Pith. sign in

REVIEW 2 major objections 5 minor 1 cited by

Coarse-grained quantum thermodynamics: Observation-dependent quantities, observation-independent laws

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read In quantum thermodynamics, coarse-grained work and entropy values depend on the observer's energy resolution, yet the second-law inequality and the quantum work fluctuation theorems keep exactly the same form.

desk verdict A useful framework with a clean Crooks/Jarzynski extension, but Eq. (22) as printed uses the wrong final state in the work definition; the fix is simple and the main message survives. read the letter →

arxiv 2507.15918 v2 pith:JK6PT4VB submitted 2025-07-21 quant-ph

Giulia Rubino , Časlav Brukner , Gonzalo Manzano This is my paper
classification quant-ph
keywords coarse-grainedthermodynamicsquantumworkfluctuationtheoremsCrooksrelationJarzynskiequalitysecondlawofmeasure-and-reprepareenergymeasurementresolutionobservationalentropy
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 asks whether standard thermodynamic quantities have objective values or depend on how finely an agent can measure energy. It introduces energy-bin coarse-graining with projectors $\Pi_J$ and a measure-and-reprepare step, and fixes the coarse-grained energy levels $E_J = -k_B T \log(Z_J/N_J)$ so that the coarse-grained thermal state is exactly the coarse-graining of the fine-grained thermal state. Under that prescription, the paper claims that the second-law inequality, the relation between dissipation and time-reversal distinguishability, and the detailed and integral quantum work fluctuation theorems (Crooks and Jarzynski) hold unchanged in form for coarse-grained quantities, as stated in Eqs. (22) and (27). A coarse-grained agent can therefore read off equilibrium free-energy differences from non-equilibrium work distributions without resolving individual energy levels. The quantities are observation-dependent; the relations between them are not.

What carries the argument

The load-bearing object is the coarse-graining map $\mathcal{C}_{\Pi_J}(\rho) = \sum_J [\mathrm{Tr}(\rho\Pi_J)/N_J]\,\Pi_J$, which flattens each energy slot into the maximally mixed state on that slot; it is completely positive, trace preserving, unital, and idempotent. The map alone does not determine the coarse-grained energies. The paper couples it with the consistency condition $\mathcal{C}(\tau_\beta+\delta\tau)=\breve{\tau}_\beta$, which forces $E_J = -k_B T \log(Z_J/N_J)$, making the coarse energies temperature-dependent and ensuring that the coarse-grained thermal state is the coarse-graining of the fine-grained one. That combination, plus a two-point measurement scheme in which the post-measurement state is reprepared as $\Pi_J/N_J$, is what makes the relative-entropy dissipation relation and the Crooks/Jarzynski identities survive coarse-graining: microreversibility gives the ratio of forward and time-reversed joint probabilities, and the temperature-dependent energies make the Gibbs form exact.

What would settle it

Simulate a driven harmonic-oscillator TPM with orthogonal energy bins, compute forward and time-reversed work distributions for bin energies from Eq. (11) and, separately, from bin midpoints; if the midpoint assignment still satisfies $\breve{P}(\breve{W})/\tilde{\breve{P}}(-\breve{W}) = e^{\beta(\breve{W}-\Delta F)}$, the consistency condition is not necessary, while if the Eq. (11) assignment fails it, the central claim collapses.

Watch

Extended reading notes

Core claim

The central discovery is that coarse-graining changes the numbers but not the laws. With a PVM-based energy coarse-graining $\{\Pi_J\}$, $N_J = \mathrm{Tr}[\Pi_J]$, a maximum-entropy coarse-grained thermal state $\breve{\tau}_\beta = \sum_J (e^{-\beta E_J}/\breve{Z})\Pi_J$, and energies fixed by the consistency condition $\mathcal{C}(\tau_\beta+\delta\tau)=\breve{\tau}_\beta$ to $E_J = -k_B T \log(Z_J/N_J)$, the authors prove $\beta(\langle \breve{W}\rangle - \Delta F) = S(\breve{\rho}(t)\,||\, \Theta^\dagger \tilde{\breve{\rho}}(\tau-t)\Theta) \ge 0$ and the detailed fluctuation theorem $\breve{P}(\breve{W})/\tilde{\breve{P}}(-\breve{W}) = e^{\beta(\breve{W}-\Delta F)}$, hence $\langle e^{-\beta(\breve{W}-\Delta F)}\rangle = 1$. These hold for every orthogonal energy-bin resolution, with the same free-energy difference $\Delta F$ as the fine-grained process. The main caveat inside the paper is structural: the results require the measure-and-reprepare scheme, and in Sec. VI the authors show Crooks-type relations fail generically when the coarse-graining is an overlapping POVM rather than orthogonal projectors.

Load-bearing premise

The load-bearing premise is the consistency condition $\mathcal{C}(\tau_\beta+\delta\tau)=\breve{\tau}_\beta$, which fixes the coarse-grained energy levels to $E_J=-k_B T \log(Z_J/N_J)$; if an agent assigns coarse energies differently, such as by slot midpoints, the simple second-law inequality and Crooks relation do not hold.

Editorial extensions

If this is right

  • For any orthogonal energy-bin resolution, the second law takes the form $\langle \breve{W}\rangle \ge \Delta F$, with the dissipated work equal to $\beta^{-1}$ times the quantum relative entropy between the forward and time-reversed coarse-grained states.
  • Coarse-grained work distributions obey the Crooks relation and the Jarzynski equality, so equilibrium free-energy differences can be estimated from non-equilibrium work data at any measurement precision, as long as $\breve{N}>1$.
  • There is no universal ordering between fine- and coarse-grained dissipation: the coarse-grained dissipative work can be larger or smaller than the fine-grained value; it is always smaller only when the coarse-graining map commutes with the driving unitary.
  • Removing the repreparation step (non-invasive TPM) breaks the correspondence between coarse-grained dissipation and measured work, and the fluctuation theorems no longer hold.
  • With overlapping POVM coarse-graining, the Crooks relation generically fails, so the invariance of the full set of relations relies on orthogonal projective coarse-graining.

Reading between the lines

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

  • The paper's temperature-dependent coarse energies imply that a coarse-grained observer's 'Hamiltonian' is not a fixed physical observable but a bookkeeping device that shifts with the bath temperature; a natural extension is to ask whether such temperature-renormalized ladders have an operational interpretation in repeated-interaction or virtual-temperature setups.
  • Because the commuting-drive analysis shows the effects come mainly from thermal weighting within slots rather than from coherences, the same invariance should hold in classical stochastic thermodynamics with energy-bin coarse-graining; a direct classical analogue with a two-level or harmonic system would be a cheap test.
  • The POVM failure suggests a sharp boundary: laws are invariant under idempotent, unital, energy-diagonal channels but not under noisy readout. A testable extension is to check whether the correction terms in the fluctuation relations scale with the POVM overlap $\sigma$ in the Gaussian model of Eq. (31), giving a quantitative handle on how far from ideal an experimental binning can be.
  • The framework leaves open the cost of the measurement apparatus itself; combining these coarse-grained fluctuation theorems with the resource cost of projective measurements could yield a hierarchy of thermodynamic bounds that depend on both precision and implementation, but that goes beyond what the paper claims.
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

2 major / 5 minor

Summary. The paper develops a framework for energy coarse-graining in quantum thermodynamics. It models limited experimental resolution through orthogonal projections in the energy basis, defines a measure-and-reprepare coarse-graining map, and fixes the coarse-grained energy levels by a consistency condition requiring the coarse-grained thermal state to equal the coarse-graining of the fine-grained thermal state. On this basis the paper derives a second-law-like inequality and detailed/integral fluctuation theorems for a two-point-measurement protocol with coarse-grained instruments, illustrates the results on driven harmonic oscillators, and contrasts the measure-and-reprepare scheme with a non-invasive projection scheme and with POVM-based coarse graining.

Significance. The intended message—that the form of the second law and of the Crooks/Jarzynski relations is preserved under finite energy resolution, even though the thermodynamic quantities themselves become observation-dependent—is interesting and timely. The fluctuation-theorem part appears sound: Eq. (26) follows from the Gibbs form of the coarse-grained initial probabilities, micro-reversibility, and cancellation of the N_J factors, and Eq. (27) is a valid detailed Crooks relation that allows free-energy estimation from coarse-grained work data. The paper is also careful to state limitations (Secs. V and VI) and makes its code available. However, the second-law part as printed contains a load-bearing algebraic error: the work variable in Eq. (22) does not follow from the paper's own Eqs. (20)–(21). The central claim is therefore not yet established in the form presented and needs correction and numerical re-verification.

major comments (2)
  1. [Sec. III, Eqs. (20)–(22)] The displayed derivation is internally inconsistent. Substituting Eqs. (21a) and (21b) into Eq. (20) gives S(˘ρ(t)||Θ†˘˜ρ(τ−t)Θ) = β(Tr[˘Hτ ˘ρ(τ)] − Tr[˘H0 ˘τβ^0] − ∆F). The paper instead defines ⟨˘W⟩ = Tr[˘Hτ ˘τβ^τ] − Tr[˘H0 ˘τβ^0], which would require Tr[˘Hτ ˘ρ(τ)] = Tr[˘Hτ ˘τβ^τ]. This equality is generically false for a non-equilibrium final state, including the driven-oscillator examples in Sec. II C. The natural coarse-grained TPM average work, obtained from the joint probabilities in Eq. (16), is Tr[˘Hτ ˘ρ(τ)] − Tr[˘H0 ˘τβ^0]; with that definition the relative-entropy identity and the inequality do follow. Please correct Eq. (22) accordingly, or, if a different 'effective work' is intended, state explicitly that it is not the work measured in the TPM protocol and reconcile the text and numerics with that choice.
  2. [Secs. II C and III, Fig. 4] The text states that in the standard coarse-grained TPM the dissipative work and the relative entropy coincide. This is only true for the corrected work variable Tr[˘Hτ ˘ρ(τ)] − Tr[˘H0 ˘τβ^0], not for the work variable printed in Eq. (22). Since Fig. 4 is the main numerical evidence for the second-law-like relation, the authors must verify which quantity was actually plotted. If the plotted work used the final thermal state ˘τβ^τ, the claimed equality cannot hold for the non-commuting drive of Sec. II C; if it used the evolved state ˘ρ(τ), then Eq. (22) must be corrected to match.
minor comments (5)
  1. [Eq. (26)] The notation ˘~P_{I,J} should be ˘˜P_{I,J} for consistency with Eq. (19).
  2. [Eq. (26)] The first equality in Eq. (26) skips the micro-reversibility identity for the transition probabilities and the cancellation of the N_J factors; please add a one-line derivation so that the displayed relation is transparent.
  3. [Sec. II C and Fig. 4] The driving-force range is inconsistent: the main text says f∈[0,5], the Fig. 4 caption says f∈[0,9.5], and the discussion below Fig. 4 refers to f∈[0,6] and f>7.
  4. [Appendix B, Eq. (B3)] The bound in Eq. (A5) is said to be proven in Appendix B, but the proof in Eq. (B3) is written for ∆E_C = Tr[HC(ρ)] − Tr[Hρ]; please make explicit that the relevant case is ρ=τβ, for which ∆E_C = Tr[H˘τβ] − Tr[Hτβ].
  5. [Sec. I, Eq. (7)] The symbol 1_J used after Eq. (7) is not defined; please state that it is the identity operator on the support of Π_J.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: coarse-grained energies are fixed by a consistency condition, not fitted to the fluctuation theorems; the printed Eq. (22) has an algebraic mismatch that is a correctness issue rather than a circular step.

full rationale

The central derivation is not circular. The coarse-grained energies E_J are fixed by the consistency condition C(τβ+δτ)=τ̄β (Eq. (9)), which is physically motivated in Appendix A by the impossibility of work extraction from a single bath; solving Eq. (9) gives E_J=-k_BT log(Z_J/N_J) (Eq. (11)). This is a construction, but it is not fitted to reproduce the fluctuation theorems: the Crooks relation (27) follows from micro-reversibility (26) together with the Gibbs form of the outcome probabilities p_I=e^{-βE_I}N_I/Z (Eqs. (10) and (15)), which are consequences of that same consistency condition. The derivation is algebraically self-contained and does not invoke any self-citation as load-bearing evidence. The external citations (Refs. [4,5,29,30]) supply the fine-grained TPM background and micro-reversibility, not the coarse-grained result. There is, however, a non-circular mathematical issue in Eq. (22): the displayed derivation combines Eq. (21b), which contains Tr[Ĥτ ρ̄(τ)], with a work definition ⟨W̄⟩=Tr[Ĥτ τ̄β^τ]-Tr[Ĥ0 τ̄β^0]. These match only if Tr[Ĥτ ρ̄(τ)]=Tr[Ĥτ τ̄β^τ], which is not true for a generic non-equilibrium final state; the inequality that follows from Eqs. (20)-(21) is for the actual coarse-grained TPM work Tr[Ĥτ ρ̄(τ)]-Tr[Ĥ0 τ̄β^0]. This is a correctness/consistency flaw in the printed algebra, not a circular reduction of the conclusion to its input. The paper also explicitly flags limitations (Sec. V non-invasive scheme; Sec. VI POVM coarse-graining) that do not affect the orthogonal measure-and-reprepare framework. Overall, no circular step is exhibited; score 0.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The paper introduces a coarse-grained Hamiltonian ˘H with temperature-dependent eigenvalues E_J(T) as an effective observable for a limited-resolution observer. This is a bookkeeping device rather than a new physical entity; no new particles, forces, or dimensions are postulated. The central results rest on standard quantum thermodynamics plus the consistency condition listed as an axiom.

free parameters (1)
  • Coarse-graining resolution δϵ = δϵ = α|ε1-ε0| with α = 2, 3, 4 in the case study (Fig. 4)
    The resolution is an input of the observer model, not fitted to data. The central results hold for arbitrary δϵ, so this parameter does not determine the form of the laws.
assumptions (5)
  • domain assumption Maximum entropy principle: the state assigned under coarse-grained energy constraints is the one maximizing von Neumann entropy.
    Invoked in Sec. I to derive the fine-grained Gibbs state (Eq. 3) and the coarse-grained thermal state (Eq. 6). It is a standard principle of statistical inference, not proved in the paper.
  • standard math Micro-reversibility for non-autonomous systems: Θ†U(τ-t,0)Θ = U†(τ,t) for the forward and time-reversed protocols.
    Used in Eq. (20) and in deriving the ratio of forward and backward joint probabilities in Eq. (26); standard in quantum fluctuation theorem literature [29].
  • domain assumption Initial and final Hamiltonians are time-reversal invariant ([H0,Θ]=[Hτ,Θ]=0).
    Stated in footnote 5 as a simplifying assumption; the authors note it can be relaxed by using the inverted thermal state as the backward initial condition.
  • domain assumption The reservoir thermalizes all fine-grained degrees of freedom (ergodicity).
    Assumed in Appendix A, footnote 9, so that the fine-grained agent correctly assigns the thermal state τβ to a system in contact with a bath; needed for the free-energy benchmark.
  • ad hoc to paper Consistency condition C(τβ+δτ)=˘τβ (Eq. 9), fixing the coarse-grained energies E_J=-k_BT log(Z_J/N_J) (Eq. 11).
    This is the load-bearing modeling assumption introduced by the authors. It guarantees the coarse-grained thermal state equals the coarse-graining of the fine-grained one, and it is what makes the derived second-law and Crooks relations take their simple form. The paper argues in Appendix A that it is implied by the second law, but it is not a standard background result.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Coarse-grained quantum thermodynamics: Observation-dependent quantities, observation-independent laws." pith.science (2026). https://pith.science/paper/JK6PT4VB

@misc{pith2026250715918,
  author       = {Pith},
  title        = {Pith review of: Coarse-grained quantum thermodynamics: Observation-dependent quantities, observation-independent laws},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JK6PT4VB}},
  note         = {Machine review of arXiv:2507.15918}
}
read the original abstract

In both classical and quantum thermodynamics, physical quantities are typically assigned objective values defined independently of our observations. We then refer to the 'work performed by a gas', or the 'entropy of the gas', regardless of how they are evaluated. Here, we question this conception in the context of quantum thermodynamics, estimating how the definition of pivotal thermodynamic quantities is affected by experimental instruments of limited precision. We find that the coarse-grained thermodynamic quantities frequently lead to different conclusions from those drawn in fine-grained scenarios. For instance, the irreversibility of a process, or its work payoff, can significantly vary with the instrument precision. We show nonetheless that coarse-grained thermodynamic quantities satisfy the same relations (i.e., the second law inequality, the relation between dissipation and distinguishability of a process from its time-reverse, and the quantum work fluctuation theorems) as their fine-grained counterparts. These results highlight the observation-independence of relations linking thermodynamic quantities which are themselves observation-dependent.

Discussion (0). Sign in 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. Equilibration of generalized subsystems: a quantum-channel approach

    quant-ph 2026-06 unverdicted novelty 7.0 of 10

    Generalized subsystems defined as quantum-channel outputs equilibrate when their dimension is small relative to the effective dimension of discarded microscopic information, with the bound holding for typical initial ...

Reference graph

Works this paper leans on

77 extracted references · 64 canonical work pages · cited by 1 Pith paper

  1. [1]

    H. S. Leff and A. F. Rex,Maxwell’s Demon 2: Entropy, Infor- mation, Computing(Princeton University Press, 2002)

    work page 2002

  2. [2]

    J. M. R. Parrondo, J. M. Horowitz, and T. Sagawa, Thermody- namics of information, Nat. Phys.11, 131 (2015)

    work page 2015

  3. [3]

    Goold, M

    J. Goold, M. Huber, A. Riera, L. del Rio, and P. Skrzypczyk, The role of quantum information in thermodynamics—a topical review, Journal of Physics A: Mathematical and Theoretical49, 143001 (2016)

    work page 2016

  4. [4]

    Kawai, J

    R. Kawai, J. M. R. Parrondo, and C. V . den Broeck, Dissipa- tion: The phase-space perspective, Phys. Rev. Lett.98, 080602 (2007)

    work page 2007

  5. [5]

    J. M. R. Parrondo, C. V . den Broeck, and R. Kawai, Entropy production and the arrow of time, New Journal of Physics11, 073008 (2009)

    work page 2009

  6. [6]

    Horowitz and C

    J. Horowitz and C. Jarzynski, Illustrative example of the rela- tionship between dissipation and relative entropy, Phys. Rev. E 79, 021106 (2009)

    work page 2009

  7. [7]

    Rahav and C

    S. Rahav and C. Jarzynski, Fluctuation relations and coarse- graining, Journal of Statistical Mechanics: Theory and Experi- ment2007, P09012 (2007). 13

    work page 2007

  8. [8]

    Gomez-Marin, J

    A. Gomez-Marin, J. M. R. Parrondo, and C. Van den Broeck, Lower bounds on dissipation upon coarse graining, Phys. Rev. E78, 011107 (2008)

    work page 2008

Show all 77 references
  1. [9]

    Puglisi, S

    A. Puglisi, S. Pigolotti, L. Rondoni, and A. Vulpiani, Entropy production and coarse graining in markov processes, Journal of Statistical Mechanics: Theory and Experiment2010, 05015 (2010)

    2010

  2. [10]

    Esposito, Stochastic thermodynamics under coarse graining, Phys

    M. Esposito, Stochastic thermodynamics under coarse graining, Phys. Rev. E85, 041125 (2012)

    2012

  3. [11]

    Altaner and J

    B. Altaner and J. V ollmer, Fluctuation-preserving coarse grain- ing for biochemical systems, Phys. Rev. Lett.108, 228101 (2012)

    2012

  4. [12]

    Esposito and J

    M. Esposito and J. M. R. Parrondo, Stochastic thermodynamics of hidden pumps, Phys. Rev. E91, 052114 (2015)

    2015

  5. [13]

    Bo and A

    S. Bo and A. Celani, Multiple-scale stochastic processes: Deci- mation, averaging and beyond, Physics Reports670, 1 (2017), multiple-scale stochastic processes: decimation, averaging and beyond

    2017

  6. [14]

    Seifert, From stochastic thermodynamics to thermodynamic inference, Annual Review of Condensed Matter Physics10, 171 (2019)

    U. Seifert, From stochastic thermodynamics to thermodynamic inference, Annual Review of Condensed Matter Physics10, 171 (2019)

    2019

  7. [15]

    Shiraishi and T

    N. Shiraishi and T. Sagawa, Fluctuation theorem for partially masked nonequilibrium dynamics, Phys. Rev. E91, 012130 (2015)

    2015

  8. [16]

    Polettini and M

    M. Polettini and M. Esposito, Effective thermodynamics for a marginal observer, Phys. Rev. Lett.119, 240601 (2017)

    2017

  9. [17]

    Bisker, M

    G. Bisker, M. Polettini, T. R. Gingrich, and J. M. Horowitz, Hierarchical bounds on entropy production inferred from par- tial information, Journal of Statistical Mechanics: Theory and Experiment2017, 093210 (2017)

    2017

  10. [18]

    Manzano, G

    G. Manzano, G. Kardes ¸, E. Rold´an, and D. H. Wolpert, Ther- modynamics of computations with absolute irreversibility, uni- directional transitions, and stochastic computation times, Phys. Rev. X14, 021026 (2024)

    2024

  11. [19]

    Ferri-Cort ´es, J

    M. Ferri-Cort ´es, J. A. Almanza-Marrero, R. L ´opez, R. Zam- brini, and G. Manzano, Conditional fluctuation theorems and entropy production for monitored quantum systems under im- perfect detection, Phys. Rev. Res.7, 013077 (2025)

    2025

  12. [20]

    von Neumann, Proof of the ergodic theorem and the h- theorem in quantum mechanics, European Phys

    J. von Neumann, Proof of the ergodic theorem and the h- theorem in quantum mechanics, European Phys. J. H35, 201 (2010), german original in Zeitschrift fuer Physik 57: 30-70 (1929)

    2010

  13. [21]

    Busch and R

    P. Busch and R. Quadt, Concepts of coarse graining in quan- tum mechanics, International Journal of Theoretical Physics32, 2261 (1993)

    1993

  14. [22]

    ˇSafr´anek, J

    D. ˇSafr´anek, J. M. Deutsch, and A. Aguirre, Quantum coarse- grained entropy and thermodynamics, Phys. Rev. A99, 010101 (2019)

    2019

  15. [23]

    ˇSafr´anek, J

    D. ˇSafr´anek, J. M. Deutsch, and A. Aguirre, Quantum coarse- grained entropy and thermalization in closed systems, Phys. Rev. A99, 012103 (2019)

    2019

  16. [24]

    Buscemi, J

    F. Buscemi, J. Schindler, and D. ˇSafr´anek, Observational entropy, coarse-grained states, and the petz recovery map: information-theoretic properties and bounds, New Journal of Physics25, 053002 (2023)

    2023

  17. [25]

    Strasberg and J

    P. Strasberg and J. Schindler, Comparative microscopic study of entropies and their production, SciPost Phys.17, 143 (2024)

    2024

  18. [26]

    Nagasawa, K

    T. Nagasawa, K. Kato, E. Wakakuwa, and F. Buscemi, Generic increase of observational entropy in isolated systems, Phys. Rev. Res.6, 043327 (2024)

    2024

  19. [27]

    Schindler, P

    J. Schindler, P. Strasberg, N. Galke, A. Winter, and M. G. Jab- bour, Unification of observational entropy with maximum en- tropy principles (2025), arXiv:2503.15612 [quant-ph]

    2025 arXiv

  20. [28]

    Meier, T

    F. Meier, T. Rivlin, T. Debarba, J. Xuereb, M. Huber, and M. P. Lock, Emergence of a second law of thermodynamics in iso- lated quantum systems, PRX Quantum6, 010309 (2025)

    2025

  21. [29]

    Campisi, P

    M. Campisi, P. H ¨anggi, and P. Talkner, Colloquium: Quantum fluctuation relations: Foundations and applications, Rev. Mod. Phys.83, 771 (2011)

    2011

  22. [30]

    Esposito, U

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

    2009

  23. [31]

    Szilard, ¨uber die entropieverminderung in einem thermody- namischen system bei eingriffen intelligenter wesen, Zeitschrift f¨ur Physik53, 840 (1929)

    L. Szilard, ¨uber die entropieverminderung in einem thermody- namischen system bei eingriffen intelligenter wesen, Zeitschrift f¨ur Physik53, 840 (1929)

    1929

  24. [32]

    Landauer, Irreversibility and heat generation in the comput- ing process, IBM Journal of Research and Development5, 183 (1961)

    R. Landauer, Irreversibility and heat generation in the comput- ing process, IBM Journal of Research and Development5, 183 (1961)

    1961

  25. [33]

    C. H. Bennett, The thermodynamics of computation—a review, International Journal of Theoretical Physics21, 905 (1982)

    1982

  26. [34]

    E. T. Jaynes, Information theory and statistical mechanics, Phys. Rev.106, 620 (1957)

    1957

  27. [35]

    E. T. Jaynes, Information theory and statistical mechanics. ii, Phys. Rev.108, 171 (1957)

    1957

  28. [36]

    Guryanova, S

    Y . Guryanova, S. Popescu, A. J. Short, R. Silva, and P. Skrzypczyk, Thermodynamics of quantum systems with mul- tiple conserved quantities, Nature Communications7, 12049 (2016)

    2016

  29. [37]

    Yunger Halpern, P

    N. Yunger Halpern, P. Faist, J. Oppenheim, and A. Winter, Mi- crocanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges, Nature Communications7, 1 (2016), arXiv:1512.01189

    2016 arXiv

  30. [38]

    H. B. Callen,Thermodynamics and an introduction to Thermo- statistics(Jonh Willey and Sons, 1985) second Ed

    1985

  31. [39]

    Maes and K

    C. Maes and K. Neto ˇcn´y, Time-reversal and entropy, Journal of Statistical Physics110, 269–310 (2003)

    2003

  32. [40]

    T. Sagawa, Second law-like inequalities with quantum relative entropy: An introduction, inLectures on Quantum Computing, Thermodynamics and Statistical Physics(World Scientific Pub- lishing, 2012) pp. 125–190

    2012

  33. [41]

    Gaveau, L

    B. Gaveau, L. Granger, M. Moreau, and L. S. Schulman, Dis- sipation, interaction, and relative entropy, Phys. Rev. E89, 032107 (2014)

    2014

  34. [42]

    C. Jarzynski, Equalities and inequalities: Irreversibility and the second law of thermodynamics at the nanoscale, An- nual Review of Condensed Matter Physics2, 329 (2011), 14 https://doi.org/10.1146/annurev-conmatphys-062910-140506

    2011 doi

  35. [43]

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

    1999

  36. [44]

    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

  37. [45]

    Liphardt, S

    J. Liphardt, S. Dumont, S. B. Smith, I. Tinoco, and C. Bustamante, Equilibrium information from nonequilibrium measurements in an experimental test of jarzynski’s equality, Science296, 1832 (2002), https://science.sciencemag.org/content/296/5574/1832.full.pdf

    2002

  38. [46]

    Collin, F

    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, Nature437, 231 (2005)

    2005

  39. [47]

    Itano, J

    W. Itano, J. Bergquist, J. Bollinger, J. Gilligan, D. Heinzen, F. Moore, M. Raizen, and D. Wineland, Quantum measure- ments of trapped ions, Vistas in Astronomy37, 169 (1993)

    1993

  40. [48]

    Keselman, Y

    A. Keselman, Y . Glickman, N. Akerman, S. Kotler, and R. Oz- eri, High-fidelity state detection and tomography of a single-ion zeeman qubit, New Journal of Physics13, 073027 (2011)

    2011

  41. [49]

    Zhang, Y

    J. Zhang, Y . xi Liu, R.-B. Wu, K. Jacobs, and F. Nori, Quan- tum feedback: Theory, experiments, and applications, Physics Reports679, 1 (2017)

    2017

  42. [50]

    A. E. Rastegin, Non-equilibrium equalities with unital quantum channels, Journal of Statistical Mechanics: Theory and Experi- ment2013, P06016 (2013)

    2013

  43. [51]

    Albash, D

    T. Albash, D. A. Lidar, M. Marvian, and P. Zanardi, Fluctua- tion theorems for quantum processes, Phys. Rev. E88, 032146 (2013)

    2013

  44. [52]

    A. E. Rastegin and K. ˙Zyczkowski, Jarzynski equality for quan- tum stochastic maps, Phys. Rev. E89, 012127 (2014)

    2014

  45. [53]

    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

  46. [54]

    Debarba, G

    T. Debarba, G. Manzano, Y . Guryanova, M. Huber, and N. Friis, Work estimation and work fluctuations in the presence of non-ideal measurements, New Journal of Physics21, 113002 (2019)

    2019

  47. [55]

    K. Ito, P. Talkner, B. P. Venkatesh, and G. Watanabe, General- ized energy measurements and quantum work compatible with fluctuation theorems, Phys. Rev. A99, 032117 (2019)

    2019

  48. [56]

    Guryanova, N

    Y . Guryanova, N. Friis, and M. Huber, Ideal Projective Mea- surements Have Infinite Resource Costs, Quantum4, 222 (2020)

    2020

  49. [57]

    Taranto, F

    P. Taranto, F. Bakhshinezhad, A. Bluhm, R. Silva, N. Friis, M. P. Lock, G. Vitagliano, F. C. Binder, T. Debarba, E. Schwarzhans, F. Clivaz, and M. Huber, Landauer versus nernst: What is the true cost of cooling a quantum system?, PRX Quantum4, 010332 (2023)

    2023

  50. [58]

    Rubino, CG-QThermo (2026), gitHub repository

    G. Rubino, CG-QThermo (2026), gitHub repository

    2026

  51. [59]

    Landauer, Information is physical, Physics Today44, 23 (1991)

    R. Landauer, Information is physical, Physics Today44, 23 (1991)

    1991

  52. [60]

    Maruyama, F

    K. Maruyama, F. Nori, and V . Vedral, Colloquium: The physics of maxwell’s demon and information, Rev. Mod. Phys.81, 1 (2009)

    2009

  53. [61]

    Kammerlander and J

    P. Kammerlander and J. Anders, Coherence and measurement in quantum thermodynamics, Sci. Rep.6, 22174 (2016)

    2016

  54. [62]

    Skrzypczyk, A

    P. Skrzypczyk, A. J. Short, and S. Popescu, Work extraction and thermodynamics for individual quantum systems, Nat. Com- mun.5, 4185 (2014)

    2014

  55. [63]

    Vedral, The role of relative entropy in quantum information theory, Rev

    V . Vedral, The role of relative entropy in quantum information theory, Rev. Mod. Phys.74, 197 (2002)

    2002

  56. [64]

    Takara, H.-H

    K. Takara, H.-H. Hasegawa, and D. Driebe, Generalization of the second law for a transition between nonequilibrium states, Physics Letters A375, 88 (2010)

    2010

  57. [65]

    Esposito and C

    M. Esposito and C. V . den Broeck, Second law and landauer principle far from equilibrium, EPL (Europhysics Letters)95, 40004 (2011)

    2011

  58. [66]

    Anders and V

    J. Anders and V . Giovannetti, Thermodynamics of discrete quantum processes, New Journal of Physics15, 033022 (2013)

    2013

  59. [67]

    Manzano, F

    G. Manzano, F. Plastina, and R. Zambrini, Optimal work ex- traction and thermodynamics of quantum measurements and correlations, Phys. Rev. Lett.121, 120602 (2018)

    2018

  60. [68]

    Z. R. Gong, H. Ian, Y .-x. Liu, C. P. Sun, and F. Nori, Effec- tive hamiltonian approach to the kerr nonlinearity in an optome- chanical system, Phys. Rev. A80, 065801 (2009)

    2009

  61. [69]

    Kerr, Xl

    J. Kerr, Xl. a new relation between electricity and light: Dielec- trified media birefringent, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science50, 337 (1875), https://doi.org/10.1080/14786447508641302

    doi

  62. [70]

    Lostaglio, D

    M. Lostaglio, D. Jennings, and T. Rudolph, Description of quantum coherence in thermodynamic processes requires con- straints beyond free energy, Nature Communications6, 6383 (2015)

    2015

  63. [71]

    Scandi, H

    M. Scandi, H. J. D. Miller, J. Anders, and M. Perarnau-Llobet, Quantum work statistics close to equilibrium, Phys. Rev. Res. 2, 023377 (2020)

    2020

  64. [72]

    Kwon and M

    H. Kwon and M. S. Kim, Fluctuation theorems for a quantum channel, Phys. Rev. X9, 031029 (2019)

    2019

  65. [73]

    ˚Aberg, Fully quantum fluctuation theorems, Phys

    J. ˚Aberg, Fully quantum fluctuation theorems, Phys. Rev. X8, 011019 (2018)

    2018

  66. [74]

    Manzano, J

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

    2018

  67. [75]

    Alicki, The quantum open system as a model of the heat engine, Journal of Physics A: Mathematical and General12, L103 (1979)

    R. Alicki, The quantum open system as a model of the heat engine, Journal of Physics A: Mathematical and General12, L103 (1979). APPENDIX A. COARSE-GRAINING AND INFORMATION THERMODYNAMICS In modern approaches to thermodynamics, the second law is considered as a consequence of ...

    1979

  68. [76]

    ergodicity

    Extracting work using fine-grained information Let us now consider two agents,CandF, equipped with in- struments of differing energy resolution. The coarse-grained agentC, whose instruments have limited precision, models the system using the coarse-grained Hamiltonian ˘Hdefine...

  69. [77]

    In particular, we have seen that a positive amount of work can be extracted by agentFby transforming˘τ β intoτ β

    Free energy loss from coarse-graining and work cost In the above, we have seen that access to fine-grained de- grees of freedom can increase one’s ability to extract work. In particular, we have seen that a positive amount of work can be extracted by agentFby transforming˘τ β ...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.