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Any coherent fermionic thermoelectric heat engine must have charge-current Fano factor above 1/2; bosons and classical carriers sit above 1.

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Heat-engine operation forces a universal Fano-factor floor of F>1/2 for fermionic coherent thermoelectric transport and F>1 for bosonic or classical carriers.

T0 review reviewed 2026-07-14 challenge →

load-bearing objection Clean, mode-specific TUR that forces F > 1/2 for fermionic coherent heat engines (and F > 1 for bosons/classical); proofs and numerics look solid under the stated Landauer–Büttiker assumptions.

arxiv 2607.11704 v1 pith:6UUIDQPK submitted 2026-07-13 cond-mat.mes-hall

Thermodynamic bound on the Fano factor of a coherent thermoelectric heat engine

Nahual Sobrino , Rosario Fazio , Matteo Acciai This is my paper
classification cond-mat.mes-hall
keywords thermodynamic uncertainty relationFano factorcoherent thermoelectric heat engineLandauer-Büttiker transportcharge-current noisequantum advantagebosonic transport
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

Thermodynamic uncertainty relations say that driving a current with low noise costs high dissipation. For coherent two-terminal thermoelectric heat engines the paper tightens that trade-off by restricting the process to heat-engine operation. For fermions the resulting bound forces the Fano factor of the charge current to stay above one-half; classical Markovian violations, often taken as a quantum advantage, are confined to a narrow window of entropy production and remain only a few percent. For bosons and classical carriers the floor rises to one and the classical relation is never broken. The bounds are shown to be tight by random sampling of boxcar transmissions that reach the predicted floors, and they convert into efficiency bounds that require finite fluctuations to run at nonzero efficiency. The result therefore tells experimentalists what electrical noise floor is unavoidable when a mesoscopic conductor is used as a heat engine.

Core claim

Selecting heat-engine operation for fermionic coherent thermoelectric transport produces a charge-current thermodynamic uncertainty relation whose right-hand side approaches 1/2 at large dissipation, so every such engine obeys F > 1/2. The same selection for bosonic or classical carriers yields a mode-independent bound that approaches 1, so F > 1 and the classical Markov TUR is never violated.

What carries the argument

The energy-resolved lower envelope ymin_EF(X) = (1 + cosh^{2}X)/sinh(2X) obtained for a perfect energy filter under the heat-engine constraint |u| ≥ |x|; convexity of this envelope supplies a tangent-line inequality that integrates against an arbitrary transmission to give the global Fano-factor bound.

Load-bearing premise

Everything rests on two-terminal coherent transport fully described by Landauer–Büttiker scattering with transmissions between zero and one; inelastic scattering, strong correlations, or extra terminals could open occupations outside the constrained sectors and drop the Fano factor below the claimed floors.

What would settle it

Fabricate a two-terminal coherent fermionic heat engine (or a numerical transmission) whose measured charge-current Fano factor falls below 1/2 while still producing positive power, or a bosonic engine whose Fano factor falls below 1.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • A coherent fermionic heat engine cannot reach finite efficiency with vanishing charge-current fluctuations; SP must stay at least δµP/2.
  • Classical-TUR violations available to a fermionic heat engine are limited to roughly 6.8 percent and only inside a narrow window of entropy production.
  • When TH ≤ 2 TC the fermionic floor jumps from 1/2 to 1 and quantum advantage disappears entirely.
  • Efficiency can be bounded from electrical measurements alone (Fano factor and voltage bias) without measuring heat currents.
  • Bosonic and classical ballistic engines share the same stricter bound F > 1 and never beat the classical Markov TUR.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If multiterminal or nonthermal reservoirs can evade the two-terminal (x,u) sector constraint, the F > 1/2 floor becomes a diagnostic of how close a device stays to ideal two-terminal coherence.
  • The same tangent-line technique may tighten other working-mode-specific figures of merit (cooling power precision, accelerator noise) once the corresponding sector geometry is mapped.
  • Because the bounds are saturated by simple boxcar filters, they give an immediate design target for engineered energy-selective transmissions in cold-atom or molecular thermoelectric platforms.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 4 minor

Summary. The manuscript derives heat-engine-specific thermodynamic uncertainty relations for coherent two-terminal thermoelectric transport in the Landauer–Büttiker framework. For fermions, heat-engine operation yields SI/|I| ≥ 1 + cosh^{2}(σ/(2kB|I|))/sinh(σ/(kB|I|)) (Eq. 3), implying the universal floor F > 1/2 and a refined efficiency bound (Eq. 2); a tighter temperature-resolved form (Eq. 4) holds for TH ≤ 2TC. For bosonic and classical carriers the mode-independent bound SI/|I| ≥ coth(σ/(2kB|I|)) (Eq. 5) enforces F > 1 and precludes classical-TUR violations. The bounds are obtained from energy-filter envelopes, convexity of the lower envelope ymin_EF, a tangent-line integration for arbitrary T(E), and Jensen’s inequality; multi-boxcar numerical sampling demonstrates that they are tight and saturatable.

Significance. The central results are load-bearing for the field: they show that classical-TUR violations (often taken as a quantum advantage) are far more restricted for heat engines than for generic processes, and they introduce hard, experimentally accessible Fano floors (F > 1/2 for fermions, F > 1 for bosons/classical). The End Matter and Supplemental Material supply complete analytic proofs under the stated assumptions, the bounds are parameter-free, and the numerical saturation evidence with random boxcar unions is reproducible. The efficiency reformulations enable thermodynamic inference from electrical quantities alone. These contributions are solid and of clear interest to mesoscopic thermodynamics and quantum transport.

minor comments (4)
  1. Fig. 3 caption and main-text discussion of the scatter plots would benefit from a brief statement of the sampled ranges for TH/TC, δμ and boxcar parameters, so that readers can judge coverage of the large-dissipation regime.
  2. End Matter, after Eq. (A8): the relation u(E) = u* + τ x(E) is central; a short sentence reminding the reader that u* is energy-independent would improve readability for non-specialists.
  3. The phrase “quantum advantage” (green shaded region in Fig. 2) is used for classical-TUR violation; a parenthetical clarification that this refers only to the charge-current Fano factor would avoid possible misreading.
  4. Supplemental Material S1.C (maximum-power comparison) is useful but could be cross-referenced more explicitly in the main text when the F > 1/2 floor is discussed.

Circularity Check

0 steps flagged

No significant circularity: heat-engine TURs follow from Landauer–Büttiker currents/noise plus convexity/Jensen under the stated two-terminal coherent assumptions.

full rationale

The central claims (fermionic HE bound SI/|I| ≥ 1 + cosh²(X)/sinh(2X) with X = σ/(2|I|), implying F > 1/2; bosonic/classical SI/|I| ≥ coth(X), implying F > 1) are obtained by direct calculation from the Landauer–Büttiker expressions for I, σ and SI (End Matter Eqs. A1–A8 and SM S1–S3). For a perfect energy filter the Fano factor reduces exactly to y(X, u(E0)); the heat-engine condition |u| ≥ |x| (or the stricter u = τx) then yields the lower envelope ymin_EF by elementary minimization. For arbitrary T(E) the same envelope is recovered by the tangent-line argument that exploits convexity of ymin_EF (or of yτ for τ ≥ 3) together with the sign constraint u* I > 0 that confines every energy-resolved point to the useful sector; the bosonic/classical case follows from the mode-independent identity g_cl_S/|g_I| = coth(|x|) plus Jensen. Brandner–Saito is recovered precisely when the heat-engine constraint is dropped, so it is an independent comparison rather than a load-bearing premise. No parameters are fitted to data, no uniqueness theorem is imported from the authors’ prior work, and the numerical saturation with boxcar unions is an a-posteriori check, not an input. The derivation is therefore self-contained under the paper’s explicit modeling assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

The paper is a first-principles derivation inside scattering theory. Load-bearing content is standard Landauer–Büttiker formulas, fermionic/bosonic/classical occupations, and elementary convexity arguments. No free parameters are fitted; no new physical entities are postulated. The only modeling choices that could fail outside the paper’s scope are the two-terminal coherent mean-field assumptions.

axioms (5)
  • domain assumption Charge and heat currents and zero-frequency noise are given by Landauer–Büttiker integrals over an arbitrary transmission 0 ≤ T(E) ≤ 1 (Eqs. A1, A4).
    Standard coherent-transport assumption; interactions only at mean-field level as stated in End Matter.
  • domain assumption Reservoir occupations are Fermi–Dirac (ζ=−1), Bose–Einstein (ζ=+1), or Maxwell–Boltzmann (ζ=0).
    Defines the three carrier classes for which the bounds are claimed.
  • domain assumption Heat-engine operation (P>0) implies u∗I>0, so energy-resolved points on the positive-current branch lie in the sector u(E)>τx(E)≥x(E).
    Key mode constraint used to replace the unconstrained Brandner–Saito envelope by ymin_EF; End Matter after Eq. A8.
  • standard math The function ymin_EF(z)=(1+cosh²z)/sinh(2z) is positive, convex, and decreasing for z>0, so its tangent line lower-bounds it.
    Used to integrate the pointwise bound into the global TUR (Eq. A11).
  • standard math For bosons, SI ≥ Scl_I and gcl_S/|gI|=coth(|x|); coth is convex and decreasing on (0,∞), so Jensen applies.
    Yields the mode-independent bosonic/classical bound (Eq. 5 / A13).

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Pith. "Pith review of Thermodynamic bound on the Fano factor of a coherent thermoelectric heat engine." pith.science (2026). https://pith.science/paper/6UUIDQPK

@misc{pith2026260711704,
  author       = {Pith},
  title        = {Pith review of: Thermodynamic bound on the Fano factor of a coherent thermoelectric heat engine},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6UUIDQPK}},
  note         = {Machine review of arXiv:2607.11704}
}
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abstract

We show that for fermionic coherent thermoelectric transport, selecting heat-engine operation yields a thermodynamic uncertainty relation for the charge current that imposes a universal lower limit of $F > 1/2$ on the corresponding Fano factor. We find that violations of the thermodynamic uncertainty relation for classical Markov processes, typically associated with a quantum advantage, are far more restricted for heat engines than what is allowed by a generic thermodynamic process. For bosonic and classical carriers, the minimum Fano factor increases to $F > 1$, and the thermodynamic uncertainty relation for classical Markov processes is never violated. We provide numerical evidence that all the obtained bounds are tight and can be saturated by properly designed transmissions.

Figures

Figures reproduced from arXiv: 2607.11704 by Matteo Acciai, Nahual Sobrino, Rosario Fazio.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of a coherent thermoelectric heat engine op [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Numerical verification of the TURs derived in this [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a), for different values of the ratio kBTC /|δµ|. In summary, Figs. 3(a) and 4(a) show in a complementary way how constrained the classical-TUR violation is for a fermionic coherent thermoelectric heat engine. Bosonic transport— In this case, we find the TUR SI |I| ≥ coth σ 2kB|I|  , (5) which is always more restrictive than the classical TUR, reducing to it only for σ ≪ 2kB|I|. Even though the focus of… view at source ↗

discussion (0)

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Works this paper leans on

73 extracted references · 6 canonical work pages · 3 internal anchors

  1. [1]

    classical expansion

    This ensures a large difference in occupation (thus increasing the current and reducing the Fano factor) and minimizes the thermal noise from the cold reservoir. So, for instance, saturation can be reached with a finite- width boxcar centered atE0 just aboveµC, withµC > µH and TH ≫TC. When TH ≤2TC the condition nH ≈1/2,nC ≈0is not allowed, and saturation ...

  2. [2]

    Ya. M. Blanter and M. Büttiker, Shot noise in mesoscopic conductors, Phys. Rep.336, 1 (2000)

    2000

  3. [3]

    Landauer, The noise is the signal, Nature392, 658 (1998)

    R. Landauer, The noise is the signal, Nature392, 658 (1998)

    1998

  4. [4]

    Strasberg,Quantum Stochastic Thermodynamics(Ox- ford University Press, Oxford, England, UK, 2024)

    P. Strasberg,Quantum Stochastic Thermodynamics(Ox- ford University Press, Oxford, England, UK, 2024)

    2024

  5. [5]

    Binder, L

    F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (Eds.),Thermodynamics in the Quan- tum Regime(Springer International Publishing, Cham, Switzerland, 2018)

    2018

  6. [6]

    Campbell, I

    S. Campbell, I. D’Amico, M. A. Ciampini, J. Anders, N. Ares, S. Artini, A. Auffèves, L. B. Oftelie, L. P. Bettmann, M. V. S. Bonança, T. Busch, M. Campisi, M. F. Cavalcante, L. A. Correa, E. Cuestas, C. B. Dag, S. Dago, S. Deffner, A. Del Campo, A. Deutschmann-Olek, S. Donadi, E. Doucet, C. Elouard, K. Ensslin, P. Erker, N. Fabbri, F. Fedele, G. Fiusa, T....

    2026

  7. [7]

    A. C. Barato and U. Seifert, Thermodynamic Uncertainty Relation for Biomolecular Processes, Phys. Rev. Lett.114, 158101 (2015)

    2015

  8. [8]

    T. R. Gingrich, J. M. Horowitz, N. Perunov, and J. L. England, Dissipation Bounds All Steady-State Current Fluctuations, Phys. Rev. Lett.116, 120601 (2016)

    2016

  9. [9]

    Polettini, A

    M. Polettini, A. Lazarescu, and M. Esposito, Tightening the uncertainty principle for stochastic currents, Phys. Rev. E94, 052104 (2016)

    2016

  10. [10]

    Brandner, T

    K. Brandner, T. Hanazato, and K. Saito, Thermodynamic Bounds on Precision in Ballistic Multiterminal Transport, Phys. Rev. Lett.120, 090601 (2018)

    2018

  11. [11]

    Proesmans and J

    K. Proesmans and J. M. Horowitz, Hysteretic thermo- dynamic uncertainty relation for systems with broken time-reversal symmetry, J. Stat. Mech.: Theory Exp. 2019(5), 054005

    2019

  12. [12]

    Dechant and S.-i

    A. Dechant and S.-i. Sasa, Fluctuation–response inequal- ity out of equilibrium, Proc. Natl. Acad. Sci. U.S.A.117, 6430 (2020)

    2020

  13. [13]

    Falasco, M

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

    2020

  14. [14]

    V. T. Vo, T. Van Vu, and Y. Hasegawa, Unified thermo- dynamic–kinetic uncertainty relation, J. Phys. A: Math. Theor.55, 405004 (2022)

    2022

  15. [15]

    Koyuk and U

    T. Koyuk and U. Seifert, Thermodynamic Uncertainty Relation in Interacting Many-Body Systems, Phys. Rev. Lett.129, 210603 (2022)

    2022

  16. [16]

    Dechant, Finite-Frequency Fluctuation-Response In- equality, Phys

    A. Dechant, Finite-Frequency Fluctuation-Response In- equality, Phys. Rev. Lett.136, 207101 (2026)

    2026

  17. [17]

    Macieszczak, K

    K. Macieszczak, K. Brandner, and J. P. Garrahan, Uni- fied Thermodynamic Uncertainty Relations in Linear Re- sponse, Phys. Rev. Lett.121, 130601 (2018)

    2018

  18. [18]

    B. K. Agarwalla and D. Segal, Assessing the validity of the thermodynamic uncertainty relation in quantum systems, Physical Review B98, 155438 (2018)

    2018

  19. [19]

    Saryal, H

    S. Saryal, H. M. Friedman, D. Segal, and B. K. Agarwalla, Thermodynamic uncertainty relation in thermal transport, Physical Review E100, 042101 (2019)

    2019

  20. [20]

    Guarnieri, G

    G. Guarnieri, G. T. Landi, S. R. Clark, and J. Goold, Thermodynamics of precision in quantum nonequilibrium steady states, Phys. Rev. Res.1, 033021 (2019)

    2019

  21. [21]

    A. M. Timpanaro, G. Guarnieri, J. Goold, and G. T. Landi, Thermodynamic Uncertainty Relations from Ex- change Fluctuation Theorems, Phys. Rev. Lett.123, 090604 (2019)

    2019

  22. [22]

    Falasco and M

    G. Falasco and M. Esposito, Dissipation-Time Uncertainty Relation, Phys. Rev. Lett.125, 120604 (2020)

    2020

  23. [23]

    Hasegawa, Thermodynamic Uncertainty Relation for General Open Quantum Systems, Phys

    Y. Hasegawa, Thermodynamic Uncertainty Relation for General Open Quantum Systems, Phys. Rev. Lett.126, 010602 (2021)

    2021

  24. [24]

    Potanina, C

    E. Potanina, C. Flindt, M. Moskalets, and K. Brand- ner, Thermodynamic bounds on coherent transport in periodically driven conductors, Phys. Rev. X11, 021013 (2021)

    2021

  25. [25]

    Van Vu and K

    T. Van Vu and K. Saito, Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Rela- tion, Minimum Dissipation, and Thermodynamic Speed Limits, Phys. Rev. X13, 011013 (2023)

    2023

  26. [26]

    D. S. P. Salazar, Quantum relative entropy uncertainty relation, Phys. Rev. E109, L012103 (2024)

    2024

  27. [27]

    A. S. Hegde, A. M. Timpanaro, and G. T. Landi, Tight- ening the thermodynamic uncertainty relations with null- entropy events: What we learn when nothing happens, Phys. Rev. E113, 034111 (2026)

    2026

  28. [28]

    Quantum Coherence Reshapes Thermodynamic Bounds for Thermal Machines

    S. Vidal, A. Mayor-Fernandez, and R. Lopez, Quan- tum coherence reshapes thermodynamic bounds for ther- mal machines, arXiv 10.48550/arXiv.2605.04648 (2026), 2605.04648

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2605.04648 2026

  29. [29]

    F. Mayo, N. Sobrino, R. Fazio, F. Taddei, and M. Gover- nale, Quantum thermodynamic uncertainty relation and macroscopic superconducting coherence, Phys. Rev. Res. 8, 013242 (2026)

    2026

  30. [30]

    Sobrino, F

    N. Sobrino, F. Taddei, R. Fazio, and M. Gover- nale, Current precision in interacting hybrid normal- superconducting systems, Phys. Rev. B113, 195407 (2026)

    2026

  31. [31]

    D. C. Ohnmacht, W. Belzig, and J. C. Cuevas, The role of charge in thermodynamic uncertainty relations, arXiv 10.48550/arXiv.2512.20558 (2025), 2512.20558

    doi:10.48550/arxiv.2512.20558 2025

  32. [32]

    A thermodynamic uncertainty relation for (hybrid) N--S coherent conductors

    S. Vidal and R. Lopez, A thermodynamic uncertainty relation for (hybrid) N–S coherent conductors, arXiv 10.48550/arXiv.2606.21555 (2026), 2606.21555

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2606.21555 2026

  33. [33]

    P. P. Potts and P. Samuelsson, Thermodynamic uncer- 6 tainty relations including measurement and feedback, Phys. Rev. E100, 052137 (2019)

    2019

  34. [34]

    Honma and T

    R. Honma and T. Van Vu, Thermodynamic Un- certainty Relation with Quantum Feedback, arXiv 10.48550/arXiv.2602.22651 (2026), 2602.22651

    doi:10.48550/arxiv.2602.22651 2026

  35. [35]

    Eriksson, M

    J. Eriksson, M. Acciai, L. Tesser, and J. Splettstoesser, General Bounds on Electronic Shot Noise in the Absence of Currents, Phys. Rev. Lett.127, 136801 (2021)

    2021

  36. [36]

    Acciai, L

    M. Acciai, L. Tesser, J. Eriksson, R. Sánchez, R. S. Whit- ney, and J. Splettstoesser, Constraints between entropy production and its fluctuations in nonthermal engines, Phys. Rev. B109, 075405 (2024)

    2024

  37. [37]

    Tesser and J

    L. Tesser and J. Splettstoesser, Out-of-Equilibrium Fluctuation-Dissipation Bounds, Phys. Rev. Lett.132, 186304 (2024)

    2024

  38. [38]

    Tesser, J

    L. Tesser, J. Balduque, and J. Splettstoesser, Fluctuation- dissipation bounds in time-dependently driven conductors, Phys. Rev. B113, 115401 (2026)

    2026

  39. [39]

    O. Pan, Z. Fan, S. Zhang, J. Li, J. Chen, and S. Su, Fluctuation-Dissipation Limits in Quantum Thermoelec- tric Transport, arXiv 10.48550/arXiv.2601.06984 (2026), 2601.06984

    work page doi:10.48550/arxiv.2601.06984 2026

  40. [40]

    Brandner and K

    K. Brandner and K. Saito, Thermodynamic uncertainty relations for coherent transport, Phys. Rev. Lett.135, 046302 (2025)

    2025

  41. [41]

    Brandner and K

    K. Brandner and K. Saito, Thermodynamic bound on current fluctuations in coherent conductors, J. Phys. A: Math. Theor.58, 435002 (2025)

    2025

  42. [42]

    Uncertainty relations for arbitrary currents in coherent transport

    L. Tesser and J. Splettstoesser, Uncertainty relations for arbitrary currents in coherent transport, arXiv 10.48550/arXiv.2607.06190 (2026), 2607.06190

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2607.06190 2026

  43. [43]

    Pietzonka and U

    P. Pietzonka and U. Seifert, Universal Trade-Off between Power, Efficiency, and Constancy in Steady-State Heat Engines, Phys. Rev. Lett.120, 190602 (2018)

    2018

  44. [44]

    Kamijima, S

    T. Kamijima, S. Otsubo, Y. Ashida, and T. Sagawa, Higher-order efficiency bound and its application to non- linear nanothermoelectrics, Phys. Rev. E104, 044115 (2021)

    2021

  45. [45]

    Kheradsoud, N

    S. Kheradsoud, N. Dashti, M. Misiorny, P. P. Potts, J. Splettstoesser, and P. Samuelsson, Power, Efficiency and Fluctuations in a Quantum Point Contact as Steady-State Thermoelectric Heat Engine, Entropy21, 10.3390/e21080777 (2019)

    doi:10.3390/e21080777 2019

  46. [46]

    Koyuk and U

    T. Koyuk and U. Seifert, Operationally accessible bounds on fluctuations and entropy production in periodically driven systems, Physical review letters122, 230601 (2019)

    2019

  47. [47]

    H. J. D. Miller, M. H. Mohammady, M. Perarnau-Llobet, and G. Guarnieri, Thermodynamic Uncertainty Relation in Slowly Driven Quantum Heat Engines, Phys. Rev. Lett. 126, 210603 (2021)

    2021

  48. [48]

    Eglinton and K

    J. Eglinton and K. Brandner, Geometric bounds on the power of adiabatic thermal machines, Phys. Rev. E105, L052102 (2022)

    2022

  49. [49]

    J. Lu, Z. Wang, J. Peng, C. Wang, J.-H. Jiang, and J. Ren, Geometric thermodynamic uncertainty relation in a periodically driven thermoelectric heat engine, Phys. Rev. B105, 115428 (2022)

    2022

  50. [50]

    Van Vu and K

    T. Van Vu and K. Saito, Geometric characterization for cyclic heat engines far from equilibrium, Phys. Rev. A 109, 042209 (2024)

    2024

  51. [51]

    See Supplemental Material for further details on the derivation and additional data

  52. [52]

    Ehrlich and G

    T. Ehrlich and G. Schaller, Broadband frequency filters with quantum dot chains, Phys. Rev. B104, 045424 (2021)

    2021

  53. [53]

    A. M. Timpanaro, G. Guarnieri, and G. T. Landi, Quan- tum thermoelectric transmission functions with minimal current fluctuations, Phys. Rev. B111, 014301 (2025)

    2025

  54. [54]

    Danielsson, H

    E. Danielsson, H. Kirchberg, and J. Splettstoesser, Opti- mizing energy conversion with nonthermal resources in steady-state quantum devices, arXiv 10.1103/dtvp-pwxk (2025), 2508.15578

    work page doi:10.1103/dtvp-pwxk 2025

  55. [55]

    Di Terlizzi and M

    I. Di Terlizzi and M. Baiesi, Kinetic uncertainty relation, J. Phys. A: Math. Theor.52, 02LT03 (2018)

    2018

  56. [56]

    Hiura and S.-i

    K. Hiura and S.-i. Sasa, Kinetic uncertainty relation on first-passage time for accumulated current, Phys. Rev. E 103, L050103 (2021)

    2021

  57. [57]

    Macieszczak, Ultimate Kinetic Uncertainty Relation and Optimal Performance of Stochastic Clocks, arXiv 10.48550/arXiv.2407.09839 (2024), 2407.09839

    K. Macieszczak, Ultimate Kinetic Uncertainty Relation and Optimal Performance of Stochastic Clocks, arXiv 10.48550/arXiv.2407.09839 (2024), 2407.09839

    Pith/arXiv arXiv doi:10.48550/arxiv.2407.09839 2024

  58. [58]

    Prech, P

    K. Prech, P. P. Potts, and G. T. Landi, Role of Quantum Coherence in Kinetic Uncertainty Relations, Phys. Rev. Lett.134, 020401 (2025)

    2025

  59. [59]

    Prech, G

    K. Prech, G. T. Landi, F. Meier, N. Nurgalieva, P. P. Potts, R. Silva, and M. T. Mitchison, Optimal Time Esti- mation and the Clock Uncertainty Relation for Stochastic Processes, Phys. Rev. X15, 031068 (2025)

    2025

  60. [60]

    Palmqvist, L

    D. Palmqvist, L. Tesser, and J. Splettstoesser, Combin- ing kinetic and thermodynamic uncertainty relations in quantum transport, Quantum Sci. Technol.10, 035059 (2025)

    2025

  61. [61]

    Palmqvist, L

    D. Palmqvist, L. Tesser, and J. Splettstoesser, Kinetic Uncertainty Relations for Quantum Transport, Phys. Rev. Lett.135, 166302 (2025)

    2025

  62. [62]

    Blasi, R

    G. Blasi, R. R. Rodríguez, M. Moskalets, R. López, and G. Haack, Quantum Kinetic Uncertainty Relations in Mesoscopic Conductors at Strong Coupling, arXiv 10.48550/arXiv.2505.13200 (2025), 2505.13200

    doi:10.48550/arxiv.2505.13200 2025

  63. [63]

    T. R. Gingrich, G. M. Rotskoff, and J. M. Horowitz, Inferring dissipation from current fluctuations, J. Phys. A: Math. Theor.50, 184004 (2017)

    2017

  64. [64]

    Seifert, From Stochastic Thermodynamics to Thermo- dynamic Inference, Annu

    U. Seifert, From Stochastic Thermodynamics to Thermo- dynamic Inference, Annu. Rev. Condens. Matter Phys. , 171 (2019)

    2019

  65. [65]

    A. C. Barato and U. Seifert, Universal bound on the fano factor in enzyme kinetics, The Journal of Physical Chemistry B119, 6555 (2015)

    2015

  66. [66]

    Brantut, C

    J.-P. Brantut, C. Grenier, J. Meineke, D. Stadler, S. Krin- ner, C. Kollath, T. Esslinger, and A. Georges, A Thermo- electric Heat Engine with Ultracold Atoms, Science342, 713 (2013)

    2013

  67. [67]

    H. M. Friedman, B. K. Agarwalla, O. Shein-Lumbroso, O. Tal, and D. Segal, Thermodynamic uncertainty relation in atomic-scale quantum conductors, Phys. Rev. B101, 195423 (2020)

    2020

  68. [68]

    Gehring, J

    P. Gehring, J. K. Sowa, C. Hsu, J. de Bruijckere, M. van der Star, J. J. Le Roy, L. Bogani, E. M. Gauger, and H. S. J. van der Zant, Complete mapping of the thermoelectric properties of a single molecule, Nat. Nan- otechnol.16, 426 (2021)

    2021

  69. [69]

    Rep.1087, 1 (2024)

    L.M.Cangemi, C.Bhadra,andA.Levy,Quantumengines and refrigerators, Phys. Rep.1087, 1 (2024)

    2024

  70. [70]

    Thermo- dynamic bound on the Fano factor of a coherent thermo- electric heat engine

    N. Sobrino, R. Fazio, and M. Acciai, Data for “Thermo- dynamic bound on the Fano factor of a coherent thermo- electric heat engine”, 10.5281/zenodo.21038772 (2026)

    work page doi:10.5281/zenodo.21038772 2026

  71. [71]

    Büttiker, A

    M. Büttiker, A. Prêtre, and H. Thomas, Dynamic con- ductance and the scattering matrix of small conductors, 7 Phys. Rev. Lett.70, 4114 (1993)

    1993

  72. [72]

    Christen and M

    T. Christen and M. Büttiker, Gauge-invariant nonlinear electric transport in mesoscopic conductors, Europhys. Lett.35, 523 (1996)

    1996

  73. [73]

    Federico II

    R. S. Whitney, Nonlinear thermoelectricity in point con- tacts at pinch off: A catastrophe aids cooling, Phys. Rev. B88, 064302 (2013). 8 End Matter Appendix: details on the derivation—We consider a hot reservoir(TH,µH)and a cold one(TC,µC),TH≥TC, connected via a coherent central region with arbitrary transmission0 ≤T(E)≤1. The conductor is modeled by sca...

    2013

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