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arxiv: 2404.09648 · v4 · submitted 2024-04-15 · 🪐 quant-ph

Thermodynamics of autonomous optical Bloch equations

Samyak Pratyush Prasad , Maria Maffei , Patrice A. Camati , Cyril Elouard , Alexia Auff\`eves This is my paper

Pith reviewed 2026-05-24 02:05 UTC · model grok-4.3

classification 🪐 quant-ph
keywords optical Bloch equationsquantum thermodynamicsautonomous systemssecond law of thermodynamicsself-drivework and heat flowsatom-field correlationsback-action
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0 comments X

The pith

Treating the atom, drive, and bath as one autonomous system identifies a self-drive term that tightens the second law.

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

The paper develops a thermodynamic framework for optical Bloch equations by modeling the atom, its drive, and the thermal bath as parts of a single joint autonomous system rather than separate classical components. This captures the atom's back-action on the field and correlations at short timescales, allowing definition of work-like flows from unitary parts and heat-like from non-unitary. The key addition is recognizing a self-drive in the atom's dynamics from its own influence on the field, with a corresponding self-work that refines the expression of the second law. This approach makes energy exchanges measurable directly in the field and relates the tightening to knowledge of the field state and potential recycling of the drive.

Core claim

By describing the atom, the drive and the bath as a joint autonomous system, the drive and the bath being parts of the same electromagnetic field, the framework captures atom-field correlations at fundamental timescales, as well as the atomic back-action on the field, allowing definition of work-like and heat-like flows. It identifies an additional unitary contribution in the atom's dynamics, the self-drive, and its energetic counterpart, the self-work, yielding a tighter expression of the second law related to extra knowledge about the field state and the potential of the interacted driving field to be recycled.

What carries the argument

The autonomous joint system of atom, drive, and bath, which treats the drive and bath as parts of the same electromagnetic field to capture back-actions and correlations.

If this is right

  • Work-like and heat-like flows become directly measurable in the field as changes of the mean field and fluctuations respectively.
  • The second law takes a tighter form than in standard analyses that treat drive and bath classically.
  • Minimal energy costs can be explored because atomic back-actions on drives and baths are now accounted for.
  • The interacted driving field carries potential for recycling due to the extra knowledge of its state after interaction.

Where Pith is reading between the lines

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

  • Similar self-drive terms may appear in other driven open quantum systems once treated autonomously.
  • The framework could be tested in circuit QED or trapped-ion experiments by tracking field statistics after interaction.
  • Recycling the post-interaction drive field might reduce net energy input in repeated quantum operations.

Load-bearing premise

The drive and the bath can be treated as parts of the same electromagnetic field so that the atom, drive, and bath form a single autonomous joint system whose correlations are captured at fundamental timescales.

What would settle it

An experiment that measures field back-action on the atom but finds no tightening of the second law beyond the classical-drive case would falsify the claim.

Figures

Figures reproduced from arXiv: 2404.09648 by Alexia Auff\`eves, Cyril Elouard, Maria Maffei, Patrice A. Camati, Samyak Pratyush Prasad.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematics of a) the open and b) autonomous model, where the atom dynamics obeys the optical Bloch [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. a) Joint atom-field system at the initial time [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Thermodynamic flows in the open and in the autonomous approach (in units of [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Time-integrated thermodynamic flows against the ratio Ω [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Steady state plots illustrating Eq. (47) with energetic quantities in units of [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
read the original abstract

Optical Bloch Equations (OBEs) are canonical equations describing the dynamics of a classically driven atom coupled to a thermal bath. Their thermodynamics is highly relevant to establish fundamental energetic bounds of key quantum processes. A consistent framework is available in the regime where the drives and baths can be treated classically, i.e. remains insensitive to the coupling with the atom. This regime, however, is not adapted to explore minimal energy costs, nor to measure atom-induced energy variations inside drives and baths -- a key ability to directly measure and optimize work and heat exchanges. This calls for a new framework accounting for atomic back-actions on drives and baths. Here we build such a framework by describing the atom, the drive and the bath as a joint autonomous system, the drive and the bath being parts of the same electromagnetic field. Our approach captures atom-field correlations at fundamental timescales, as well as the atomic back-action on the field, allowing us to define work-like (heat-like) flows as energy flows stemming from effective unitary dynamics induced by one system on the other (non-unitary correlating dynamics). Time-integrated work-like and heat-like flows are directly measurable in the field, as changes of the mean field and fluctuations, respectively. Our approach differs from standard analyses by identifying an additional unitary contribution in the atom's dynamics, the self-drive, and its energetic counterpart, the self-work, yielding a tighter expression of the second law. We relate this tightening to the extra knowledge about the field state, as well as the potential of the interacted driving field to be recycled. Our autonomous framework deepens the current understanding of thermodynamics in the quantum regime and its potential for energy management at quantum scales.

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 develops a thermodynamic framework for optical Bloch equations by modeling the atom, coherent drive, and thermal bath as components of a single autonomous joint system, with drive and bath as parts of the same quantized electromagnetic field. This captures atom-induced back-action and correlations at fundamental timescales, defines work-like (unitary-induced) and heat-like (non-unitary correlating) flows that are measurable in the field, and identifies an additional unitary 'self-drive' term in the atom dynamics together with its energetic counterpart 'self-work', which tightens the second law relative to standard analyses that treat the drive classically.

Significance. If the derivations are sound, the framework would be significant for quantum thermodynamics by enabling direct accounting of minimal energy costs, atom-induced field variations, and tighter bounds tied to extra knowledge of the field state and potential recycling of the driving field.

major comments (2)
  1. [Abstract (and any derivation of the reduced atom dynamics)] The central claim that the joint autonomous treatment produces a distinct unitary self-drive contribution (absent in the standard classical-drive approximation) while recovering the optical Bloch equations is load-bearing for the novelty and the tightening of the second law. The abstract provides no explicit derivation or equation showing how the joint-field model generates this term; the skeptic's concern therefore lands and requires a concrete section or appendix with the reduced dynamics.
  2. [Sections defining work/heat and the second-law expression] The definitions of work-like and heat-like flows as energy flows stemming from effective unitary vs. non-unitary dynamics induced by one subsystem on another must be shown to be consistent with the unitary/non-unitary split of the joint evolution; without this, it is unclear whether the self-work term tightens the second law independently or follows tautologically from the joint-system construction.
minor comments (2)
  1. [Measurement discussion] Clarify how the time-integrated work-like and heat-like flows are extracted from changes in mean field and fluctuations, including any explicit formulas or measurement protocols.
  2. [Discussion of the tightened bound] The relation between the tightening and 'extra knowledge about the field state' should be stated more precisely, ideally with a quantitative comparison to the standard second-law expression.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments highlight important points on clarity of the central derivations and consistency of the thermodynamic quantities. We address each below and have revised the manuscript to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract (and any derivation of the reduced atom dynamics)] The central claim that the joint autonomous treatment produces a distinct unitary self-drive contribution (absent in the standard classical-drive approximation) while recovering the optical Bloch equations is load-bearing for the novelty and the tightening of the second law. The abstract provides no explicit derivation or equation showing how the joint-field model generates this term; the skeptic's concern therefore lands and requires a concrete section or appendix with the reduced dynamics.

    Authors: The manuscript derives the reduced atom dynamics (including the self-drive term) from the joint autonomous Hamiltonian in Section II, recovering the standard OBEs while isolating the additional unitary contribution from atom-induced field correlations. To directly respond to the request for a concrete, self-contained presentation, we have added Appendix A that extracts this reduction step-by-step, explicitly contrasting the joint-field case with the classical-drive limit. revision: yes

  2. Referee: [Sections defining work/heat and the second-law expression] The definitions of work-like and heat-like flows as energy flows stemming from effective unitary vs. non-unitary dynamics induced by one subsystem on another must be shown to be consistent with the unitary/non-unitary split of the joint evolution; without this, it is unclear whether the self-work term tightens the second law independently or follows tautologically from the joint-system construction.

    Authors: Section III already defines the flows via the effective unitary and non-unitary generators on each subsystem. In the revision we have inserted a new paragraph that derives these flows directly from the decomposition of the joint Liouvillian into unitary and dissipator parts, confirming that self-work is the energetic counterpart of the unitary self-drive and that the tighter second-law bound arises from the extra field-state information retained in the joint description rather than from the construction itself. revision: yes

Circularity Check

0 steps flagged

No circularity: framework derives self-drive and tightened second law directly from explicit joint-field modeling assumption.

full rationale

The paper explicitly adopts the premise that drive and bath are components of one quantized EM field, forming an autonomous joint system with the atom. Within this model the reduced dynamics yields an additional unitary self-drive term whose energetic counterpart is self-work; the tighter second-law bound is then obtained by standard thermodynamic accounting on the joint unitary evolution. This chain is self-contained under the stated modeling choice and does not reduce any claimed result to a fit, a self-citation, or a redefinition of its own inputs. No load-bearing step matches the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

Abstract supplies the modeling choice that the drive and bath belong to one electromagnetic field but lists no numerical free parameters or external benchmarks.

axioms (1)
  • domain assumption Drive and bath are parts of the same electromagnetic field allowing a joint autonomous system description
    Explicitly invoked to capture atom-field correlations and back-action at fundamental timescales.
invented entities (2)
  • self-drive no independent evidence
    purpose: Additional unitary contribution to the atom's dynamics arising from back-action
    Introduced to account for the atom affecting the field; no independent evidence supplied.
  • self-work no independent evidence
    purpose: Energetic counterpart of the self-drive that tightens the second law
    Defined from the self-drive; no independent falsifiable prediction given.

pith-pipeline@v0.9.0 · 5844 in / 1296 out tokens · 21584 ms · 2026-05-24T02:05:26.074639+00:00 · methodology

discussion (0)

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Forward citations

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Reference graph

Works this paper leans on

93 extracted references · 93 canonical work pages · cited by 1 Pith paper

  1. [1]

    Fluctuations of work from quantum subensembles: The case against quantum work-fluctuation theorems,

    A. E. Allahverdyan and Th. M. Nieuwenhuizen, “Fluctuations of work from quantum subensembles: The case against quantum work-fluctuation theorems,” Phys. Rev. E 71, 066102 (2005)

    work page 2005

  2. [2]

    Fluctuation theorems: Work is not an observable,

    P. Talkner, E. Lutz, and P. H¨ anggi, “Fluctuation theorems: Work is not an observable,” Phys. Rev. E 75, 050102 (2007)

    work page 2007

  3. [3]

    Measuring the Characteristic Function of the Work Distribution,

    L. Mazzola, G. De Chiara, and M. Paternostro, “Measuring the Characteristic Function of the Work Distribution,” Phys. Rev. Lett. 110, 230602 (2013)

    work page 2013

  4. [4]

    Work extraction and thermodynamics for individual quantum systems,

    P. Skrzypczyk, A. J. Short, and S. Popescu, “Work extraction and thermodynamics for individual quantum systems,” Nat. Commun. 5, 1–8 (2014)

    work page 2014

  5. [5]

    No- Go Theorem for the Characterization of Work Fluctuations in Coherent Quantum Systems,

    M. Perarnau-Llobet, E. B¨ aumer, K. V. Hovhannisyan, M. Huber, and A. Acin, “No- Go Theorem for the Characterization of Work Fluctuations in Coherent Quantum Systems,” Phys. Rev. Lett. 118, 070601 (2017)

    work page 2017

  6. [6]

    Two- point measurement of entropy production from the outcomes of a single experiment with correlated photon pairs,

    G. H. Aguilar, T. L. Silva, T. E. Guimar˜ aes, R. S. Piera, L. C. C´ eleri, and G. T. Landi, “Two- point measurement of entropy production from the outcomes of a single experiment with correlated photon pairs,” Phys. Rev. A 106, L020201 (2022)

    work page 2022

  7. [7]

    Probabilistically violating the first law of thermodynamics in a quantum heat engine,

    T. Kerremans, P. Samuelsson, and P. Potts, “Probabilistically violating the first law of thermodynamics in a quantum heat engine,” SciPost Physics 12, 168 (2022)

    work page 2022

  8. [8]

    Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies,

    D. Collin, F. Ritort, C. Jarzynski, S. B. Smith, I. Tinoco, and C. Bustamante, “Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies,” Nature 437, 231–234 (2005)

    work page 2005

  9. [9]

    Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality,

    S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, “Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality,” Nat. Phys. 6, 988–992 (2010)

    work page 2010

  10. [10]

    Experimental verification of landauer’s principle linking information and thermodynamics,

    A. B´ erut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of landauer’s principle linking information and thermodynamics,” Nature 483, 187–189 (2012)

    work page 2012

  11. [11]

    Stochastic thermodynamics, fluctuation theorems and molecular machines,

    U. Seifert, “Stochastic thermodynamics, fluctuation theorems and molecular machines,” Rep. Prog. Phys. 75, 126001 (2012)

    work page 2012

  12. [12]

    Information and thermodynamics: experimental verification of Landauer’s Erasure principle,

    A. B´ erut, A. Petrosyan, and S. Ciliberto, “Information and thermodynamics: experimental verification of Landauer’s Erasure principle,” J. Stat. Mech.: Theory Exp. 2015, P06015 (2015)

    work page 2015

  13. [13]

    H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, England, UK, 2009)

    work page 2009

  14. [14]

    The role of quantum measurement in stochastic thermodynamics,

    C. Elouard, D. A. Herrera-Mart´ ı, M. Clusel, and A. Auff` eves, “The role of quantum measurement in stochastic thermodynamics,” npj Quantum Inf. 3, 9 20 (2017)

    work page 2017

  15. [15]

    Reversible work extraction in a hybrid opto- mechanical system,

    C. Elouard, M. Richard, and A. Auff` eves, “Reversible work extraction in a hybrid opto- mechanical system,” New J. Phys. 17, 055018 (2015)

    work page 2015

  16. [16]

    Calorimetric measurement of work for a driven harmonic oscillator,

    R. Sampaio, S. Suomela, and T. Ala-Nissila, “Calorimetric measurement of work for a driven harmonic oscillator,” Phys. Rev. E 94, 062122 (2016)

    work page 2016

  17. [17]

    An autonomous quantum machine to measure the thermodynamic arrow of time,

    J. Monsel, C. Elouard, and A. Auff` eves, “An autonomous quantum machine to measure the thermodynamic arrow of time,” Npj Quantum Inf. 4, 1–9 (2018)

    work page 2018

  18. [18]

    Concepts of work in autonomous quantum heat engines,

    W. Niedenzu, M. Huber, and E. Boukobza, “Concepts of work in autonomous quantum heat engines,” Quantum 3, 195 (2019), 1907.01353v2

    work page arXiv 2019

  19. [19]

    Extractable work in quantum electromechanics,

    O. Culhane, M. T. Mitchison, and J. Goold, “Extractable work in quantum electromechanics,” Phys. Rev. E 106, L032104 (2022)

    work page 2022

  20. [20]

    Observing a quantum Maxwell demon at work,

    N. Cottet, S. Jezouin, L. Bretheau, P. Campagne- Ibarcq, Q. Ficheux, J. Anders, A. Auff` eves, R. Azouit, P. Rouchon, and B. Huard, “Observing a quantum Maxwell demon at work,” Proc. Natl. Acad. Sci. U.S.A. 114, 7561–7564 (2017)

    work page 2017

  21. [21]

    Ultrasensitive Calorimetric Detection of Single Photons from Qubit Decay,

    J. P. Pekola and B. Karimi, “Ultrasensitive Calorimetric Detection of Single Photons from Qubit Decay,” Phys. Rev. X 12, 011026 (2022)

    work page 2022

  22. [22]

    Calorimetry of a phase slip in a Josephson junction,

    E. G¨ um¨ u¸ s, D. Majidi, D. Nikoli´ c, P. Raif, B. Karimi, J. T. Peltonen, E. Scheer, J. P. Pekola, H. Courtois, W. Belzig, and C. B. Winkelmann, “Calorimetry of a phase slip in a Josephson junction,” Nature Physics 19, 196–200 (2023)

    work page 2023

  23. [23]

    The theory of open quantum systems,

    H.-P. Breuer, F. Petruccione, et al., “The theory of open quantum systems,” (2002)

    work page 2002

  24. [24]

    Minimum energy requirements for quantum computation,

    J. Gea-Banacloche, “Minimum energy requirements for quantum computation,” Phys. Rev. Lett. 89, 217901 (2002)

    work page 2002

  25. [25]

    Energy-efficient quantum computing,

    J. Ikonen, J. Salmilehto, and M. M¨ ott¨ onen, “Energy-efficient quantum computing,” npj Quantum Inf. 3, 17 (2017)

    work page 2017

  26. [26]

    Local effective dynamics of quantum systems: A generalized approach to work and heat,

    H. Weimer, M. J. Henrich, F. Rempp, H. Schr¨ oder, and G. Mahler, “Local effective dynamics of quantum systems: A generalized approach to work and heat,” EPL 83, 30008 (2008)

    work page 2008

  27. [27]

    Work, heat and entropy production in bipartite quantum systems,

    H. Hossein-Nejad, E. J. O’Reilly, and A. Olaya- Castro, “Work, heat and entropy production in bipartite quantum systems,” New J. Phys. 17, 075014 (2015)

    work page 2015

  28. [28]

    Correlations in quantum thermodynamics: Heat, work, and entropy production,

    S. Alipour, F. Benatti, F. Bakhshinezhad, M. Afsary, S. Marcantoni, and A. T. Rezakhani, “Correlations in quantum thermodynamics: Heat, work, and entropy production,” Scientific Reports 6, 1–14 (2016)

    work page 2016

  29. [29]

    Probing nonclassical light fields with energetic witnesses in waveguide quantum electrodynamics,

    M. Maffei, P. A. Camati, and A. Auff` eves, “Probing nonclassical light fields with energetic witnesses in waveguide quantum electrodynamics,” Phys. Rev. Res. 3, L032073 (2021)

    work page 2021

  30. [30]

    Extending the laws of thermodynamics for arbitrary autonomous quantum systems,

    C. Elouard and C. L. Latune, “Extending the laws of thermodynamics for arbitrary autonomous quantum systems,” PRX Quantum 4, 020309 (2023)

    work page 2023

  31. [31]

    Experimental analysis of energy transfers between a quantum emitter and light fields,

    I. Maillette de Buy Wenniger, S. E. Thomas, M. Maffei, S. C. Wein, M. Pont, N. Belabas, S. Prasad, A. Harouri, A. Lemaˆ ıtre, I. Sagnes, N. Somaschi, A. Auff` eves, and P. Senellart, “Experimental analysis of energy transfers between a quantum emitter and light fields,” Phys. Rev. Lett. 131, 260401 (2023)

    work page 2023

  32. [32]

    Quantum information with rydberg atoms,

    M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010)

    work page 2010

  33. [33]

    Coherent control of macroscopic quantum states in a single-Cooper-pair box,

    Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai, “Coherent control of macroscopic quantum states in a single-Cooper-pair box,” Nature 398, 786–788 (1999)

    work page 1999

  34. [34]

    Superconducting Circuits and Quantum Information,

    J. Q. You and F. Nori, “Superconducting Circuits and Quantum Information,” Physics Today 58, 42– 47 (2005)

    work page 2005

  35. [35]

    Trapped-ion quantum computing: Progress and challenges,

    C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, “Trapped-ion quantum computing: Progress and challenges,” Appl. Phys. Rev. 6, 021314 (2019)

    work page 2019

  36. [36]

    Single-atom single-photon quantum interface,

    T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science 317, 488–490 (2007)

    work page 2007

  37. [37]

    The quantum internet,

    H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008)

    work page 2008

  38. [38]

    Quantum information processing and quantum optics with circuit quantum electrodynamics,

    A. Blais, S. M. Girvin, and W. D. Oliver, “Quantum information processing and quantum optics with circuit quantum electrodynamics,” Nat. Phys. 16, 247–256 (2020)

    work page 2020

  39. [39]

    Quantum technologies need a quantum energy initiative,

    A. Auff` eves, “Quantum technologies need a quantum energy initiative,” PRX Quantum 3, 020101 (2022)

    work page 2022

  40. [40]

    Atom-photon interactions,

    C. C. Tannoudji, G. Grynberg, and J. Dupont-Roe, “Atom-photon interactions,” (1992)

    work page 1992

  41. [41]

    On the relaxation of a two-level system driven by a strong electromagnetic field,

    E. Geva, R. Kosloff, and J. L. Skinner, “On the relaxation of a two-level system driven by a strong electromagnetic field,” J. Chem. Phys. 102, 8541– 8561 (1995)

    work page 1995

  42. [42]

    Markovian master equation and thermodynamics of a two-level system in a strong laser field,

    K. Szczygielski, D. Gelbwaser-Klimovsky, and R. Alicki, “Markovian master equation and thermodynamics of a two-level system in a strong laser field,” Phys. Rev. E 87, 012120 (2013)

    work page 2013

  43. [43]

    Stochastic thermodynamics of rapidly driven systems,

    G. B. Cuetara, A. Engel, and M. Esposito, “Stochastic thermodynamics of rapidly driven systems,” New J. Phys. 17, 055002 (2015)

    work page 2015

  44. [44]

    Thermodynamics of optical bloch equations,

    C. Elouard, D. Herrera-Mart´ ı, M. Esposito, and A. Auff` eves, “Thermodynamics of optical bloch equations,” New J. Phys. 22, 103039 (2020)

    work page 2020

  45. [45]

    Quantifying the quantum heat contribution from a driven superconducting circuit,

    C. Elouard, G. Thomas, O. Maillet, J. P. Pekola, and A. N. Jordan, “Quantifying the quantum heat contribution from a driven superconducting circuit,” Phys. Rev. E 102, 030102 (2020)

    work page 2020

  46. [46]

    Bosonic quantum error correction codes in superconducting quantum circuits,

    C. Weizhou, M. Yuwei, W. Weiting, Z. Chang- Ling, and S. Luyan, “Bosonic quantum error correction codes in superconducting quantum circuits,” Fundamental Research 1, 50–67 (2021)

    work page 2021

  47. [47]

    Microwave photonics with superconducting quantum circuits,

    X. Gu, A. F. Kockum, A. Miranowicz, Y.-x. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1 (2017). 21

    work page 2017

  48. [48]

    Input- output formalism for few-photon transport in one- dimensional nanophotonic waveguides coupled to a qubit,

    S. Fan, S. E. Kocaba¸ s, and J.-T. Shen, “Input- output formalism for few-photon transport in one- dimensional nanophotonic waveguides coupled to a qubit,” Phys. Rev. A 82, 063821 (2010)

    work page 2010

  49. [49]

    Photonic-fock-state scattering in a waveguide-qed system and their correlation functions,

    Y. Shen and J.-T. Shen, “Photonic-fock-state scattering in a waveguide-qed system and their correlation functions,” Phys. Rev. A 92, 033803 (2015)

    work page 2015

  50. [50]

    Waveguide quantum electrodynamics,

    F. Ciccarello, P. Lodahl, and D. Schneble, “Waveguide quantum electrodynamics,” Opt. Photon. News 35, 34–41 (2024)

    work page 2024

  51. [51]

    Quantum collision models: Open system dynamics from repeated interactions,

    F. Ciccarello, S. Lorenzo, V. Giovannetti, and G. M. Palma, “Quantum collision models: Open system dynamics from repeated interactions,” Phys. Rep. 954, 1–70 (2022)

    work page 2022

  52. [52]

    Thermodynamics of weakly coherent collisional models,

    F. L. S. Rodrigues, G. De Chiara, M. Paternostro, and G. T. Landi, “Thermodynamics of weakly coherent collisional models,” Phys. Rev. Lett. 123, 140601 (2019)

    work page 2019

  53. [53]

    From Repeated to Continuous Quantum Interactions,

    S. Attal and Y. Pautrat, “From Repeated to Continuous Quantum Interactions,” Ann. Henri Poincar´ e7, 59–104 (2006)

    work page 2006

  54. [54]

    Quantum and Information Thermodynamics: A Unifying Framework Based on Repeated Interactions,

    P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, “Quantum and Information Thermodynamics: A Unifying Framework Based on Repeated Interactions,” Phys. Rev. X 7, 021003 (2017)

    work page 2017

  55. [55]

    Collision models in open system dynamics: A versatile tool for deeper insights?

    S. Campbell and B. Vacchini, “Collision models in open system dynamics: A versatile tool for deeper insights?” Europhys. Lett. 133, 60001 (2021)

    work page 2021

  56. [56]

    Quantum Collision Models: A Beginner Guide,

    S. Cusumano, “Quantum Collision Models: A Beginner Guide,” Entropy 24, 1258 (2022)

    work page 2022

  57. [57]

    The energetic cost of work extraction,

    J. Monsel, M. Fellous-Asiani, B. Huard, and A. Auff` eves, “The energetic cost of work extraction,” Phys. Rev. Lett. 124, 130601 (2020)

    work page 2020

  58. [58]

    Topologically protected quantum dynamo effect in a driven spin-boson model,

    E. Bernhardt, C. Elouard, and K. Le Hur, “Topologically protected quantum dynamo effect in a driven spin-boson model,” Phys. Rev. A 107, 022219 (2023)

    work page 2023

  59. [59]

    A thermodynamic framework for coherently driven systems,

    M. Schrauwen, A. Daniel, M. Janovitch, and P. P. Potts, “A thermodynamic framework for coherently driven systems,” arXiv preprint arXiv:2505.08558 (2025), 10.48550/arXiv.2505.08558

    work page doi:10.48550/arxiv.2505.08558 2025

  60. [60]

    Directly probing work extraction from a single qubit engine fueled by quantum measurements,

    R. Dassonneville, C. Elouard, R. Cazali, R. Assouly, A. Bienfait, A. Auff` eves, and B. Huard, “Directly probing work extraction from a single qubit engine fueled by quantum measurements,” arXiv preprint arXiv:2501.17069 (2025), 10.48550/arXiv.2501.17069

    work page doi:10.48550/arxiv.2501.17069 2025

  61. [61]

    Energetics of a single qubit gate,

    J. Stevens, D. Szombati, M. Maffei, C. Elouard, R. Assouly, N. Cottet, R. Dassonneville, Q. Ficheux, S. Zeppetzauer, A. Bienfait, et al., “Energetics of a single qubit gate,” Phys. Rev. Lett. 129, 110601 (2022)

    work page 2022

  62. [62]

    The quantum open system as a model of the heat engine,

    Robert Alicki, “The quantum open system as a model of the heat engine,” J. Phys. A Math. Gen. 12, L103 (1979)

    work page 1979

  63. [63]

    Thermodynamics in the quantum regime: fundamental aspects and new directions,

    F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, “Thermodynamics in the quantum regime: fundamental aspects and new directions,” (2019)

    work page 2019

  64. [64]

    Entanglement boost for extractable work from ensembles of quantum batteries,

    R. Alicki and M. Fannes, “Entanglement boost for extractable work from ensembles of quantum batteries,” Phys. Rev. E 87, 042123 (2013)

    work page 2013

  65. [65]

    Entropy production as correlation between system and reservoir,

    M. Esposito, K. Lindenberg, and C. Van den Broeck, “Entropy production as correlation between system and reservoir,” New J. Phys. 12, 013013 (2010)

    work page 2010

  66. [66]

    Irreversible entropy production: From classical to quantum,

    G. T. Landi and M. Paternostro, “Irreversible entropy production: From classical to quantum,” Rev. Mod. Phys. 93, 035008 (2021)

    work page 2021

  67. [67]

    Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate,

    K. Kojima, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Efficiencies for the single-mode operation of a quantum optical nonlinear shift gate,” Phys. Rev. A 70, 013810 (2004)

    work page 2004

  68. [68]

    Detecting an itinerant optical photon twice without destroying it,

    E. Distante, S. Daiss, S. Langenfeld, L. Hartung, P. Thomas, O. Morin, G. Rempe, and S. Welte, “Detecting an itinerant optical photon twice without destroying it,” Phys. Rev. Lett.126, 253603 (2021)

    work page 2021

  69. [69]

    Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,

    C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985)

    work page 1985

  70. [70]

    Scattering into one-dimensional waveguides from a coherently-driven quantum- optical system,

    K. A. Fischer, R. Trivedi, V. Ramasesh, I. Siddiqi, and J. Vuˇ ckovi´ c, “Scattering into one-dimensional waveguides from a coherently-driven quantum- optical system,” Quantum 2, 69 (2018)

    work page 2018

  71. [71]

    Input-output theory with quantum pulses,

    A. H. Kiilerich and K. Mølmer, “Input-output theory with quantum pulses,” Phys.Rev.Lett. 123, 123604 (2019)

    work page 2019

  72. [72]

    On the exponential solution of differential equations for a linear operator,

    W. Magnus, “On the exponential solution of differential equations for a linear operator,” Commun. pure appl. math. 7, 649–673 (1954)

    work page 1954

  73. [73]

    A pedagogical approach to the magnus expansion,

    S. Blanes, F. Casas, J. A. Oteo, and J. Ros, “A pedagogical approach to the magnus expansion,” Eur. J. Phys. 31, 907 (2010)

    work page 2010

  74. [74]

    Collision models in quantum optics,

    F. Ciccarello, “Collision models in quantum optics,” Quantum Meas. Quantum Metrol. 4, 53–63 (2017)

    work page 2017

  75. [75]

    Collisional picture of quantum optics with giant emitters,

    D. Cilluffo, A. Carollo, S. Lorenzo, J. A. Gross, G. M. Palma, and F. Ciccarello, “Collisional picture of quantum optics with giant emitters,” Phys. Rev. Res. 2, 043070 (2020)

    work page 2020

  76. [76]

    Qubit models of weak continuous measurements: Markovian conditional and open- system dynamics,

    J. A. Gross, C. M. Caves, G. J. Milburn, and J. Combes, “Qubit models of weak continuous measurements: Markovian conditional and open- system dynamics,” Quantum Sci. Technol.3, 024005 (2018)

    work page 2018

  77. [77]

    Large collective power enhancement in dissipative charging of a quantum battery,

    S. Pokhrel and J. Gea-Banacloche, “Large collective power enhancement in dissipative charging of a quantum battery,” Phys. Rev. Lett. 134, 130401 (2025)

    work page 2025

  78. [78]

    Correlations in quantum thermodynamics: Heat, work, and entropy production,

    S. Alipour, F. Benatti, F. Bakhshinezhad, M. Afsary, S. Marcantoni, and A. T. Rezakhani, “Correlations in quantum thermodynamics: Heat, work, and entropy production,” Sci. Rep. 6, 35568 (2016)

    work page 2016

  79. [79]

    Vacuum fluctuations and radiation reaction : identification of their respective contributions,

    J. Dalibard, J. Dupont-Roc, and C. Cohen- Tannoudji, “Vacuum fluctuations and radiation reaction : identification of their respective contributions,” J. Phys. 43, 1617–1638 (1982). 22

    work page 1982

  80. [80]

    Quantum reservoir engineering with laser cooled trapped ions,

    J. F. Poyatos, J. I. Cirac, and P. Zoller, “Quantum reservoir engineering with laser cooled trapped ions,” Phys. Rev. Lett. 77, 4728–4731 (1996)

    work page 1996

Showing first 80 references.