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arxiv: 2604.28155 · v1 · submitted 2026-04-30 · ❄️ cond-mat.stat-mech · quant-ph

Optimal current-based sensing of phonon temperature using a finite reservoir

Sindre Brattegard , Stephanie Matern , Mark T. Mitchison , Saulo V. Moreira This is my paper

Pith reviewed 2026-05-07 06:58 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph
keywords quantum dotfinite reservoirphonon thermometryFisher informationcurrent sensingnanoscale transportheat exchangelong-time limit
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The pith

Monitoring quanta exchanged with a finite phonon reservoir achieves optimal precision for current-based temperature sensing.

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

The paper examines thermometry of a phonon bath with finite heat capacity using a quantum dot coupled to it and to an infinite electronic reservoir. It compares three long-time strategies: counting quanta exchanged between the dot and the finite reservoir, measuring the total current flowing into the infinite reservoir, and tracking the quantum dot's occupation. For large but finite reservoirs the Fisher information for all three strategies includes shared factors that reflect the reservoir's temperature response to heat exchange. The analysis establishes that the quanta-monitoring strategy reaches the highest precision. The work also shows how to maximize precision in each current-based approach by adjusting the gate voltage.

Core claim

In a quantum-dot setup coupled to a finite phonon reservoir, the Fisher information for temperature estimation in the long-time limit contains common factors from the reservoir's finite heat capacity for three distinct measurement strategies. Monitoring the quanta exchanged between the dot and the finite reservoir yields the highest Fisher information and therefore the optimal precision. Within each strategy, maximal precision is obtained by tuning the gate voltage that controls the dot's energy level.

What carries the argument

Fisher information for phonon temperature, evaluated from the statistics of quanta exchanged or current flowing in a quantum dot coupled to a finite heat-capacity reservoir whose temperature changes with exchanged energy.

If this is right

  • The finite reservoir's temperature response enters the Fisher information of every strategy through the same multiplicative factors.
  • Quanta monitoring outperforms both total-current measurement and occupation measurement in the long-time regime.
  • Gate-voltage tuning can be used to reach the highest possible precision allowed by each of the three strategies.

Where Pith is reading between the lines

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

  • The shared-factor structure may allow a general correction for back-action in any nanoscale thermometer that exchanges heat with a finite bath.
  • The result supplies a concrete benchmark for comparing counting versus averaging readouts in future quantum-dot thermometry experiments.
  • The same thermodynamic framework could be applied to other finite-reservoir sensing tasks, such as measuring chemical potential or magnetic field.

Load-bearing premise

The system must reach the long-time limit and the reservoir must be large enough for the common-factor form of the Fisher information to hold yet still finite enough that its temperature responds to heat exchange.

What would settle it

A calculation or experiment in which the Fisher information for quanta monitoring is not strictly larger than that for total-current or occupation measurements when the reservoir size is varied while holding all other parameters fixed.

Figures

Figures reproduced from arXiv: 2604.28155 by Mark T. Mitchison, Saulo V. Moreira, Sindre Brattegard, Stephanie Matern.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of the finite-size reservoir at stationary tem view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Sensitivity rate of the three thermometry schemes view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Optimised sensitivity rate over gate voltage as the view at source ↗
read the original abstract

In realistic nanoscale transport set-ups, electron-phonon coupling leads to the exchange of heat between phonon baths and electronic reservoirs with finite heat capacities. Such exchange affects the finite reservoir's temperature. However, this sensitivity of the finite reservoir temperature to the exchange of heat with the finite reservoir has remained unexplored for thermometry. Here, we fill this gap by combining current metrology techniques with a thermodynamic framework encompassing finite reservoirs. We focus on an experimentally realizable set-up with a quantum dot coupled to a finite reservoir and consider two distinct current-based strategies in the long time limit, namely monitoring quanta exchanged between the quantum dot and finite reservoir and the measurement of the total current flowing from the quantum dot into an infinite reservoir. A third strategy involves measurements of the quantum dot occupation. For a large but finite reservoir, we show that the Fisher information for all three strategies captures the finite reservoir's contribution to sensitivity through common factors. We also demonstrate that monitoring quanta exchanged between the system and finite reservoir in the long time limit achieves optimal precision. Finally, we provide an optimization analysis that explores how maximal precision can be achieved within each of the current-based strategies by tuning the gate voltage.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript examines current-based thermometry of a finite phonon reservoir coupled to a quantum dot. It analyzes three long-time-limit strategies—monitoring quanta exchanged with the finite reservoir, measuring total current into an infinite reservoir, and tracking quantum-dot occupation—showing that their Fisher informations share common multiplicative factors arising from the reservoir's finite heat capacity. The quanta-monitoring strategy is claimed to be optimal, and gate-voltage optimization is performed to maximize precision within each current-based approach.

Significance. If the derivations hold, the work supplies a concrete optimality result for phonon-temperature sensing in experimentally relevant nanoscale devices where reservoir heat capacity is finite. The common-factor structure in the Fisher information is a potentially useful organizing principle that separates reservoir-size effects from strategy-specific contributions. The gate-voltage optimization further provides actionable guidance for experiments.

major comments (2)
  1. [§3 (master equation and rate equations)] §3 (master equation and rate equations): the transition rates are written with a fixed reservoir temperature T, yet the finite-reservoir contribution to sensitivity is introduced precisely through the temperature drift induced by each detected quantum (dT/dt ∝ heat current / C_V(N)). The long-time Fisher information is then computed under the stationary distribution p(n|θ) with θ = T fixed. When the drift is restored, the likelihood becomes explicitly time-dependent, so the Cramér-Rao form no longer factors into the same common reservoir terms for all three strategies. The paper must either derive the non-stationary Fisher information or delineate the scaling regime (N large enough for drift to be negligible over the observation window yet small enough for finite-size sensitivity to appear) in which the common-factor claim survives.
  2. [§4 (Fisher-information comparison)] §4 (Fisher-information comparison): the statement that 'all three strategies capture the finite reservoir's contribution through common factors' is central to both the optimality proof and the practical utility of the result. Explicit expressions for I_quanta(θ), I_total(θ), and I_occupation(θ) must be displayed side-by-side so that the common multiplicative factors (presumably involving C_V or N) can be verified by inspection. Without these expressions it is impossible to confirm that the optimality of quanta monitoring is not an artifact of the fixed-T approximation.
minor comments (2)
  1. [Abstract] The abstract asserts optimality without quoting the explicit Fisher-information expressions; a single sentence indicating the common factor (e.g., 'proportional to C_V / T^2') would improve readability.
  2. [Notation] Notation for reservoir size, heat capacity, and the long-time observation window should be introduced once and used consistently; several symbols appear to be redefined between sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We address the major comments below and will incorporate revisions to clarify the approximations and provide explicit expressions as requested.

read point-by-point responses

  1. Referee: §3 (master equation and rate equations): the transition rates are written with a fixed reservoir temperature T, yet the finite-reservoir contribution to sensitivity is introduced precisely through the temperature drift induced by each detected quantum (dT/dt ∝ heat current / C_V(N)). The long-time Fisher information is then computed under the stationary distribution p(n|θ) with θ = T fixed. When the drift is restored, the likelihood becomes explicitly time-dependent, so the Cramér-Rao form no longer factors into the same common reservoir terms for all three strategies. The paper must either derive the non-stationary Fisher information or delineate the scaling regime (N large enough for drift to be negligible over the observation window yet small enough for finite-size sensitivity to appear) in which the common-factor claim survives.

    Authors: We agree that a fully time-dependent treatment would be more rigorous. However, the manuscript focuses on the long-time limit for a large but finite reservoir where the temperature drift is negligible over the observation time scale (i.e., the total energy exchanged is a small fraction of the reservoir's energy content). In this regime, the stationary distribution provides a valid approximation, and the common factors emerge from the sensitivity of the transition rates to temperature, modulated by the heat capacity. We will revise §3 to explicitly delineate this scaling regime: observation times t such that the number of detected quanta is large (for good statistics) but ΔE << C_V T, ensuring the fixed-T approximation holds while finite-size effects appear through C_V in the Fisher information. If the referee deems a full non-stationary derivation necessary, we can outline it in an appendix, but we believe the delineated regime suffices for the claims made. revision: partial

  2. Referee: §4 (Fisher-information comparison): the statement that 'all three strategies capture the finite reservoir's contribution through common factors' is central to both the optimality proof and the practical utility of the result. Explicit expressions for I_quanta(θ), I_total(θ), and I_occupation(θ) must be displayed side-by-side so that the common multiplicative factors (presumably involving C_V or N) can be verified by inspection. Without these expressions it is impossible to confirm that the optimality of quanta monitoring is not an artifact of the fixed-T approximation.

    Authors: We appreciate this suggestion for improving clarity. In the revised manuscript, we will include a new subsection or table in §4 presenting the explicit forms of the Fisher informations for the three strategies side-by-side. This will explicitly show the common multiplicative factors arising from the finite heat capacity C_V(N) = N k_B (for phonons or similar), multiplied by strategy-specific terms. The optimality of quanta monitoring will then be evident from the comparison of these expressions. We confirm that these factors are not artifacts but follow directly from the thermodynamic relation between heat exchange and temperature change in the finite reservoir. revision: yes

Circularity Check

0 steps flagged

No circularity: Fisher information and optimality derived from master equation without definitional reduction

full rationale

The paper constructs the likelihoods and Fisher information for the three strategies (quanta exchange, total current, dot occupation) directly from the long-time stationary solution of the master equation for the quantum-dot occupation probabilities under fixed reservoir temperature. The common multiplicative factors for finite-reservoir sensitivity appear as explicit algebraic consequences of the heat-capacity term in the rate equations; the optimality statement for quanta monitoring follows from direct comparison of the resulting I(θ) expressions. No parameter is fitted to a subset of data and then re-used as a prediction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled in. The long-time limit is an explicit modeling choice whose validity is discussed separately from the algebraic derivation; it does not render the optimality result true by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on standard quantum-transport assumptions for a quantum dot coupled to two reservoirs, one finite. No new particles or forces are introduced. The finite-reservoir temperature response is treated as a thermodynamic input rather than derived from microscopic dynamics.

axioms (2)
  • domain assumption The system reaches a long-time stationary regime in which Fisher information can be computed from the steady-state statistics.
    Invoked when the authors restrict the analysis to the long-time limit for all three strategies.
  • domain assumption Electron-phonon coupling allows heat exchange that alters the finite reservoir temperature while the reservoir remains large enough for a common sensitivity factor to appear.
    Central to the claim that Fisher information captures the finite-reservoir contribution through common factors.

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Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    Beechem, S

    T. Beechem, S. Graham, S. P. Kearney, L. M. Phin- ney, and J. R. Serrano, Invited article: Simultaneous mapping of temperature and stress in microdevices using micro-raman spectroscopy, Rev. Sci. Instrum.78, 061301 (2007)

    work page 2007

  2. [2]

    Beechem, L

    T. Beechem, L. Yates, and S. Graham, Invited review article: Error and uncertainty in raman thermal con- ductivity measurements, Rev. Sci. Instrum.86, 041101 (2015)

    work page 2015

  3. [3]

    Sandell, E

    S. Sandell, E. Chávez-Ángel, A. El Sachat, J. He, C. M. Sotomayor Torres, and J. Maire, Thermoreflectance tech- niques and raman thermometry for thermal property characterization of nanostructures, J. Appl. Phys.128, 131101 (2020)

    work page 2020

  4. [4]

    P. P. Hofer, J. B. Brask, M. Perarnau-Llobet, and N. Brunner, Quantum thermal machine as a thermome- ter, Phys. Rev. Lett.119, 090603 (2017)

    work page 2017

  5. [5]

    Maradan, L

    D. Maradan, L. Casparis, T.-M. Liu, D. E. F. Biesinger, C. P. Scheller, D. M. Zumbühl, J. D. Zimmerman, and A. C. Gossard, GaAs Quantum Dot Thermometry Us- ing Direct Transport and Charge Sensing, J. Low Temp. Phys.175, 784 (2014)

    work page 2014

  6. [6]

    J. Yang, C. Elouard, J. Splettstoesser, B. Sothmann, R. Sánchez, and A. N. Jordan, Thermal transistor and thermometer based on coulomb-coupled conductors, Phys. Rev. B100, 045418 (2019)

    work page 2019

  7. [7]

    Mihailescu, A

    G. Mihailescu, A. Kiely, and A. K. Mitchell, Quantum sensing with nanoelectronics: Fisher information for an applied perturbation (2025), arXiv:2406.18662 [quant- ph]

    work page arXiv 2025

  8. [8]

    Khandelwal, G

    S. Khandelwal, G. T. Landi, G. Haack, and M. T. Mitchi- son, Current-based metrology with two-terminal meso- scopic conductors, Phys. Rev. B112, L161409 (2025)

    work page 2025

  9. [9]

    Boeyens, B

    J. Boeyens, B. Annby-Andersson, P. Bakhshinezhad, G. Haack, M. Perarnau-Llobet, S. Nimmrichter, P. P. Potts, and M. Mehboudi, Probe thermometry with con- tinuous measurements, New J. Phys.25, 123009 (2023)

    work page 2023

  10. [10]

    J. P. Pekola and B. Karimi, Colloquium: Quantum heat transport in condensed matter systems, Rev. Mod. Phys. 93, 041001 (2021)

    work page 2021

  11. [11]

    Dutta, D

    B. Dutta, D. Majidi, N. W. Talarico, N. Lo Gullo, H. Courtois, and C. B. Winkelmann, Single-quantum-dot heat valve, Phys. Rev. Lett.125, 237701 (2020)

    work page 2020

  12. [12]

    Spiecker, P

    M. Spiecker, P. Paluch, N. Gosling, N. Drucker, S. Matityahu, D. Gusenkova, S. Günzler, 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, Two-level sys- tem hyperpolarization using a quantum szilard engine, Nat. Phys.19, 1320 (2023)

    work page 2023

  13. [13]

    Spiecker, A

    M. Spiecker, A. I. Pavlov, A. Shnirman, and I. M. Pop, Solomon equations for qubit and two-level systems: In- sights into non-poissonian quantum jumps, Phys. Rev. A 109, 052218 (2024)

    work page 2024

  14. [14]

    Champain, V

    V. Champain, V. Schmitt, B. Bertrand, H. Niebojewski, R. Maurand, X. Jehl, C. Winkelmann, S. De Franceschi, and B. Brun, Real-time millikelvin thermometry in a semiconductor-qubit architecture, Phys. Rev. Appl.21, 064039 (2024)

    work page 2024

  15. [15]

    Pothier, S

    H. Pothier, S. Guéron, N. O. Birge, D. Esteve, and M. H. Devoret, Energy distribution function of quasiparticles in mesoscopic wires, Phys. Rev. Lett.79, 3490 (1997)

    work page 1997

  16. [16]

    D. R. Schmidt, R. J. Schoelkopf, and A. N. Cle- land, Photon-mediated thermal relaxation of electrons in nanostructures, Phys. Rev. Lett.93, 045901 (2004)

    work page 2004

  17. [17]

    Gallego-Marcos, G

    F. Gallego-Marcos, G. Platero, C. Nietner, G. Schaller, and T. Brandes, Nonequilibrium relaxation transport of ultracold atoms, Phys. Rev. A90, 033614 (2014)

    work page 2014

  18. [18]

    Schaller, C

    G. Schaller, C. Nietner, and T. Brandes, Relaxation dynamics of meso-reservoirs, New J. Phys.16, 125011 (2014)

    work page 2014

  19. [19]

    Grenier, C

    C. Grenier, C. Kollath, and A. Georges, Thermoelectric transport and peltier cooling of cold atomic gases, C. R. Phys.17, 1161 (2016)

    work page 2016

  20. [20]

    Amato, H.-P

    G. Amato, H.-P. Breuer, S. Wimberger, A. Rodríguez, and A. Buchleitner, Noninteracting many-particle quan- tum transport between finite reservoirs, Phys. Rev. A 102, 022207 (2020)

    work page 2020

  21. [21]

    Matern, S

    S. Matern, S. V. Moreira, P. Samuelsson, and M. Leijnse, Thermoelectric cooling of a finite reservoir coupled to a quantum dot, Phys. Rev. B110, 205423 (2024)

    work page 2024

  22. [22]

    P.StrasbergandA.Winter,Firstandsecondlawofquan- tum thermodynamics: A consistent derivation based on a microscopic definition of entropy, PRX Quantum2, 030202 (2021)

    work page 2021

  23. [23]

    Riera-Campeny, A

    A. Riera-Campeny, A. Sanpera, and P. Strasberg, Quan- tum systems correlated with a finite bath: Nonequilib- rium dynamics and thermodynamics, PRX Quantum2, 010340 (2021)

    work page 2021

  24. [24]

    Riera-Campeny, A

    A. Riera-Campeny, A. Sanpera, and P. Strasberg, Open quantum systems coupled to finite baths: A hierarchy of master equations, Phys. Rev. E105, 054119 (2022)

    work page 2022

  25. [25]

    Elouard and C

    C. Elouard and C. Lombard Latune, Extending the laws of thermodynamics for arbitrary autonomous quantum systems, PRX Quantum4, 020309 (2023)

    work page 2023

  26. [26]

    S. V. Moreira, P. Samuelsson, and P. P. Potts, Stochastic thermodynamics ofa quantum dotcoupled toa finite-size reservoir, Phys. Rev. Lett.131, 220405 (2023)

    work page 2023

  27. [27]

    H.Yuan, Y.-H.Ma,andC.P.Sun,Optimizingthermody- namic cycles with two finite-sized reservoirs, Phys. Rev. E105, L022101 (2022)

    work page 2022

  28. [28]

    Strasberg, M

    P. Strasberg, M. G. Díaz, and A. Riera-Campeny, Clau- sius inequality for finite baths reveals universal efficiency improvements, Phys. Rev. E104, L022103 (2021)

    work page 2021

  29. [29]

    I. N. Mamede, S. V. Moreira, M. T. Mitchison, and C. E. Fiore, Steady-state heat engines driven by finite reser- 7 voirs, Phys. Rev. E113, 014115 (2026)

    work page 2026

  30. [30]

    Donvil and J

    B. Donvil and J. Ankerhold, Apparent heating due to imperfect calorimetric measurements, J. Phys. A: Math. Theor.55, 225303 (2022)

    work page 2022

  31. [32]

    Karimi, F

    B. Karimi, F. Brange, P. Samuelsson, and J. P. Pekola, Reaching the ultimate energy resolution of a quantum detector, Nature Communications11, 367 (2020)

    work page 2020

  32. [33]

    Ingold and Y

    G.-L. Ingold and Y. V. Nazarov, Charge tunneling rates in ultrasmall junctions, inSingle Charge Tunneling, edited by H. Grabert and M. H. Devoret (Springer, New York, 1992) Chap. 2, pp. 21–107

    work page 1992

  33. [34]

    V. N. Golovach, X. Jehl, M. Houzet, M. Pierre, B. Roche, M. Sanquer, and L. I. Glazman, Single-dopant resonance in a single-electron transistor, Phys. Rev. B83, 075401 (2011)

    work page 2011

  34. [35]

    Brange, P

    F. Brange, P. Samuelsson, B. Karimi, and J. P. Pekola, Nanoscale quantum calorimetry with electronic temper- ature fluctuations, Phys. Rev. B98, 205414 (2018)

    work page 2018

  35. [36]

    J. P. Pekola and B. Karimi, Quantum Noise of Elec- tron–Phonon Heat Current, J. Low Temp. Phys.191, 373 (2018)

    work page 2018

  36. [37]

    E. Chow, H. P. Wei, S. M. Girvin, and M. Shayegan, Phonon emission from a 2d electron gas: Evidence of transition to the hydrodynamic regime, Phys. Rev. Lett. 77, 1143 (1996)

    work page 1996

  37. [38]

    Giazotto, T

    F. Giazotto, T. T. Heikkilä, A. Luukanen, A. M. Savin, and J. P. Pekola, Opportunities for mesoscopics in ther- mometry and refrigeration: Physics and applications, Rev. Mod. Phys.78, 217 (2006)

    work page 2006

  38. [39]

    Wiesner, K

    M. Wiesner, K. Koski, A. Laitinen, J. Manninen, A. A. Zyuzin, and P. Hakonen, Electron–phonon coupling in copper intercalated bi2se3, Sci. Rep.12, 12097 (2022)

    work page 2022

  39. [40]

    Singh, M

    P. Singh, M. Seong, and S. Sinha, Detailed consider- ation of the electron-phonon thermal conductance at metal-dielectric interfaces, Appl. Phys. Lett.102, 181906 (2013)

    work page 2013

  40. [41]

    Cramér,Mathematical Methods of Statistics(Prince- ton University Press, Princeton, NJ, 1946)

    H. Cramér,Mathematical Methods of Statistics(Prince- ton University Press, Princeton, NJ, 1946)

    work page 1946

  41. [42]

    C. R. Rao,Linear Statistical Inference and Its Applica- tions(Wiley, New York, 1973)

    work page 1973

  42. [43]

    S. M. Kay,Fundamentals of Statistical Signal Process- ing. 1: Estimation Theory, 20th ed. (Prentice Hall PTR, Upper Saddle River, NJ, 2013)

    work page 2013

  43. [44]

    Radaelli, G

    M. Radaelli, G. T. Landi, K. Modi, and F. C. Binder, Fisher information of correlated stochastic processes, New J. Phys.25, 053037 (2023)

    work page 2023

  44. [45]

    J. A. Smiga, M. Radaelli, F. C. Binder, and G. T. Landi, Stochastic metrology and the empirical distribu- tion, Phys. Rev. Res.5, 033150 (2023)

    work page 2023

  45. [46]

    M. G. A. Paris, Quantum estimation for quantum tech- nology, Int. J. Quantum Inf.07, 125 (2009)

    work page 2009

  46. [47]

    Gammelmark and K

    S. Gammelmark and K. Mølmer, Fisher information and the quantum cramér-rao sensitivity limit of continuous measurements, Phys. Rev. Lett.112, 170401 (2014)

    work page 2014

  47. [48]

    Esposito, U

    M. Esposito, U. Harbola, and S. Mukamel, Nonequilib- rium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Rev. Mod. Phys.81, 1665 (2009)

    work page 2009

  48. [49]

    G. T. Landi, M. J. Kewming, M. T. Mitchison, and P. P. Potts, Current fluctuations in open quantum sys- tems: Bridging the gap between quantum continuous measurements and full counting statistics, PRX Quan- tum5, 020201 (2024)

    work page 2024

  49. [50]

    Vigneau, F

    F. Vigneau, F. Fedele, A. Chatterjee, D. Reilly, F. Kuem- meth, M. F. Gonzalez-Zalba, E. Laird, and N. Ares, Probingquantumdeviceswithradio-frequencyreflectom- etry, Applied Physics Reviews10, 021305 (2023)

    work page 2023

  50. [51]

    Wadhia, F

    V. Wadhia, F. Meier, F. Fedele, R. Silva, N. Nurgalieva, D. L. Craig, D. Jirovec, J. Saez-Mollejo, A. Ballabio, D. Chrastina, G. Isella, M. Huber, M. T. Mitchison, P. Erker, and N. Ares, Entropic Costs of Extracting Clas- sical Ticks from a Quantum Clock, Physical Review Let- ters135, 200407 (2025)

    work page 2025

  51. [52]

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

    work page 2000

  52. [53]

    Yamamoto and N

    K. Yamamoto and N. Hatano, Thermodynamics of the mesoscopic thermoelectric heat engine beyond the linear- response regime, Phys. Rev. E92, 042165 (2015)

    work page 2015

  53. [54]

    Gorini, A

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

    work page 1976

  54. [55]

    Lindblad, On the generators of quantum dynamical semigroups, Commun

    G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys.48, 119 (1976). 1 Supplemental information In this supplemental information, we provide derivations and motivations for different concepts introduced in the main text. In Section I, we derive linear response equations for the transport between the infinite and finite reserv...

    work page 1976