

    2019

  34. [42]

    Polettini, A

    M. Polettini, A. Lazarescu, and M. Esposito, Phys. Rev. E 94, 052104 (2016)

    2016

  35. [43]

    Falasco, M

    G. Falasco, M. Esposito, and J.-C. Delvenne, New J. Phys. 22, 053046 (2020)

    2020

  36. [44]

    A. M. Timpanaro, G. Guarnieri, J. Goold, and G. T. Landi, Phys. Rev. Lett. 123, 090604 (2019)

    2019

  37. [45]

    Hasegawa and T

    Y . Hasegawa and T. Van Vu, Phys. Rev. Lett. 123, 110602 (2019)

    2019

  38. [46]

    Dechant, J

    A. Dechant, J. Phys. A: Math. Theor. 52, 035001 (2018)

    2018

  39. [47]

    Hasegawa and T

    Y . Hasegawa and T. Van Vu, Phys. Rev. E99, 062126 (2019)

    2019

  40. [48]

    Dechant and S.-i

    A. Dechant and S.-i. Sasa, Proc. Nat. Acad. Sci. 117, 6430 (2020)

    2020

  41. [49]

    Ptaszy ´nski, Phys

    K. Ptaszy ´nski, Phys. Rev. B 98, 085425 (2018)

    2018

  42. [50]

    B. K. Agarwalla and D. Segal, Phys. Rev. B 98, 155438 (2018)

    2018

  43. [51]

    Brandner, T

    K. Brandner, T. Hanazato, and K. Saito, Phys. Rev. Lett. 120, 090601 (2018)

    2018

  44. [52]

    Liu and D

    J. Liu and D. Segal, Phys. Rev. E 99, 062141 (2019)

    2019

  45. [53]

    Guarnieri, G

    G. Guarnieri, G. T. Landi, S. R. Clark, and J. Goold, Phys. Rev. Research 1, 033021 (2019)

    2019

  46. [54]

    H. J. D. Miller, M. H. Mohammady, M. Perarnau-Llobet, and G. Guarnieri, arXiv:2006.07316 [quant-ph] (2020)

    2020 arXiv

  47. [55]

    Macieszczak, K

    K. Macieszczak, K. Brandner, and J. P. Garrahan, Phys. Rev. Lett. 121, 130601 (2018)

    2018

  48. [56]

    Carollo, R

    F. Carollo, R. L. Jack, and J. P. Garrahan, Phys. Rev. Lett. 122, 130605 (2019)

    2019

  49. [57]

    Hasegawa, Phys

    Y . Hasegawa, Phys. Rev. Lett.125, 050601 (2020)

    2020

  50. [58]

    Hasegawa, arXiv:2003.08557 [cond-mat.stat-mech] (2020)

    Y . Hasegawa, arXiv:2003.08557 [cond-mat.stat-mech] (2020)

    2020 arXiv

  51. [59]

    Segal, Phys

    D. Segal, Phys. Rev. E 97, 052145 (2018)

    2018

  52. [60]

    Saryal, H

    S. Saryal, H. M. Friedman, D. Segal, and B. K. Agarwalla, Phys. Rev. E 100, 042101 (2019)

    2019

  53. [61]

    Bu ffoni and M

    L. Bu ffoni and M. Campisi, Quantum Sci. Tech. 5, 035013 (2020)

    2020

  54. [62]

    Benenti, G

    G. Benenti, G. Casati, and J. Wang, Phys. Rev. E 102, 040103 (2020)

    2020

  55. [63]

    Y . Wen, N. Ares, F. J. Schupp, T. Pei, G. A. D. Briggs, and E. A. Laird, Nature Phys. 16, 75 (2019)

    2019

  56. [64]

    Tonner and G

    F. Tonner and G. Mahler, Phys. Rev. E 72, 066118 (2005)

    2005

  57. [65]

    Boukobza and D

    E. Boukobza and D. J. Tannor, Phys. Rev. A74, 063822 (2006)

    2006

  58. [66]

    Youssef, G

    M. Youssef, G. Mahler, and A.-S. F. Obada, Phys. Rev. E 80, 061129 (2009)

    2009

  59. [67]

    Brunner, N

    N. Brunner, N. Linden, S. Popescu, and P. Skrzypczyk, Phys. Rev. E 85, 051117 (2012)

    2012

  60. [68]

    Gelbwaser-Klimovsky, R

    D. Gelbwaser-Klimovsky, R. Alicki, and G. Kurizki, Europhys. Lett. 103, 60005 (2013)

    2013

  61. [69]

    A. Mari, A. Farace, and V . Giovannetti, J. Phys. B: Atom. Mol. Opt. Phys. 48, 175501 (2015)

    2015

  62. [70]

    A. Levy, L. Di ´osi, and R. Koslo ff, Phys. Rev. A 93, 052119 (2016)

    2016

  63. [71]

    Niedenzu, M

    W. Niedenzu, M. Huber, and E. Boukobza, Quantum 3, 195 (2019)

    2019

  64. [72]

    Linden, S

    N. Linden, S. Popescu, and P. Skrzypczyk, Phys. Rev. Lett. 105, 130401 (2010)

    2010

  65. [73]

    Skrzypczyk, R

    P. Skrzypczyk, R. Silva, and N. Brunner, Phys. Rev. E 91, 052133 (2015)

    2015

  66. [74]

    Barra, Sci

    F. Barra, Sci. Rep. 5, 14873 (2015)

    2015

  67. [75]

    Barra and C

    F. Barra and C. Lled ´o, Euro. Phys. J. Special Topics 227, 231 (2018)

    2018

  68. [76]

    De Chiara, G

    G. De Chiara, G. Landi, A. Hewgill, B. Reid, A. Ferraro, A. J. Roncaglia, and M. Antezza, New J. Phys. 20, 113024 (2018)

    2018

  69. [77]

    Levy and R

    A. Levy and R. Kosloff, Europhys. Lett. 107, 20004 (2014)

    2014

  70. [78]

    J. T. Stockburger and T. Motz, Fortsch. Phys. 65, 1600067 (2016)

    2016

  71. [79]

    Spohn, J

    H. Spohn, J. Math. Phys. 19, 1227 (1978)

    1978

  72. [80]

    M. T. Mitchison and M. B. Plenio, New J. Phys. 20, 033005 (2018)

    2018

  73. [81]

    P. P. Hofer, M. Perarnau-Llobet, L. D. M. Miranda, G. Haack, R. Silva, J. B. Brask, and N. Brunner, New J. Phys. 19, 123037 (2017)

    2017

  74. [82]

    Shiraishi, K

    N. Shiraishi, K. Saito, and H. Tasaki, Phys. Rev. Lett. 117, 190601 (2016)

    2016

  75. [83]

    Holubec and A

    V . Holubec and A. Ryabov, Phys. Rev. Lett. 121, 120601 (2018)

    2018

  76. [84]

    Abiuso and M

    P. Abiuso and M. Perarnau-Llobet, Phys. Rev. Lett.124, 110606 (2020)

    2020

  77. [85]

    Silva, G

    R. Silva, G. Manzano, P. Skrzypczyk, and N. Brunner, Phys. Rev. E 94, 032120 (2016)

    2016

  78. [86]

    A. Usui, W. Niedenzu, and M. Huber, arXiv:2009.03832 [quant-ph] (2020), 2009.03832

    2020 arXiv

  79. [87]

    Francica, F

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

    2020

  80. [88]

    A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Eu- rophys. Lett. 67, 565 (2004)

    2004

  81. [89]

    Esposito and C

    M. Esposito and C. V . den Broeck, Europhys. Lett. 95, 40004 13 (2011)

    2011

  82. [90]

    Uzdin, A

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

    2015

  83. [91]

    Smirne, D

    A. Smirne, D. Eglo ff, M. G. D ´ıaz, M. B. Plenio, and S. F. Huelga, Quantum Sci. Tech. 4, 01LT01 (2018)

    2018

  84. [92]

    Klatzow, J

    J. Klatzow, J. N. Becker, P. M. Ledingham, C. Weinzetl, K. T. Kaczmarek, D. J. Saunders, J. Nunn, I. A. Walmsley, R. Uzdin, and E. Poem, Phys. Rev. Lett. 122, 110601 (2019)

    2019

  85. [93]

    Verteletsky and K

    K. Verteletsky and K. Mølmer, Phys. Rev. A 101, 010101 (2020)

    2020

  86. [94]

    Lostaglio, arXiv:2004.01213 [quant-ph] (2020)

    M. Lostaglio, arXiv:2004.01213 [quant-ph] (2020)

    2020 arXiv

  87. [95]

    Levy and M

    A. Levy and M. Lostaglio, PRX Quantum 1, 010309 (2020)

    2020

  88. [96]

    J. O. Gonz ´alez, J. P. Palao, D. Alonso, and L. A. Correa, Phys. Rev. E 99, 062102 (2019)

    2019

  89. [97]

    Hanbury Brown and R

    R. Hanbury Brown and R. Q. Twiss, Nature 177, 27 (1956); R. Q. Twiss, A. G. Little, and R. Hanbury Brown, Nature 180, 324 (1957)

    1956

  90. [98]

    H. J. Kimble, M. Dagenais, and L. Mandel, Phys. Rev. Lett. 39, 691 (1977)

    1977

  91. [99]

    Breuer and F

    H.-P. Breuer and F. Petruccione, The theory of open quantum systems (Oxford University Press, Oxford, 2002)

    2002

  92. [100]

    Rivas, A

    ´A. Rivas, A. D. K. Plato, S. F. Huelga, and M. B. Plenio, New J. Phys. 12, 113032 (2010)

    2010

Pith tools

Reviewed August 27, 2026 · model on record in the stance chip above.