Pith. sign in

REVIEW 1 major objections 6 minor 1 cited by

Quantum thermodynamics of continuous feedback control

T0 review · 1 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read The paper derives exact thermodynamic first and second laws for open quantum systems under continuous measurement and feedback, introducing a new stochastic quantity, measurement entropy, that captures the irreversibility of a…

desk verdict Classical first law and fluctuation theorem are solid and carefully derived; the quantum extension rests on an unverified coarse-grained measurement entropy whose only numerical check is circular. read the letter →

arxiv 2505.16615 v1 pith:N2DXTWAR submitted 2025-05-22 quant-ph cond-mat.stat-mech

Kacper Prech , Joël Aschwanden , Patrick P. Potts This is my paper · ORCID
classification quant-phcond-mat.stat-mech
keywords continuousfeedbackcontrolquantumthermodynamicsfluctuationtheoremsmeasuremententropyFokker-PlanckMasterEquationbackactionSzilardengineMaxwell'sdemon
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 aims to put the thermodynamics of continuous measurement-and-feedback control on the same footing as ordinary open quantum systems, including the experimentally realistic case of a detector with finite bandwidth. It derives an exact first law that splits energy change into power, heat, and a measurement-energy term, and it derives fluctuation theorems containing a new stochastic quantity, measurement entropy, which quantifies irreversibility caused by the detector's delay. If the paper is right, second-law bounds for feedback-controlled engines must be corrected by this entropy, and measurement backaction can be a legitimate source of work.

What carries the argument

The central object is the Quantum Fokker-Planck Master Equation (QFPME), which describes the joint state of the system and a detector outcome $D$ evolving as a low-pass-filtered (Ornstein-Uhlenbeck) measurement with bandwidth $\gamma$ and measurement strength $\lambda$. The load-bearing new identity is the measurement entropy $\sigma_m$, defined as the log-ratio of forward and backward detector-trajectory probabilities, which equals $\frac{8\lambda}{\gamma}\int_0^\tau (a_t - D_t)\, dD_t - \gamma\tau - \ln\frac{P_{\rm ini}[D_\tau|a_\tau]}{P_{\rm ini}[D_0|a_0]}$ in the continuous-time limit. In the quantum extension, Keldysh quasi-probability trajectories carry the argument, with only the classical branch entering $\sigma_m$, so that integrating out the quantum branch yields a coarse-grained fluctuation theorem for the experimentally accessible detector trajectory.

What would settle it

In a two-level system under threshold (bang-bang) feedback, vary the detector bandwidth $\gamma$ and measurement strength $\lambda$, reconstruct the joint trajectory $(a_t,D_t)$ from the measurement record, compute $\sigma_m$ via Eq. (40), and test the integral fluctuation theorem $\langle e^{-\sigma-\sigma_m}\rangle = 1$ and the bound $\langle\sigma\rangle \ge -\langle\sigma_m\rangle$; the theorem should fail if the actual detector memory deviates from the Ornstein-Uhlenbeck low-pass filter.

Watch

Extended reading notes

Core claim

For any system described by the Quantum Fokker-Planck Master Equation, the rate of energy change separates exactly as $\partial_t U = P + J + \dot{E}_M$, with power, heat current, and measurement-energy rate given by explicit formulas involving the detector outcome $D$, the measurement strength $\lambda$, and the detector bandwidth $\gamma$. The paper further derives a detailed fluctuation theorem $P[\bar{a}, \bar{D}]/P[a,D] = e^{-\sigma - \sigma_m}$ whose new term, the measurement entropy $\sigma_m$, is an Itô integral along the detector trajectory and measures the asymmetry between measurement outcomes that lag behind the system and those that anticipate it. The same structure is extended to open quantum systems using Keldysh quasi-probabilities, yielding a coarse-grained fluctuation theorem that depends only on the detector trajectory and a generalized second law $\langle\sigma\rangle \ge -\langle\sigma_m\rangle$.

Load-bearing premise

The backward experiment is taken to be the exact time reversal of the forward one, with feedback depending only on the current detector outcome; combined with the QFPME's Gaussian, low-pass-filtered noise model, this assumption is what lets detector lag be reinterpreted as a new entropy rather than as an uncontrolled error.

Editorial extensions

If this is right

  • For QFPME dynamics the first law holds exactly with three terms, so energy-balance analyses of continuously measured engines must include the measurement-energy rate $\lambda\langle\mathcal{D}[\hat{A}]\hat{U}\rangle$.
  • Fluctuation theorems for feedback with finite-bandwidth detection must include $\sigma_m$; the standard fluctuation theorem without it is violated, as the paper's Monte Carlo simulations show.
  • The average entropy production can be negative under feedback, but it is bounded below by $-\langle\sigma_m\rangle$, giving a generalized second law of thermodynamics.
  • Measurement backaction can act as a fuel: the continuous-measurement-driven engine converts $\dot{E}_M$ into work and can even absorb heat from the environment for some parameters.
  • Coarse-graining yields a fluctuation theorem involving only the detector trajectory, so the second-law bound is testable without knowing the hidden system trajectory.

Reading between the lines

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

  • A testable prediction not spelled out by the paper: the rate of measurement entropy equals $8\lambda$ times the excess mean squared detector error relative to the static-detector variance, so directly measuring $\langle(D_t-a_t)^2\rangle$ should expose the second-law correction without trajectory reconstruction.
  • The framework suggests that continuous feedback with a finite-bandwidth detector carries an information cost encoded in $\sigma_m$; optimizing work extraction may amount to trading output power against this entropy cost.
  • If the detector filter is not a first-order low-pass (for example, a high-pass or non-Markovian filter), the measurement-entropy expression would need replacement and the fluctuation theorem would likely change; the paper explicitly leaves such extensions open.
  • For quantum systems, $\sigma_m$ depends only on the classical Keldysh branch, hinting that the measurement-entropy correction is essentially classical even when work extraction exploits coherence; a coherent-work experiment could isolate that part.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 6 minor

Summary. The paper develops a thermodynamics framework for open quantum systems under continuous measurement and feedback described by the Quantum Fokker-Planck Master Equation (QFPME). It derives a first-law decomposition of the average energy change into power, heat current, and a measurement-induced energy rate, Eqs. (9)-(12), and illustrates it on a bang-bang two-level system and a continuous-measurement-driven engine. It then derives a classical fluctuation theorem, Eq. (38), in which a new stochastic term called measurement entropy, Eq. (40), accounts for the detector's finite bandwidth and delay, together with the resulting second law, Eq. (42). The framework is extended to quantum systems using Keldysh quasi-probabilities, leading to the coarse-grained fluctuation theorem Eq. (52) and the quantum second law Eq. (53).

Significance. If correct, the paper provides a consistent thermodynamic description for continuous feedback with a finite-bandwidth detector, and it identifies a delay-induced measurement entropy that is distinct from the information terms previously studied in feedback fluctuation theorems. The main strengths are the detailed derivations in Apps. A, D, and F, the consistency check of the fast-detector limit against Eq. (47) from Ref. [50], and the two worked examples with Monte-Carlo simulations. The quantum extension, however, rests on signed quasi-probabilities, and the paper does not explicitly prove the positivity that the quantum second law requires; the numerical demonstration in Fig. 6 also computes the coarse-grained measurement entropy by inverting the fluctuation theorem rather than by evaluating its defining integral. These issues are local and repairable, but they affect the quantum-regime claim.

major comments (1)
  1. [§IV.C-D and Fig. 6] Eq. (51) defines e^{-sigma_m,cg[D]} as an integral of e^{-sigma_m[a_c,D]} over the conditional quasi-probability P[a_c|Gamma,D]=P[Gamma,a_c,D]/P[Gamma,D]. Since P[Gamma,a_c,D] is a signed measure that can take negative values, this integral is not manifestly positive, and the second law in Eq. (53) requires sigma_m,cg to be real. Positivity does follow if one integrates Eq. (49) over a_c, because then e^{-sigma_m,cg[D]} equals P[barGamma,barD]e^{sigma[Gamma,D]}/P[Gamma,D], which is positive, but this argument is not given. Moreover, the numerical evidence in Fig. 6 obtains sigma_m,cg by inverting Eq. (52), not by evaluating the integral in Eq. (51), so it cannot detect a failure of the defining integral to match the fluctuation theorem. Please add an explicit proof that the integral in Eq. (51) is positive and that P[Gamma,D] is a well-defined nonnegative probability, or provide an independent numerical evaluation of Eq. (51).
minor comments (6)
  1. [§III.E] The text near Eq. (21) writes 'Heavyside step function'; this should be 'Heaviside step function'.
  2. [§IV.A.1] In the paragraph after Eq. (38), 'time-revered versions' should read 'time-reversed versions'.
  3. [§III.C] In the discussion following Eq. (14), 'the terms on the right-hand site' should read 'the terms on the right-hand side'.
  4. [App. D.1] The sentence 'Here, each D_n≥1 is contingent upon ...' is confusing; presumably the intended statement is about indices n≥1, not about the values of D_n.
  5. [Fig. 6 caption] The parameter line 'gamma=10kappa=5g=5lambda=omega' is ambiguous; please list the five parameters separately, and report statistical uncertainties for the Monte-Carlo histograms.
  6. [App. E] In App. E.1, 'classical countertpart' should read 'classical counterpart'.

Circularity Check

1 steps flagged · score 2.0 of 10

Analytic derivations are self-contained given the QFPME; only the numerical illustration of the quantum coarse-grained FT is circular because σ_m,cg is computed by inverting the same FT it is used to illustrate.

  1. other [Sec. IV E (continuous-measurement-driven engine), Fig. 6 and surrounding text after Eq. (52)]
    "For each numerically sampled trajectory (Γ,D), we compute the corresponding probabilities P[Γ,D] and P[Γ̄,D̄], which we use to obtain the associated σ_m,cg[D] using the detailed FT in Eq. (52). ... The corresponding −⟨σ_m,cg⟩ (vertical black dotted line) lies on the left from ⟨σ⟩ (vertical black dashed line), which illustrates the second law in Eq. (53)."

    Eq. (51) defines e^{−σ_m,cg} as a conditional quasi-probability integral over a_c, and Eq. (52) is derived from Eqs. (49) and (51). In Fig. 6 the authors do not evaluate the defining integral; instead they compute P[Γ,D] and P[Γ̄,D̄] and read σ_m,cg off the detailed FT, Eq. (52). The plotted inequality ⟨σ⟩ ≥ −⟨σ_m,cg⟩ then follows from Eq. (52) by Jensen's inequality for any real σ_m,cg, so the 'illustration' of the second law is guaranteed by the same relation used to generate σ_m,cg. This is a self-consistency check, not independent numerical evidence for Eq. (52) or for positivity of the Eq. (51) integral. The analytic derivation of Eq. (52) is independent and remains the substantive basis for the result.

full rationale

The paper's central results are derived, not fitted. The first law (Eqs. 9-12) follows by direct stochastic calculus from the QFPME and the Belavkin equation. The classical fluctuation theorem (Eq. 38) is obtained by writing the path probabilities P[a,D] and P_B[ā,D̄] as in Eqs. (D1)-(D14), defining the measurement entropy as the log ratio of detector path probabilities, and reducing the system part to the standard Crooks/Seifert entropy production; no fitted parameter is renamed as a prediction. The quantum fluctuation theorem (Eq. 49) is derived from the Keldysh quasi-probability construction in App. F, and the coarse-grained Eq. (52) follows by marginalizing over the classical Keldysh path. The QFPME itself is imported from Ref. [50], including by co-authors, but it is a published model serving as the input assumption rather than a self-citation used to forbid alternatives; the paper's claims are conditional on that model. The only genuinely circular element is numerical: Fig. 6 computes σ_m,cg by inverting Eq. (52), then uses the resulting inequality to illustrate the second law of Eq. (53). That is a consistency check rather than a test, and it cannot detect a failure of the defining integral in Eq. (51) to be positive. Since this circularity affects only the numerical illustration and not the analytic derivation, the overall circularity score is low.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the QFPME model of detection and on standard assumptions of weak, Markovian system-bath coupling. There are no fitted parameters, and no new physical entities are introduced; the measurement entropy is a derived stochastic functional, not an independent postulate.

assumptions (6)
  • domain assumption The QFPME, Eq. (1), correctly describes the joint state of a continuously measured and feedback-controlled open quantum system with finite detector bandwidth.
    Used as the starting master equation for the entire paper; the results inherit its validity. It was proposed in Ref. [50], whose authors overlap with the present paper.
  • domain assumption Weak coupling and a Markovian reservoir allow the feedback Liouvillian to take Lindblad form, L(D)ρ = -i[H(D),ρ] + L_B ρ, Eq. (2).
    Needed for the heat current in Eq. (6) and for the thermodynamic frameworks in Sec. III A.
  • domain assumption The measured signal is a continuously monitored Gaussian process passed through a first-order low-pass filter, giving the Ornstein-Uhlenbeck detector dynamics in Eq. (14).
    Underlies the path probability Pm[D|a] in Eq. (D4) and hence the measurement entropy expression in Eq. (40).
  • domain assumption The feedback protocol depends only on the current detector outcome, so the time-reversed protocol obeys Λ(bar D) = bar Λ(D), Eq. (D19).
    This is the load-bearing reversibility assumption that makes the backward experiment the time reverse of the forward one and enables the fluctuation theorem in Eq. (38).
  • standard math Itô stochastic calculus and standard path-ensemble identities, including Jensen's inequality and the log-ratio form of detailed fluctuation theorems, are used.
    Used in Apps. A and D; these are standard unproved background results.
  • standard math The Keldysh quasi-probability formalism can assign signed but normalized trajectory distributions for quantum systems under continuous measurement.
    Used in Sec. IV C and App. F to extend the FT to quantum dynamics; negative values are acknowledged in the text.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum thermodynamics of continuous feedback control." pith.science (2026). https://pith.science/paper/N2DXTWAR

@misc{pith2026250516615,
  author       = {Pith},
  title        = {Pith review of: Quantum thermodynamics of continuous feedback control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N2DXTWAR}},
  note         = {Machine review of arXiv:2505.16615}
}
read the original abstract

The laws of thermodynamics are a cornerstone for describing nanoscale and open quantum systems. However, formulating these laws for systems under continuous feedback control and under experimentally relevant conditions is challenging. In this work, we lay out a formalism for the laws of thermodynamics in an open quantum system under continuous measurement and feedback described by a Quantum Fokker Planck Master Equation. We derive expressions for work, heat, and measurement-induced energy changes, and we investigate entropy production and fluctuation theorems. We illustrate our results with a continuous version of a measurement-driven Szilard engine, as well as a work extraction scheme in a two-level system under bang-bang control. Our results provide insights into the energetics as well as the irreversibility of classical and quantum systems under continuous feedback control.

Figures

Figures reproduced from arXiv: 2505.16615 by the authors.

Figure 1
Figure 1. FIG. 1. The general setting of the QFPME. A quantum system inter [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Extracted power for the two-level system under bang [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The first law of thermodynamics for the continuous [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Integral FT for the two-level system under bang-bang con [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The second law of thermodynamics for the two-level system [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The FT and the second law for the continuous-measurement [PITH_FULL_IMAGE:figures/full_fig_p010_6.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. Deterministic Equations for Feedback Control of Open Quantum Systems II: Properties of the memory function

    quant-ph 2025-12 conditional novelty 5.0 of 10

    For feedback-driven monitored quantum systems, the memory function's statistics follow from a deterministic hybrid classical-quantum state; demonstrated on qubit cooling and Rabi stabilization.

Reference graph

Works this paper leans on

163 extracted references · 70 canonical work pages · cited by 1 Pith paper

  1. [50]

    Jarzynski, Nonequilibrium equality for free energy differ- ences, Phys

    C. Jarzynski, Nonequilibrium equality for free energy differ- ences, Phys. Rev. Lett.78, 2690 (1997)

    1997

  2. [1]

    (38) and the second law in Eq

    Fluctuation theorems Having presented the FTs in Eq. (38) and the second law in Eq. (42) for classical systems, we now show their counterparts for quantum dynamics. For open quantum systems described the Lindblad master equation ∂t ˆρt =−i[ ˆHt,ˆρt]+ X k D[ ˆLk]ˆρt,(48) where ˆLk are Lindblad jump operators, a trajectory of the system is typically defined...

  3. [2]

    E 1 for a deriva- tion

    Fast-detector limit When the detector is much faster than the dynamics of the system (γ≫κ), the steady-state rate of change of the average measurement entropy⟨σm⟩ can be obtained analytically: ∂t⟨σm⟩ = 8λκ γ 1+2n B−Erf(2 p λ/γ)− e−4λ/γ 2 p πλ/γ ,(46) where Erf(•) is the error function; see App. E 1 for a deriva- tion. In order to demonstrate...

  4. [3]

    (16) usingdD c in Eq

    Derivation ofd ˆUin Eq.(16) We first show how to obtaind ˆUin Eq. (16) usingdD c in Eq. (14) and It ˆo’s lemma in stochastic calculus. The differential of the Hamiltonian ˆU= ˆUt(D) is given by d ˆU=∂ t ˆUdt+∂ D ˆUdD+ 1 2∂2 t ˆU(dt) 2 + 1 2∂2 D ˆU(dD) 2 +... ,(A1) where ˆU= ˆUt(D),∂ D ˆU=∂ D ˆUt(D), and∂ 2 D ˆU=∂ 2 D ˆUt(D) ought to be viewed as operators...

  5. [4]

    ∂t ˆU+γ ⟨ ˆA⟩c−D ∂D ˆU+ γ2 8λ∂2 D ˆU # L(Dc)ˆρc +λD[A]ˆρc dt2 + γ 2 √ λ ∂D ˆU ! L(Dc)ˆρc +λD[A]ˆρc dtdW +

    Calculation ofE[Tr{d ˆUˆρc}],E[Tr{ ˆUdˆρc}], andE[Tr{d ˆUdˆρc}] Next, we derive the expectation valuesE[Tr{d ˆUˆρc}],E[Tr{ ˆUdˆρc}], andE[Tr{d ˆUdˆρc}], which appear in Eq. (15). To find E[Tr{ ˆUdˆρc}], we substitute the Belavkin equation (13) fordˆρc: E[Tr{ ˆUdˆρc}]=E[Tr{ ˆUL(D c)ˆρcdt+ ˆUλD[ ˆA]ˆρcdt+ ˆU √ λ{ ˆA−⟨ ˆA⟩c,ˆρc}dW}] =E[Tr{−i ˆU[ ˆH,ˆρc]+ ˆUL...

  6. [5]

    Power and heat We first show the expression for power in Eq. (25). The first derivative of the Hamiltonian (21) with respect toDis given by ∂D ˆH=∂ D (θ(D)ω|0⟩⟨0|+(1−θ(D))ω|1⟩⟨1| ) =ωδ(D) (|0⟩⟨0|−|1⟩⟨1| ) (B1) where we have used∂ Dθ(D)=δ(D). Here,δ(D) is the Dirac-delta distribution, and recall thatθ(D) is the Heavyside step function. For the drift term i...

  7. [6]

    It is convenient to defineq +(D)=p 0(D)+p −(D) andq−(D)=p 0(D)−p −(D), which allows us to rewrite Eq

    Steady-state solution From the QFPME (1) with the LiouvillianL(D) (22), we obtain a pair of coupled differential equations,  ∂t p0(D)=Jp 0(D)+γ∂ D p0(D)+θ(D) (κnB p1(D)−κ(1+n B)p0(D)) +(1−θ(D)) (κ(1+n B)p1(D)−κn B p0(D)), ∂t p1(D)=Jp 1(D)−γ∂ D p1(D)+θ(D) (κ(1+n B)p0(D)−κn B p1(D)) +(1−θ(D)) (κnB p0(D)−κ(1+n B)p1(D)), (B5) where we have introduced t...

  8. [7]

    Here, ˆV=e itω 2 ˆσz

    Rotating frame Let us denote the density matrix in the laboratory frame and in the rotating frame as ˆϱt(D) and ˆρt(D)= ˆVˆϱt(D) ˆV†, respectively. Here, ˆV=e itω 2 ˆσz. The laboratory-frame density matrix ˆϱ t(D) follows the QFPME (1) with the laboratory-frame Hamiltonian ˆHlab (28), and the observable ˆAlab = ˆV† ˆσx ˆVis continuously measured. In the r...

Show all 163 references
  1. [8]

    (9) are in the laboratory frame, which means they are evaluated with respect to ˆϱt(D)

    Power, heat, and measurement energy All expressions that appear in the first law of thermodynamics in Eq. (9) are in the laboratory frame, which means they are evaluated with respect to ˆϱt(D). However, we would like to compute them in the rotating frame, with respect to ˆρt(D...

  2. [9]

    Steady-state solution The joint state of the quantum system and the measurement outcome ˆρt(D) can be expressed as ˆρt(D)= 1 2 Pt(D) ˆI+a x,t(D) ˆσx +a y,t(D) ˆσy +a z,t(D) ˆσz ,(C12) where ˆIis the identity matrix and (a x,a y,a z) is the Bloch vector for a givenDat the timet...

  3. [10]

    18 Appendix D: Fluctuation theorems for classical systems

    This means thatP+J+ ˙EM =0, which is consistent with the steady-state solution. 18 Appendix D: Fluctuation theorems for classical systems

  4. [11]

    [98, 99]

    General setting When introducing the general setting of the QFPME-based feedback control, we largely follow the notation of Refs. [98, 99]. At the start of the forward experiment, the system and de- tector are prepared in the statesa0 andD 0 according the initial joint distrib...

  5. [12]

    Derivation of the FTs in Eq.(38)andσ m in Eq.(40) Suppose that in the forward experiment, the system and de- tector’s measurement outcome follow particular trajectoriesa andD, which happens with the probabilityP[a,D] given in Eq. (D1). We now introduce the backward experiment ...

  6. [13]

    (43) fromσ m in Eq

    The average measurement entropy in Eq.(43) Here, we show how to obtain ⟨σm⟩ in Eq. (43) fromσ m in Eq. (40) using both time-continuous and time-discrete de- scriptions. We insertdD t in Eq. (41) intoσ m in Eq. (40), resulting in σm =8λ γ Z τ 0 γ(at−D t)2dt+ 8λ γ Z τ 0 γ 2 √ λ ...

  7. [14]

    Our starting point is Eq

    Coarse-graining We have the marginal probability distributionsP B[ ¯D]=R d¯aPB[¯a, ¯D] andP[D]= R daP[a,D]. Our starting point is Eq. (38): PB[¯a, ¯D]=P[a,D]e −σ[a,D]−σm[a,D].(D31) InsertingP[a|D]=P[a,D]/P[D] results in PB[¯a, ¯D]=P[D]P[a|D]e −σ[a,D]−σm[a,D].(D32) 21 Upon inte...

  8. [15]

    −κ(1+n B)κn B κ(1+n B)−κn B # +(1−θ(D))

    Equation(46)in the fast-detector limit Let us introduce a vector of probabilities ⃗p= [p−1(D),p 1(D)]T , wherep a(D) is the joint probability ofa andDin the steady state. When the detector evolves much faster that the system (γ≫κ), we can approximate [50] ⃗p= 1 2 [π−1(D),π 1(D...

  9. [16]

    FT formin Eq.(47) The trajectoriesaandDuniquely determinem[a,D], and, therefore, their joint probability is given by P[D,a,m]=δ(m[D,a]−m)P[D,a].(E9) From the detailed FT in Eq. (38) and the relationm[ ¯a, ¯D]= −m[a,D], it follows that (here we drop the subscript ”B”) P[ ¯D, ¯a...

  10. [17]

    Forward trajectory At the timet=0, the system is prepared in the initial state ˆρ ini = P vi pvi|vi⟩⟨vi|. The probability of the trajectory of the measurement outcomes,D=(D 0,D 1,...,D N+1), is given by [50] P[D]=P ini[D0] 1 γδt !N+1 Tr ( K DN+1−e−γδtDN γδt ! eL(DN)δt...eL(D1)...

  11. [18]

    Backward trajectory In the backward experiment, signified by subscript ”B”, we perform measurement and feedback just like in the forward one, but the measurement operator isP a a|˜a⟩⟨˜a|, where|˜a⟩= Θ|a⟩, withΘdenoting the anti-Hermitian time-reversal operator, and we prepare ...

  12. [19]

    (D15) but witha c n instead ofa n

    Fluctuation theorem By combining the forward and backward trajectories, we find PB[¯Γ, ¯aL, ¯aR, ¯D] P[Γ,a L,a R,D] =AB(¯Γ, ¯aL, ¯aR, ¯D) A(Γ,a L,a R,D) e−σm[ac,D],(F12) where the measurement entropy is given by σm[ac,D]= 4λ γ NX n=0 2ac n−(D n+1 +D n) (Dn+1−D n) −ln Pini,B[DN...

  13. [20]

    de Groot and P

    S. de Groot and P. Mazur, Non-equilibrium thermodynamics, inFrom Microphysics to Macrophysics: Methods and Ap- plications of Statistical Physics(Springer Berlin Heidelberg, Berlin, Heidelberg, 2007) pp. 241–330. 25

    2007

  14. [21]

    Ciliberto, Experiments in stochastic thermodynamics: Short history and perspectives, Phys

    S. Ciliberto, Experiments in stochastic thermodynamics: Short history and perspectives, Phys. Rev. X7, 021051 (2017)

    2017

  15. [22]

    Z. K. Minev, Z. K. Minev, S. O. Mundhada, S. Shankar, P. Reinhold, R. Gutierrez-Jauregui, R. J. Schoelkopf, M. Mir- rahimi, M. Mirrahimi, H. Carmichael, and M. H. Devoret, To catch and reverse a quantum jump mid-flight, Nature570, 200 (2018)

    2018

  16. [23]

    Guerlin, J

    C. Guerlin, J. Bernu, S. Del ´eglise, C. Sayrin, S. Gleyzes, S. Kuhr, M. Brune, J.-M. Raimond, and S. Haroche, Progres- sive field-state collapse and quantum non-demolition photon counting, Nature448, 889 (2007)

    2007

  17. [24]

    Del ´eglise, I

    S. Del ´eglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.- M. Raimond, and S. Haroche, Reconstruction of non-classical cavity field states with snapshots of their decoherence, Nature 455, 510 (2008)

    2008

  18. [25]

    Kurzmann, P

    A. Kurzmann, P. Stegmann, J. Kerski, R. Schott, A. Ludwig, A. D. Wieck, J. K¨onig, A. Lorke, and M. Geller, Optical detec- tion of single-electron tunneling into a semiconductor quan- tum dot, Phys. Rev. Lett.122, 247403 (2019)

    2019

  19. [26]

    Hofmann, V

    A. Hofmann, V . F. Maisi, C. Gold, T. Kr¨ahenmann, C. R¨ossler, J. Basset, P. M ¨arki, C. Reichl, W. Wegscheider, K. Ensslin, and T. Ihn, Measuring the degeneracy of discrete energy lev- els using a GaAs/AlGaAs quantum dot, Phys. Rev. Lett.117, 206803 (2016)

    2016

  20. [27]

    G. G. Gillett, R. B. Dalton, B. P. Lanyon, M. P. Almeida, M. Barbieri, G. J. Pryde, J. L. O’Brien, K. J. Resch, S. D. Bartlett, and A. G. White, Experimental feedback control of quantum systems using weak measurements, Phys. Rev. Lett. 104, 080503 (2010)

    2010

  21. [28]

    M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, Adaptive homodyne measurement of optical phase, Phys. Rev. Lett.89, 133602 (2002)

    2002

  22. [29]

    X. Zhou, I. Dotsenko, B. Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, and S. Haroche, Field locked to a fock state by quantum feedback with single photon corrections, Phys. Rev. Lett.108, 243602 (2012)

    2012

  23. [30]

    Rist `e, C

    D. Rist `e, C. C. Bultink, K. W. Lehnert, and L. DiCarlo, Feed- back control of a solid-state qubit using high-fidelity projec- tive measurement, Phys. Rev. Lett.109, 240502 (2012)

    2012

  24. [31]

    Campagne-Ibarcq, E

    P. Campagne-Ibarcq, E. Flurin, N. Roch, D. Darson, P. Morfin, M. Mirrahimi, M. H. Devoret, F. Mallet, and B. Huard, Persis- tent control of a superconducting qubit by stroboscopic mea- surement feedback, Phys. Rev. X3, 021008 (2013)

    2013

  25. [32]

    Sekimoto, Kinetic characterization of heat bath and the en- ergetics of thermal ratchet models, J

    K. Sekimoto, Kinetic characterization of heat bath and the en- ergetics of thermal ratchet models, J. Phys. Soc. Jpn.66, 1234 (1997)

    1997

  26. [33]

    Sekimoto, Langevin Equation and Thermodynamics, Prog

    K. Sekimoto, Langevin Equation and Thermodynamics, Prog. Theor. Phys. Supp.130, 17 (1998)

    1998

  27. [34]

    Sekimoto,Stochastic Energetics(Springer Berlin, Heidel- berg, 2010)

    K. Sekimoto,Stochastic Energetics(Springer Berlin, Heidel- berg, 2010)

    2010

  28. [35]

    Avanzini, M

    F. Avanzini, M. Bilancioni, V . Cavina, S. D. Cengio, M. Es- posito, G. Falasco, D. Forastiere, N. Freitas, A. Garilli, P. E. Harunari, V . Lecomte, A. Lazarescu, S. G. M. Srinivas, C. Moslonka, I. Neri, E. Penocchio, W. D. Pi ˜neros, M. Polet- tini, A. Raghu, P. Raux, K. Seki...

    2024

  29. [36]

    Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep

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

    2012

  30. [37]

    Pusz and S

    W. Pusz and S. Woronowicz, Passive states and kms states for general quantum systems, Commun. Math. Phys.58, 273 (1978)

    1978

  31. [38]

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

    R. Alicki, The quantum open system as a model of the heat engine, J. Phys. A Math. Gen.12, L103 (2001)

    2001

  32. [39]

    P. P. Potts, A. A. S. Kalaee, and A. Wacker, A thermodynami- cally consistent markovian master equation beyond the secular approximation, New J. Phys.23, 123013 (2021)

    2021

  33. [40]

    G. T. Landi and M. Paternostro, Irreversible entropy produc- tion: From classical to quantum, Rev. Mod. Phys.93, 035008 (2021)

    2021

  34. [41]

    Esposito and C

    M. Esposito and C. V . den Broeck, Second law and landauer principle far from equilibrium, EPL95, 40004 (2011)

    2011

  35. [42]

    Esposito, K

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

    2010

  36. [43]

    Spohn, Entropy production for quantum dynamical semi- groups, J

    H. Spohn, Entropy production for quantum dynamical semi- groups, J. Math. Phys.19, 1227 (1978)

    1978

  37. [44]

    Lindblad, Completely positive maps and entropy inequali- ties, Commun

    G. Lindblad, Completely positive maps and entropy inequali- ties, Commun. Math. Phys.40, 147 (1975)

    1975

  38. [45]

    M. T. Mitchison and P. P. Potts, Physical implementations of quantum absorption refrigerators, inThermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer International Publis...

    2018

  39. [46]

    Ghosh, W

    A. Ghosh, W. Niedenzu, V . Mukherjee, and G. Kurizki, Ther- modynamic principles and implementations of quantum ma- chines, inThermodynamics in the Quantum Regime: Funda- mental Aspects and New Directions, edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso...

    2018

  40. [47]

    Levy and D

    A. Levy and D. Gelbwaser-Klimovsky, Quantum features and signatures of quantum thermal machines, inThermodynamics in the Quantum Regime: Fundamental Aspects and New Di- rections, edited by F. Binder, L. A. Correa, C. Gogolin, J. An- ders, and G. Adesso (Springer International ...

  41. [48]

    Roßnagel, S

    J. Roßnagel, S. T. Dawkins, K. N. Tolazzi, O. Abah, E. Lutz, F. Schmidt-Kaler, and K. Singer, A single-atom heat engine, Science352, 325 (2016)

    2016

  42. [49]

    Seifert, Entropy production along a stochastic trajectory and an integral fluctuation theorem, Phys

    U. Seifert, Entropy production along a stochastic trajectory and an integral fluctuation theorem, Phys. Rev. Lett.95, 040602 (2005)

    2005

  43. [51]

    Jarzynski, Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach, Phys

    C. Jarzynski, Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach, Phys. Rev. E56, 5018 (1997)

    1997

  44. [52]

    G. E. Crooks, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Phys. Rev. E60, 2721 (1999)

    1999

  45. [53]

    G. E. Crooks, Path-ensemble averages in systems driven far from equilibrium, Phys. Rev. E61, 2361 (2000)

    2000

  46. [54]

    J. M. Horowitz, Quantum-trajectory approach to the stochastic thermodynamics of a forced harmonic oscillator, Phys. Rev. E 85, 031110 (2012)

    2012

  47. [55]

    J. M. Horowitz and J. M. R. Parrondo, Entropy production along nonequilibrium quantum jump trajectories, New J. Phys. 15, 085028 (2013)

    2013

  48. [56]

    Manzano, J

    G. Manzano, J. M. Horowitz, and J. M. R. Parrondo, Nonequi- librium potential and fluctuation theorems for quantum maps, Phys. Rev. E92, 032129 (2015)

    2015

  49. [57]

    Manzano, J

    G. Manzano, J. M. Horowitz, and J. M. R. Parrondo, Quan- tum fluctuation theorems for arbitrary environments: Adia- batic and nonadiabatic entropy production, Phys. Rev. X8, 031037 (2018)

    2018

  50. [58]

    Manzano and R

    G. Manzano and R. Zambrini, Quantum thermodynamics un- der continuous monitoring: A general framework, A VS Quan- 26 tum Sci.4, 025302 (2022)

    2022

  51. [59]

    Breuer, Quantum jumps and entropy production, Phys

    H.-P. Breuer, Quantum jumps and entropy production, Phys. Rev. A68, 032105 (2003)

    2003

  52. [60]

    F. W. J. Hekking and J. P. Pekola, Quantum jump approach for work and dissipation in a two-level system, Phys. Rev. Lett. 111, 093602 (2013)

    2013

  53. [61]

    H. M. Wiseman and G. J. Milburn, Quantum theory of optical feedback via homodyne detection, Phys. Rev. Lett.70, 548 (1993)

    1993

  54. [62]

    H. M. Wiseman, Quantum theory of continuous feedback, Phys. Rev. A49, 2133 (1994)

    1994

  55. [63]

    A. C. Doherty and K. Jacobs, Feedback control of quantum systems using continuous state estimation, Phys. Rev. A60, 2700 (1999)

    1999

  56. [64]

    A. N. Korotkov, Selective quantum evolution of a qubit state due to continuous measurement, Phys. Rev. B63, 115403 (2001)

    2001

  57. [65]

    Zhang, Y

    J. Zhang, Y . xi Liu, R.-B. Wu, K. Jacobs, and F. Nori, Quantum feedback: Theory, experiments, and applications, Phys. Rep. 679, 1 (2017)

    2017

  58. [66]

    V . P. Belavkin, Nondemolition measurements, nonlinear fil- tering and dynamic programming of quantum stochastic processes, inModeling and Control of Systems, edited by A. Blaqui´ere (Springer Berlin Heidelberg, Berlin, Heidelberg,

  59. [67]

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

    2009

  60. [68]

    Jacobs,Quantum Measurement Theory and its Applications (Cambridge University Press, 2014)

    K. Jacobs,Quantum Measurement Theory and its Applications (Cambridge University Press, 2014)

    2014

  61. [69]

    Annby-Andersson, F

    B. Annby-Andersson, F. Bakhshinezhad, D. Bhattacharyya, G. De Sousa, C. Jarzynski, P. Samuelsson, and P. P. Potts, Quantum fokker-planck master equation for continuous feed- back control, Phys. Rev. Lett.129, 050401 (2022)

    2022

  62. [70]

    D’Urso, B

    B. D’Urso, B. Odom, and G. Gabrielse, Feedback cooling of a one-electron oscillator, Phys. Rev. Lett.90, 043001 (2003)

    2003

  63. [71]

    Bushev, D

    P. Bushev, D. Rotter, A. Wilson, F. m. c. Dubin, C. Becher, J. Eschner, R. Blatt, V . Steixner, P. Rabl, and P. Zoller, Feed- back cooling of a single trapped ion, Phys. Rev. Lett.96, 043003 (2006)

    2006

  64. [72]

    De Sousa, P

    G. De Sousa, P. Bakhshinezhad, B. Annby-Andersson, P. Samuelsson, P. P. Potts, and C. Jarzynski, Continuous feed- back protocols for cooling and trapping a quantum harmonic oscillator, Phys. Rev. E111, 014152 (2025)

    2025

  65. [73]

    Kumasaki, T

    K. Kumasaki, T. Yada, K. Funo, and T. Sagawa, Thermody- namic approach to quantum cooling limit of continuous gaus- sian feedback (2025), arXiv:2503.04270

    2025 arXiv

  66. [74]

    Debiossac, D

    M. Debiossac, D. Grass, J. Alonso, E. Lutz, and N. Kiesel, Thermodynamics of continuous non-markovian feedback con- trol, Nature Comms.11, 1360 (2020)

    2020

  67. [75]

    R. P. Vijay, C. Macklin, D. H. Slichter, S. J. Weber, K. W. Murch, R. K. Naik, A. N. Korotkov, and I. Siddiqi, Stabiliz- ing rabi oscillations in a superconducting qubit using quantum feedback, Nature490, 77 (2012)

    2012

  68. [76]

    W. P. Smith, J. E. Reiner, L. A. Orozco, S. Kuhr, and H. M. Wiseman, Capture and release of a conditional state of a cavity qed system by quantum feedback, Phys. Rev. Lett.89, 133601 (2002)

    2002

  69. [77]

    Sayrin, I

    C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. Raimond, and S. Haroche, Real-time quantum feedback prepares and stabilizes photon number states, Nature477, 73 (2011)

    2011

  70. [78]

    W. Feng, P. Wang, X. Ding, L. Xu, and X.-Q. Li, Generating and stabilizing the greenberger-horne-zeilinger state in circuit qed: Joint measurement, zeno effect, and feedback, Phys. Rev. A83, 042313 (2011)

    2011

  71. [79]

    Z. Liu, L. Kuang, K. Hu, L. Xu, S. Wei, L. Guo, and X.-Q. Li, Deterministic creation and stabilization of entanglement in circuit qed by homodyne-mediated feedback control, Phys. Rev. A82, 032335 (2010)

    2010

  72. [80]

    H. M. Wiseman and G. J. Milburn, Squeezing via feedback, Phys. Rev. A49, 1350 (1994)

    1994

  73. [81]

    Sarovar, C

    M. Sarovar, C. Ahn, K. Jacobs, and G. J. Milburn, Practical scheme for error control using feedback, Phys. Rev. A69, 052324 (2004)

    2004

  74. [82]

    M. T. Mitchison, J. Goold, and J. Prior, Charging a quantum battery with linear feedback control, Quantum5, 500 (2021)

    2021

  75. [83]

    Maxwell,Theory of Heat(Longmans, Green, and Company, London, 1872)

    J. Maxwell,Theory of Heat(Longmans, Green, and Company, London, 1872)

  76. [84]

    Szilard, ¨uber die entropieverminderung in einem thermody- namischen system bei eingriffen intelligenter wesen, Z

    L. Szilard, ¨uber die entropieverminderung in einem thermody- namischen system bei eingriffen intelligenter wesen, Z. Phys. 53, 840 (1929)

    1929

  77. [85]

    Rex, Maxwell’s demon—a historical review, Entropy19, 240 (2017)

    A. Rex, Maxwell’s demon—a historical review, Entropy19, 240 (2017)

    2017

  78. [86]

    Lloyd, Quantum-mechanical Maxwell’s demon, Phys

    S. Lloyd, Quantum-mechanical Maxwell’s demon, Phys. Rev. A56, 3374 (1997)

    1997

  79. [87]

    Annby-Andersson, D

    B. Annby-Andersson, D. Bhattacharyya, P. Bakhshinezhad, D. Holst, G. De Sousa, C. Jarzynski, P. Samuelsson, and P. P. Potts, Maxwell’s demon across the quantum-to-classical tran- sition, Phys. Rev. Res.6, 043216 (2024)

    2024

  80. [88]

    Elouard, D

    C. Elouard, D. Herrera-Mart ´ı, B. Huard, and A. Auff`eves, Ex- tracting work from quantum measurement in Maxwell’s de- mon engines, Phys. Rev. Lett.118, 260603 (2017)

    2017

  81. [89]

    Annby-Andersson, P

    B. Annby-Andersson, P. Samuelsson, V . F. Maisi, and P. P. Potts, Maxwell’s demon in a double quantum dot with contin- uous charge detection, Phys. Rev. B101, 165404 (2020)

    2020

  82. [90]

    S ´anchez, P

    R. S ´anchez, P. Samuelsson, and P. P. Potts, Autonomous con- version of information to work in quantum dots, Phys. Rev. Res.1, 033066 (2019)

    2019

  83. [91]

    R. K. Schmitt, P. P. Potts, H. Linke, J. Johansson, P. Samuels- son, M. Rico-Pasto, and F. Ritort, Information-to-work con- version in single-molecule experiments: From discrete to con- tinuous feedback, Phys. Rev. E107, L052104 (2023)

    2023

  84. [92]

    Esposito and G

    M. Esposito and G. Schaller, Stochastic thermodynamics for ”Maxwell demon” feedbacks, EPL99(2012)

    2012

  85. [93]

    Strasberg, G

    P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Ther- modynamics of a physical model implementing a Maxwell de- mon, Phys. Rev. Lett.110, 040601 (2013)

    2013

  86. [94]

    Schaller, C

    G. Schaller, C. Emary, G. Kiesslich, and T. Brandes, Probing the power of an electronic Maxwell’s demon: Single-electron transistor monitored by a quantum point contact, Phys. Rev. B 84, 085418 (2011)

    2011

  87. [95]

    D. V . Averin, M. M¨ott¨onen, and J. P. Pekola, Maxwell’s demon based on a single-electron pump, Phys. Rev. B84, 245448 (2011)

    2011

  88. [96]

    Deffner, Information-driven current in a quantum Maxwell demon, Phys

    S. Deffner, Information-driven current in a quantum Maxwell demon, Phys. Rev. E88, 062128 (2013)

    2013

  89. [97]

    Strasberg, G

    P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, Quan- tum and information thermodynamics: A unifying framework based on repeated interactions, Phys. Rev. X7, 021003 (2017)

    2017

  90. [98]

    H. T. Quan, Y . D. Wang, Y .-x. Liu, C. P. Sun, and F. Nori, Maxwell’s demon assisted thermodynamic cycle in supercon- ducting quantum circuits, Phys. Rev. Lett.97, 180402 (2006)

    2006

  91. [99]

    Ito and T

    S. Ito and T. Sagawa, Maxwell’s demon in biochemical signal transduction, Nat. Commun.6(2014)

    2014

  92. [100]

    Cottet, S

    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, 27 Proc. Natl. Acad. Sci. U.S.A.114(2017)

    2017

  93. [101]

    Masuyama, K

    Y . Masuyama, K. Funo, Y . Murashita, A. Noguchi, S. Kono, Y . Tabuchi, R. Yamazaki, M. Ueda, and Y . Nakamura, Information-to-work conversion by Maxwell’s demon in a su- perconducting circuit quantum electrodynamical system, Nat. Comm.9(2018)

    2018

  94. [102]

    Naghiloo, J

    M. Naghiloo, J. J. Alonso, A. Romito, E. Lutz, and K. W. Murch, Information gain and loss for a quantum Maxwell’s demon, Phys. Rev. Lett.121, 030604 (2018)

    2018

  95. [103]

    J. V . Koski, V . F. Maisi, T. Sagawa, and J. P. Pekola, Exper- imental observation of the role of mutual information in the nonequilibrium dynamics of a Maxwell demon, Phys. Rev. Lett.113, 030601 (2014)

    2014

  96. [104]

    Koski, V

    J. Koski, V . Maisi, J. Pekola, and D. Averin, Experimental re- alization of a szilard engine with a single electron, Proc. Natl. Acad. Sci. U.S.A.111(2014)

    2014

  97. [105]

    J. V . Koski, A. Kutvonen, I. M. Khaymovich, T. Ala-Nissila, and J. P. Pekola, On-chip Maxwell’s demon as an information- powered refrigerator, Phys. Rev. Lett.115, 260602 (2015)

    2015

  98. [106]

    Barker, M

    D. Barker, M. Scandi, S. Lehmann, C. Thelander, K. A. Dick, M. Perarnau-Llobet, and V . F. Maisi, Experimental verification of the work fluctuation-dissipation relation for information-to- work conversion, Phys. Rev. Lett.128, 040602 (2022)

    2022

  99. [107]

    M. D. Vidrighin, O. Dahlsten, M. Barbieri, M. S. Kim, V . Ve- dral, and I. A. Walmsley, Photonic Maxwell’s demon, Phys. Rev. Lett.116, 050401 (2016)

    2016

  100. [108]

    Archambault, C

    A. Archambault, C. Crauste-Thibierge, A. Imparato, C. Jarzynski, S. Ciliberto, and L. Bellon, First-passage information engine (2024), arXiv:2407.17414 [cond-mat.stat- mech]

    2024

  101. [109]

    Archambault, C

    A. Archambault, C. Crauste-Thibierge, S. Ciliberto, and L. Bellon, Inertial effects in discrete sampling information en- gines (2024), arXiv:2407.06672 [cond-mat.stat-mech]

    2024 arXiv

  102. [110]

    P. A. Camati, J. P. S. Peterson, T. B. Batalh ˜ao, K. Mi- cadei, A. M. Souza, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, Experimental rectification of entropy production by Maxwell’s demon in a quantum system, Phys. Rev. Lett.117, 240502 (2016)

    2016

  103. [111]

    Yada, P.-J

    T. Yada, P.-J. Stas, A. Suleymanzade, E. N. Knall, N. Yosh- ioka, T. Sagawa, and M. D. Lukin, Experimentally probing entropy reduction via iterative quantum information transfer (2024), arXiv:2411.06709

    2024 arXiv

  104. [112]

    Toyabe, T

    S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, Experimental demonstration of information-to-energy conver- sion and validation of the generalized jarzynski equality, Nat. Phys.6(2010)

    2010

  105. [113]

    Rold´an, I

    ´E. Rold´an, I. A. Mart ´ınez, J. M. R. Parrondo, and D. Petrov, Universal features in the energetics of symmetry breaking, Nat. Phys.10, 457 (2013)

    2013

  106. [114]

    Paneru, D

    G. Paneru, D. Y . Lee, T. Tlusty, and H. K. Pak, Lossless brow- nian information engine, Phys. Rev. Lett.120, 020601 (2018)

    2018

  107. [115]

    T. K. Saha, J. N. E. Lucero, J. Ehrich, D. A. Sivak, and J. Bech- hoefer, Bayesian information engine that optimally exploits noisy measurements, Phys. Rev. Lett.129, 130601 (2022)

    2022

  108. [116]

    Admon, S

    T. Admon, S. Rahav, and Y . Roichman, Experimental realiza- tion of an information machine with tunable temporal correla- tions, Phys. Rev. Lett.121, 180601 (2018)

    2018

  109. [117]

    Sagawa and M

    T. Sagawa and M. Ueda, Nonequilibrium thermodynamics of feedback control, Phys. Rev. E85, 021104 (2012)

    2012

  110. [118]

    P. P. Potts and P. Samuelsson, Detailed fluctuation relation for arbitrary measurement and feedback schemes, Phys. Rev. Lett. 121, 210603 (2018)

    2018

  111. [119]

    Prech and P

    K. Prech and P. P. Potts, Quantum fluctuation theorem for ar- bitrary measurement and feedback schemes, Phys. Rev. Lett. 133, 140401 (2024)

    2024

  112. [120]

    T. Yada, N. Yoshioka, and T. Sagawa, Quantum fluctuation theorem under quantum jumps with continuous measurement and feedback, Phys. Rev. Lett.128, 170601 (2022)

    2022

  113. [121]

    Sagawa and M

    T. Sagawa and M. Ueda, Second law of thermodynamics with discrete quantum feedback control, Phys. Rev. Lett.100, 080403 (2008)

    2008

  114. [122]

    Sagawa and M

    T. Sagawa and M. Ueda, Generalized jarzynski equality un- der nonequilibrium feedback control, Phys. Rev. Lett.104, 090602 (2010)

    2010

  115. [123]

    J. M. Horowitz and S. Vaikuntanathan, Nonequilibrium de- tailed fluctuation theorem for repeated discrete feedback, Phys. Rev. E82, 061120 (2010)

    2010

  116. [124]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information: 10th Anniversary Edition(Cambridge University Press, 2010)

    2010

  117. [125]

    Elouard, D

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

    2017

  118. [126]

    Jacobs, Second law of thermodynamics and quantum feed- back control: Maxwell’s demon with weak measurements, Phys

    K. Jacobs, Second law of thermodynamics and quantum feed- back control: Maxwell’s demon with weak measurements, Phys. Rev. A80, 012322 (2009)

    2009

  119. [127]

    Brandner, M

    K. Brandner, M. Bauer, M. T. Schmid, and U. Seifert, Coherence-enhanced efficiency of feedback-driven quantum engines, New J. Phys.17, 065006 (2015)

    2015

  120. [128]

    J. Yi, P. Talkner, and Y . W. Kim, Single-temperature quan- tum engine without feedback control, Phys. Rev. E96, 022108 (2017)

    2017

  121. [129]

    Abdelkhalek, Y

    K. Abdelkhalek, Y . Nakata, and D. Reeb, Fundamental en- ergy cost for quantum measurement (2018), arXiv:1609.06981 [quant-ph]

    2018 arXiv

  122. [130]

    Z. Gong, Y . Ashida, and M. Ueda, Quantum-trajectory ther- modynamics with discrete feedback control, Phys. Rev. A94, 012107 (2016)

    2016

  123. [131]

    Rossi, L

    M. Rossi, L. Mancino, G. T. Landi, M. Paternostro, A. Schliesser, and A. Belenchia, Experimental assessment of entropy production in a continuously measured mechanical resonator, Phys. Rev. Lett.125, 080601 (2020)

    2020

  124. [132]

    Belenchia, L

    A. Belenchia, L. Mancino, G. T. Landi, and M. Paternostro, Entropy production in continuously measured quantum sys- tems, npj Quantum Inf.6(2020)

    2020

  125. [133]

    G. T. Landi, M. Paternostro, and A. Belenchia, Informational steady states and conditional entropy production in continu- ously monitored systems, PRX Quantum3, 010303 (2022)

    2022

  126. [134]

    Belenchia, M

    A. Belenchia, M. Paternostro, and G. T. Landi, Informational steady states and conditional entropy production in continu- ously monitored systems: The case of gaussian systems, Phys. Rev. A105, 022213 (2022)

    2022

  127. [135]

    M. J. Kewming and S. Shrapnel, Entropy production and fluc- tuation theorems in a continuously monitored optical cavity at zero temperature, Quantum6, 685 (2022)

    2022

  128. [136]

    Elouard, S

    C. Elouard, S. K. Manikandan, A. N. Jordan, and G. Haack, Revealing the fuel of a quantum continuous measurement- based refrigerator (2024), arXiv:2502.10349 [quant-ph]

    2024

  129. [137]

    J. J. Alonso, E. Lutz, and A. Romito, Thermodynamics of weakly measured quantum systems, Phys. Rev. Lett.116, 080403 (2016)

    2016

  130. [138]

    Bhandari and A

    B. Bhandari and A. N. Jordan, Continuous measurement boosted adiabatic quantum thermal machines, Phys. Rev. Res. 4, 033103 (2022)

    2022

  131. [139]

    Yanik, B

    K. Yanik, B. Bhandari, S. K. Manikandan, and A. N. Jordan, Thermodynamics of quantum measurement and maxwell’s de- mon’s arrow of time, Phys. Rev. A106, 042221 (2022)

    2022

  132. [140]

    S. K. Manikandan, C. Elouard, K. W. Murch, A. Auff`eves, and 28 A. N. Jordan, Efficiently fueling a quantum engine with in- compatible measurements, Phys. Rev. E105, 044137 (2022)

    2022

  133. [141]

    Cavina, A

    V . Cavina, A. Mari, A. Carlini, and V . Giovannetti, Optimal thermodynamic control in open quantum systems, Phys. Rev. A98, 012139 (2018)

    2018

  134. [142]

    G. F. Diotallevi, B. Annby-Andersson, P. Samuelsson, A. Tavakoli, and P. Bakhshinezhad, Steady-state entanglement production in a quantum thermal machine with continuous feedback control, New J. Phys.26, 053005 (2024)

    2024

  135. [143]

    P. P. Hofer, Quasi-probability distributions for observables in dynamic systems, Quantum1, 32 (2017)

    2017

  136. [144]

    Y . V . Nazarov and M. Kindermann, Full counting statistics of a general quantum mechanical variable, Eur. Phys. J. B35, 413 (2003)

    2003

  137. [145]

    Levitov, H

    L. Levitov, H. Lee, and G. Lesovik, Electron counting statis- tics and coherent states of electric current, J. Math. Phys.37 (1996)

    1996

  138. [146]

    P. P. Hofer and A. A. Clerk, Negative full counting statistics arise from interference effects, Phys. Rev. Lett.116, 013603 (2016)

    2016

  139. [147]

    A. A. Clerk, Full counting statistics of energy fluctuations in a driven quantum resonator, Phys. Rev. A84, 043824 (2011)

    2011

  140. [148]

    Jacobs and D

    K. Jacobs and D. Steck, A straightforward introduction to con- tinuous quantum measurement, Contemp. Phys.47(2006)

    2006

  141. [149]

    Bednorz, W

    A. Bednorz, W. Belzig, and A. Nitzan, Nonclassical time cor- relation functions in continuous quantum measurement, New J. Phys.14, 013009 (2012)

    2012

  142. [150]

    T. A. Wheatley, D. W. Berry, H. Yonezawa, D. Nakane, H. Arao, D. T. Pope, T. C. Ralph, H. M. Wiseman, A. Fu- rusawa, and E. H. Huntington, Adaptive optical phase esti- mation using time-symmetric quantum smoothing, Phys. Rev. Lett.104, 093601 (2010)

    2010

  143. [151]

    Sarovar, H.-S

    M. Sarovar, H.-S. Goan, T. P. Spiller, and G. J. Milburn, High- fidelity measurement and quantum feedback control in circuit qed, Phys. Rev. A72, 062327 (2005)

    2005

  144. [152]

    Warszawski and H

    P. Warszawski and H. M. Wiseman, Quantum trajectories for realistic photodetection: I. general formalism, J. Opt. B: Quan- tum Semiclassical Opt.5, 1 (2002)

    2002

  145. [153]

    Warszawski and H

    P. Warszawski and H. M. Wiseman, Quantum trajectories for realistic photodetection: Ii. application and analysis, J. Opt. B: Quantum Semiclassical Opt.5, 15 (2002)

    2002

  146. [154]

    Albash, S

    T. Albash, S. Boixo, D. A. Lidar, and P. Zanardi, Quantum adi- abatic markovian master equations, New J. Phys.14, 123016 (2012)

    2012

  147. [155]

    Novotn ´y, Investigation of apparent violation of the second law of thermodynamics in quantum transport studies, EPL59, 648 (2002)

    T. Novotn ´y, Investigation of apparent violation of the second law of thermodynamics in quantum transport studies, EPL59, 648 (2002)

    2002

  148. [156]

    Levy and R

    A. Levy and R. Kosloff, The local approach to quantum trans- port may violate the second law of thermodynamics, EPL107, 20004 (2014)

    2014

  149. [157]

    A. S. Trushechkin and I. V . V olovich, Perturbative treatment of inter-site couplings in the local description of open quantum networks, EPL113, 30005 (2016)

    2016

  150. [158]

    P. P. Hofer, M. Perarnau-Llobet, L. D. M. Miranda, G. Haack, R. Silva, J. B. Brask, and N. Brunner, Markovian master equa- tions for quantum thermal machines: local versus global ap- proach, New J. Phys.19, 123037 (2017)

    2017

  151. [159]

    J. O. Gonz ´alez, L. A. Correa, G. Nocerino, J. P. Palao, D. Alonso, and G. Adesso, Testing the validity of the ‘lo- cal’ and ‘global’ gkls master equations on an exactly solvable model, Open Syst. Inf. Dyn.24, 1740010 (2017)

    2017

  152. [160]

    De Chiara, G

    G. De Chiara, G. Landi, A. Hewgill, B. Reid, A. Ferraro, A. J. Roncaglia, and M. Antezza, Reconciliation of quantum local master equations with thermodynamics, New J. Phys.20, 113024 (2018)

    2018

  153. [161]

    Hewgill, G

    A. Hewgill, G. De Chiara, and A. Imparato, Quantum ther- modynamically consistent local master equations, Phys. Rev. Res.3, 013165 (2021)

    2021

  154. [162]

    Jacobs,Stochastic Processes for Physicists: Understanding Noisy Systems(Cambridge University Press, 2010)

    K. Jacobs,Stochastic Processes for Physicists: Understanding Noisy Systems(Cambridge University Press, 2010)

    2010

  155. [163]

    Campisi, P

    M. Campisi, P. Talkner, and P. H¨anggi, Fluctuation theorem for arbitrary open quantum systems, Phys. Rev. Lett.102, 210401 (2009)

    2009

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.