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Quantum stochastic thermodynamics of macroscopic systems: an algebraic approach

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Pith's one-line read A tunable algebra of few observables yields second laws, fluctuation theorems, and heat/work that unify macroscopic and quantum stochastic thermodynamics without the full density matrix.

desk verdict Solid algebraic extension of observational entropy that actually delivers second laws, FTs, and heat/work with explicit internal-resource corrections; usable toolbox if you accept the scale-divisibility premise. read the letter →

arxiv 2607.09242 v1 pith:ZEKEO5EV submitted 2026-07-10 quant-ph

Antoine Rignon-Bret , Cyril Elouard This is my paper · ORCID
classification quant-ph PACS 05.70.Ln03.65.Yz05.30.-d03.67.-a
keywords quantumthermodynamicsobservationalentropyvonNeumannalgebracoarse-grainingfluctuationtheoremsstochasticheatandworkinternalequilibrium
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 builds a thermodynamic description for large quantum systems that only needs the statistics of a few accessible observables, not the full density matrix. Those observables define a subalgebra; Jaynes maximization then produces a coarse-grained state and an algebra-dependent entropy that sits between von Neumann entropy (no coarse-graining) and observational/Boltzmann entropy (classical macrostates). Given initial and final measurement schemes linked by unitary or open dynamics, this entropy obeys a second law whose usual positive-entropy-production form holds when the ignored degrees of freedom start at internal equilibrium (or do not back-act on the macro-dynamics); otherwise explicit correction terms quantify the hidden resources. Fluctuation theorems constrain the stochastic coarse-grained quantities, and along quasi-static paths of measurement schemes the authors extract heat and work increments that satisfy the first and second laws, including work paid to change the accessible algebra itself via constraints or measurement back-action. The framework is meant to let experimentalists and theorists dial the level of coarse-graining until the thermodynamic laws become useful for many-body or field systems that cannot be fully tomographed.

What carries the argument

Algebra-dependent coarse-grained entropy S_A(ρ): the von Neumann entropy of the Jaynes/Petz state that maximizes entropy subject to the expectation values of all operators in a chosen type-I von Neumann subalgebra A; it interpolates between observational entropy (commutative case) and full von Neumann entropy and is the quantity that enters every second law and fluctuation theorem.

What would settle it

In a many-body or waveguide-emitter experiment, choose two different accessible algebras (e.g., single temporal modes versus a long wave-train) and check whether measured entropy production, heat, and work match the paper’s predicted algebra dependence and whether the I_int correction remains negligible once the system has locally equilibrated.

Watch

Extended reading notes

Core claim

Given initial and final accessible subalgebras connected by internal or environment-induced dynamics, the algebra-dependent coarse-grained entropy obeys a second law of the form ΔS_A − Δ⟨K⟩ ≥ −I_ext − I_int (and autonomous mutual-information variants). When the system starts at internal equilibrium relative to the algebra, or the dynamics is scale-divisible, the corrections vanish and one recovers ordinary positive entropy production; fluctuation theorems and quasi-static heat/work definitions, including work from algebra manipulation, follow in the same setting.

Load-bearing premise

The usual Clausius form of the second law holds only when ignored internal degrees of freedom are already at equilibrium with respect to the chosen algebra, or their dynamics never feeds back onto the observables one tracks; otherwise the correction term can dominate and the simple inequality fails.

Editorial extensions

If this is right

  • Thermodynamic analysis of many-body systems and fields becomes possible from partial tomography of a few observables rather than full state reconstruction.
  • Changing the measurement basis or the set of accessible operators appears as an explicit work contribution, so measurement back-action and external constraints enter the first law on equal footing with driving.
  • Fluctuation theorems for coarse-grained heat remain valid with imperfect or noisy environment monitoring, extending stochastic thermodynamics to larger systems.
  • Apparent second-law violations diagnose either residual internal nonequilibrium or information back-flow from ignored degrees of freedom, and are quantified by I_int.
  • Different observers with different measurement capabilities obtain different thermodynamic balances, making thermodynamics explicitly observer- and algebra-dependent.

Reading between the lines

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

  • The same algebraic entropy and scale-divisibility condition could be used to decide, for a given many-body Hamiltonian, the coarsest measurement set that still yields a useful second law, turning equilibration theorems into operational design rules.
  • Extending the construction from type-I to type-II/III algebras would give a thermodynamic reading of entanglement across horizons or compact regions in quantum field theory without requiring a density matrix.
  • In quantum engines or batteries built from many-body working media, the algebra-manipulation work term may set a lower bound on the cost of continuous weak monitoring needed to keep the machine on a designed thermodynamic cycle.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 4 minor

Summary. The manuscript constructs a thermodynamic framework for macroscopic quantum systems based on accessible subalgebras of observables rather than the full density operator. For commutative algebras generated by projective measurements it recovers observational entropy; for general type-I von Neumann subalgebras it defines an algebra-dependent entropy via Jaynes maximization (Eqs. 2.19–2.22) that interpolates between von Neumann and observational entropies. From two-point measurements connected by open or autonomous dynamics it derives a second law of the form ΔS_A − Δ⟨K⟩ ≥ −I_ext − I_int (Eqs. 3.8, 5.5) and autonomous mutual-information variants, together with integral fluctuation theorems. Along continuous unitary paths of algebras it identifies heat and work increments (including work from algebra manipulation) that satisfy first and second laws. Appendices supply proofs, a Maxwell-demon toy model, and worked examples (qubit, spontaneous emission, waveguide emitter).

Significance. If the inequalities hold as stated, the work supplies a tunable, measurement-based bridge between macroscopic thermodynamics (observational/Boltzmann entropy, internal equilibration) and quantum stochastic thermodynamics (relative-entropy second laws, fluctuation theorems). The algebraic formulation cleanly unifies commutative and non-commutative coarse-grainings, makes the internal-equilibrium premise explicit via the correction I_int, and yields an experimentally natural work contribution from rotating the accessible algebra. Strengths include detailed Appendix-A proofs based on standard relative-entropy monotonicity under CPTP maps, explicit bounds after measurement back-action (Eq. 3.14), and concrete illustrations that different algebras produce different heat/work partitions. The framework is therefore a genuine methodological advance for analyzing large quantum systems with limited observables.

minor comments (4)
  1. Several figures (Fig. 1, Fig. 3, Fig. 4) are referenced with useful conceptual content but would benefit from slightly more self-contained captions that restate the key maps (C, Petz recovery, connection A_i,f) without forcing the reader back into the main text.
  2. Notation for the modular Hamiltonian K and its representatives (K_i, K_f, K_t) is consistent but dense; a short notation table early in Sec. 3 would help readers navigating the open-system versus autonomous viewpoints.
  3. App. H sketches the POVM extension but leaves the general case for future work; a one-sentence pointer in the main text (Sec. 2.1) would clarify the present scope.
  4. Minor typos appear (e.g., “Exemple” in App. F title, occasional missing spaces around equations); a final proof-reading pass would polish the manuscript.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: second laws and fluctuation theorems follow from relative-entropy monotonicity under CPTP coarse-graining maps; heat/work are definitional identifications along quasi-static algebra paths, not fitted predictions.

full rationale

The paper constructs an algebra-dependent coarse-grained entropy via Jaynes maximization (or equivalently Petz recovery with uniform prior) under constraints of accessible observables (Eqs. 2.4, 2.19–2.22). The second-law inequalities (3.8, 5.5 and autonomous variants 3.20, 5.10) are obtained by applying monotonicity of relative entropy to the composed CPTP maps (coarse-graining + dynamics + connection/Petz), with proofs in App. A; the correction terms −I_ext − I_int are explicit and vanish under the stated internal-equilibrium or scale-divisibility assumptions (Sec. 2.3, Eq. 3.12), which are premises rather than hidden fits. Fluctuation theorems (3.42, 4.28, 5.36) follow from the usual forward/backward trajectory probability ratio with Petz time-reversal. Heat and work increments (4.12–4.13, 5.19–5.21) are identified by decomposing the modular Hamiltonian of the instantaneous fixed point in an orthogonal basis of the accessible algebra along a continuous path of unitarily related algebras; this is a definitional bookkeeping that unifies known quantum and macroscopic expressions, not a prediction forced by data fitting. Self-citations to observational entropy and open-system entropy production supply background definitions; they do not force the new inequalities or uniqueness of the framework. No fitted parameters enter the central claims, and no uniqueness theorem is imported to forbid alternatives. Score 1 reflects only ordinary background self-citation, not load-bearing circularity.

Assumptions & free parameters 0 free parameters · 7 assumptions · 4 invented entities

Central claims rest on standard quantum information tools (relative entropy monotonicity, CPTP maps, Petz recovery, type-I von Neumann structure) plus domain modeling choices: Jaynes maxent with uniform prior on inaccessible sectors, internal equilibrium or scale divisibility, existence of modular fixed points, and unitary continuous deformation of algebras preserving volumes. No free parameters are fitted to data. Invented entities are definitional constructs (algebra-dependent entropy, connection maps, scale divisibility), not new physical particles.

assumptions (7)
  • standard math Relative entropy is monotone under CPTP maps; used to prove all second-law inequalities.
    Invoked throughout Sec. 3–5 and App. A; standard QI fact.
  • standard math Type-I von Neumann subalgebras admit the block form ⊕_J B(H_J)⊗1_{H'_J} (up to unitary).
    Sec. 2.2, representation theorem [49,50]; restricts the framework to type I.
  • domain assumption Jaynes maximum-entropy principle with uniform (microcanonical) prior on inaccessible sectors defines ρ_cg_A and S_A.
    Eqs. (2.4), (2.19)–(2.20); alternative priors allowed in remarks but default is uniform.
  • domain assumption Internal equilibrium ρ=ρ_cg_A or scale divisibility of dynamics makes I_int vanish so the second law takes Clausius form.
    Sec. 2.3, Eq. (3.12); load-bearing for usual thermodynamic form.
  • domain assumption Open dynamics induced by initially factorized system-environment states is CPTP and admits a full-rank fixed point σ used as modular Hamiltonian reference.
    Sec. 3.1.1; existence assumed when maps are not CPTP.
  • ad hoc to paper Continuous algebra paths are unitary conjugations preserving projector ranks/volumes; heat/work defined only along such quasi-static paths.
    Sec. 4.1, Eq. (4.3)–(4.4); rank-changing coarse-graining left for future work.
  • domain assumption Positive effective temperature can be restored by reparametrizing modular Hamiltonian with chemical-potential-like terms (App. B).
    App. B; needed for thermodynamic interpretation of heat.
invented entities (4)
  • Algebra-dependent coarse-grained entropy S_A
    purpose: Interpolate between von Neumann and observational entropy for non-commutative accessible subalgebras.
    Defined via Jaynes under algebra constraints (2.19)–(2.22); related to prior algebraic entropy [51] but retains Boltzmann term for thermodynamics.
  • Scale-divisible dynamics
    purpose: Formalize absence of information backflow from ignored micro-degrees of freedom to accessible macro-observables.
    Eq. (3.12); algebraic analogue of CP-divisibility; not independently measured outside the framework.
  • Connection map A_{i,f} between final and initial algebras
    purpose: Define protocol-relative fixed points when initial and final measurement bases differ.
    Eqs. (3.4)–(3.5), (5.3); definitional for open-system equilibrium relative to the protocol.
  • Work contribution from algebra manipulation
    purpose: Account for energy change when constraints/measurement basis rotate the accessible algebra.
    Sec. 4.2.1, (4.6), (4.13); identified with measurement back-action / Zeno rotation energy; interpretation depends on framework.

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Cite this review

Pith. "Pith review of Quantum stochastic thermodynamics of macroscopic systems: an algebraic approach." pith.science (2026). https://pith.science/paper/ZEKEO5EV

@misc{pith2026260709242,
  author       = {Pith},
  title        = {Pith review of: Quantum stochastic thermodynamics of macroscopic systems: an algebraic approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZEKEO5EV}},
  note         = {Machine review of arXiv:2607.09242}
}
read the original abstract

We build a framework for the thermodynamics of macroscopic quantum systems. In contrast with approaches requiring access to the full density matrix, our framework relies on a coarse-grained description, based on measurement statistics of a few observables. When these observables commute, the outcomes define classical macrostates whose entropy is quantified by observational entropy, accounting for uncertainty about both the macrostate and the microstate within it. We extend this notion to non-commuting observables forming a subalgebra of the operator space, and use Jaynes' principle to define an algebra-dependent entropy interpolating between von Neumann and observational entropies. Given initial and final measurement sets, connected by internal and/or environment-induced dynamics, we derive a second law for the coarse-grained dynamics. Unlike formulations based on von Neumann entropy, our inequality captures irreversibility from both non-unitary environment-induced dynamics and internal equilibration. It takes the usual form of a positive entropy production when the system is initially at internal equilibrium, while correction terms capture nonequilibrium resources ignored by the coarse-graining. We also derive fluctuation theorems for coarse-grained thermodynamic quantities. Along a quasi-static path of measurement schemes, we identify quantum macroscopic notions of work and heat fulfilling the first and second laws, including an additional work contribution from manipulating the algebra to which the system is confined, through external constraints or quantum measurement backaction. Finally, we apply our framework to examples illustrating the impact of varying the coarse-graining scheme. Our approach unifies macroscopic and stochastic thermodynamics in a genuinely quantum framework, laying the basis for a versatile, experimentally friendly toolbox to analyze complex quantum dynamics.

Figures

Figures reproduced from arXiv: 2607.09242 by the authors.

Figure 1
Figure 1. a) Coarse-graining and macrostate. Accessing the system via a coarse measurement leads to a statistical mixture of macrostates |J⟩ ∈ H¯, each associated to a subspace of dimension VJ of the original system Hilbert space H associated to projector ΠJ (represented by a green shaded rectangle). The micro-macro map C maps a microstate from H onto the corresponding macrostate in H¯. The Petz recovery map PC,u, or equivale… view at source ↗
Figure 2
Figure 2. This diagram provides a visual representation of the framework. The vertical direction is [PITH_FULL_IMAGE:figures/full_fig_p020_2.png] view at source ↗
Figure 3
Figure 3. Thermodynamic analysis of a dissipative qubit: An arbitrary qubit state is conve￾niently represented by a vector ⃗r in the Bloch sphere. We assume that the dynamics of the qubit is ruled by a GKLS equation (described explicitly in App. (E), Eq. (E.8)) inducing thermalization. The latter generates a flow (indicated by the green arrows) driving any initial state towards the thermal fixed point σ at inverse temperature… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Application to an emitter coupled to a 1D propagating field. In the weak emitter￾field coupling regime, the situation can be mapped onto a collision model [80], where the total algebra of the electromagnetic field is decomposed into temporal modes (depicted as black sp…
Figure 4.2
Figure 4.2. Figure 4.2: figure 4.2.2, we have assumed that rates appearing in the GKLS equation verify [PITH_FULL_IMAGE:figures/full_fig_p062_4_2.png]

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Reference graph

Works this paper leans on

106 extracted references · 1 linked inside Pith

  1. [1]

    Callen.Thermodynamics and an Introduction to Thermostatistics, 2nd Edition

    Herbert B. Callen.Thermodynamics and an Introduction to Thermostatistics, 2nd Edition. Wi- ley, Hoboken, NJ, USA, January 1991

    1991

  2. [2]

    Boltzmann’sEntropyandTime’sArrow.PHYSICSTODAY,October2025

    J.Lebowitz. Boltzmann’sEntropyandTime’sArrow.PHYSICSTODAY,October2025. [Online; accessed 26. Jun. 2026]. 73

    2026

  3. [3]

    Stochastic Energetics

    Ken Sekimoto. Stochastic Energetics. Springer, Berlin, Germany, 2010

    2010

  4. [4]

    Stochastic thermodynamics, fluctuation theorems and molecular machines.Reports on Progress in Physics, 75(12):126001, November 2012

    Udo Seifert. Stochastic thermodynamics, fluctuation theorems and molecular machines.Reports on Progress in Physics, 75(12):126001, November 2012

    2012

  5. [5]

    R. Alicki. The quantum open system as a model of the heat engine. Journal of Physics A: Mathematical and General, 12(5):L103, May 1979

    1979

  6. [6]

    Entropy Production along a Stochastic Trajectory and an Integral Fluctuation Theorem

    Udo Seifert. Entropy Production along a Stochastic Trajectory and an Integral Fluctuation Theorem. Physical Review Letters, 95(4):040602, July 2005

    2005

  7. [7]

    Entropy production as correlation between system and reservoir.New Journal of Physics, 12(1):013013, January 2010

    Massimiliano Esposito, Katja Lindenberg, and Christian Van den Broeck. Entropy production as correlation between system and reservoir.New Journal of Physics, 12(1):013013, January 2010

    2010

  8. [8]

    Gallavotti and E

    G. Gallavotti and E. G. D. Cohen. Dynamical Ensembles in Nonequilibrium Statistical Mechan- ics. Physical Review Letters, 74(14):2694–2697, April 1995

    1995

Show all 106 references
  1. [9]

    Jarzynski

    C. Jarzynski. Nonequilibrium Equality for Free Energy Differences.Physical Review Letters, 78(14):2690–2693, April 1997

    1997

  2. [10]

    Gavin E. Crooks. Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences.Physical Review E, 60(3):2721–2726, September 1999

    1999

  3. [11]

    E. G. D. Cohen and G. Gallavotti. Note on Two Theorems in Nonequilibrium Statistical Me- chanics. Journal of Statistical Physics, 96(5):1343–1349, September 1999

    1999

  4. [12]

    A Quantum Fluctuation Theorem.ArXiv e-prints, July 2000

    Jorge Kurchan. A Quantum Fluctuation Theorem.ArXiv e-prints, July 2000

    2000

  5. [13]

    Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems.Reviews of Modern Physics, 81(4):1665–1702, December 2009

    Massimiliano Esposito, Upendra Harbola, and Shaul Mukamel. Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems.Reviews of Modern Physics, 81(4):1665–1702, December 2009

    2009

  6. [14]

    Colloquium: Quantum fluctuation relations: Foundations and applications.Reviews of Modern Physics, 83(3):771–791, July 2011

    Michele Campisi, Peter Hänggi, and Peter Talkner. Colloquium: Quantum fluctuation relations: Foundations and applications.Reviews of Modern Physics, 83(3):771–791, July 2011

    2011

  7. [15]

    Theroleofquantum measurement in stochastic thermodynamics.npj Quantum Information, 3(9):9, March 2017

    CyrilElouard, DavidA.Herrera-Martí, MaximeClusel, andAlexiaAuffèves. Theroleofquantum measurement in stochastic thermodynamics.npj Quantum Information, 3(9):9, March 2017

    2017

  8. [16]

    Horowitz, and Juan M

    Gonzalo Manzano, Jordan M. Horowitz, and Juan M. R. Parrondo. Quantum Fluctuation The- orems for Arbitrary Environments: Adiabatic and Nonadiabatic Entropy Production.Physical Review X, 8(3):031037, August 2018

    2018

  9. [17]

    J. M. Deutsch. Quantum statistical mechanics in a closed system.PhysicalReviewA, 43(4):2046– 2049, February 1991

  10. [18]

    Short, and Andreas Winter

    Noah Linden, Sandu Popescu, Anthony J. Short, and Andreas Winter. Quantum mechanical evolution towards thermal equilibrium.Physical Review E, 79(6):061103, June 2009

    2009

  11. [19]

    Anthony J. Short. Equilibration of quantum systems and subsystems.New Journal of Physics, 13(5):053009, May 2011. 74

    2011

  12. [20]

    Huse, Joel L

    Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, and Roderich Tumulka. Thermal equilib- rium of a macroscopic quantum system in a pure state.ArXiv e-prints, June 2015

    2015

  13. [21]

    Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.Reports on Progress in Physics, 79(5):056001, April 2016

    Christian Gogolin and Jens Eisert. Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.Reports on Progress in Physics, 79(5):056001, April 2016

    2016

  14. [22]

    Observing a quantum Maxwell demon at work.Proceedings of the National Academyof Sciences, 114(29):7561–7564, July 2017

    Nathanaël Cottet, Sébastien Jezouin, Landry Bretheau, Philippe Campagne-Ibarcq, Quentin Ficheux, Janet Anders, Alexia Auffèves, Rémi Azouit, Pierre Rouchon, and Benjamin Huard. Observing a quantum Maxwell demon at work.Proceedings of the National Academyof Sciences, 114(29):75...

    2017

  15. [23]

    L. L. Yan, T. P. Xiong, K. Rehan, F. Zhou, D. F. Liang, L. Chen, J. Q. Zhang, W. L. Yang, Z. H. Ma, and M. Feng. Single-Atom Demonstration of the Quantum Landauer Principle.Physical Review Letters, 120(21):210601, May 2018

    2018

  16. [24]

    John P. S. Peterson, Tiago B. Batalhão, Marcela Herrera, Alexandre M. Souza, Roberto S. Sarthour, Ivan S. Oliveira, and Roberto M. Serra. Experimental Characterization of a Spin Quantum Heat Engine.Physical Review Letters, 123(24):240601, December 2019

    2019

  17. [25]

    von Lindenfels, O

    D. von Lindenfels, O. Gräb, C. T. Schmiegelow, V. Kaushal, J. Schulz, Mark T. Mitchison, John Goold, F. Schmidt-Kaler, and U. G. Poschinger. Spin Heat Engine Coupled to a Harmonic- Oscillator Flywheel. Physical Review Letters, 123(8):080602, August 2019

    2019

  18. [26]

    Becker, Patrick M

    James Klatzow, Jonas N. Becker, Patrick M. Ledingham, Christian Weinzetl, Krzysztof T. Kacz- marek, Dylan J. Saunders, Joshua Nunn, Ian A. Walmsley, Raam Uzdin, and Eilon Poem. Experimental Demonstration of Quantum Effects in the Operation of Microscopic Heat Engines. Physical...

    2019

  19. [27]

    Dassonneville, C

    R. Dassonneville, C. Elouard, R. Cazali, R. Assouly, A. Bienfait, A. Auffèves, and B. Huard. Am- plifying microwave pulses with a single qubit engine fueled by quantum measurements.Physical Review Research, 8(1):013228, March 2026

    2026

  20. [28]

    Batalhão, Alexandre M

    Tiago B. Batalhão, Alexandre M. Souza, Laura Mazzola, Ruben Auccaise, Roberto S. Sarthour, Ivan S. Oliveira, John Goold, Gabriele De Chiara, Mauro Paternostro, and Roberto M. Serra. Experimental Reconstruction of Work Distribution and Study of Fluctuation Relations in a Closed...

    2014

  21. [29]

    Shuoming An, Jing-Ning Zhang, Mark Um, Dingshun Lv, Yao Lu, Junhua Zhang, Zhang-Qi Yin, H. T. Quan, and Kihwan Kim. Experimental test of the quantum Jarzynski equality with a trapped-ion system.Nature Physics, 11:193–199, February 2015

    2015

  22. [30]

    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.Physical Review Letters, 121(3):030604, July 2018

    2018

  23. [31]

    Exper- imental test of fluctuation relations for driven open quantum systems with an NV center.New Journal of Physics, 23(6):065004, June 2021

    Santiago Hernández-Gómez, Nicolas Staudenmaier, Michele Campisi, and Nicole Fabbri. Exper- imental test of fluctuation relations for driven open quantum systems with an NV center.New Journal of Physics, 23(6):065004, June 2021

    2021

  24. [32]

    Onishchenko, G

    O. Onishchenko, G. Guarnieri, P. Rosillo-Rodes, D. Pijn, J. Hilder, U. G. Poschinger, M. Perarnau-Llobet, J. Eisert, and F. Schmidt-Kaler. Probing coherent quantum thermody- namics using a trapped ion.Nature Communications, 15(6974):6974, August 2024. 75

    2024

  25. [33]

    Quantum coarse-grained entropy and thermodynamics

    Dominik Šafránek, Joshua M Deutsch, and Anthony Aguirre. Quantum coarse-grained entropy and thermodynamics. Physical Review A, 99(1):010101, 2019

    2019

  26. [34]

    Quantum coarse-grained entropy and thermalization in closed systems.Physical Review A, 99(1):012103, 2019

    Dominik Šafránek, JM Deutsch, and Anthony Aguirre. Quantum coarse-grained entropy and thermalization in closed systems.Physical Review A, 99(1):012103, 2019

    2019

  27. [35]

    Dominik Šafránek, Anthony Aguirre, and J. M. Deutsch. Classical dynamical coarse-grained entropy and comparison with the quantum version.Physical Review E, 102(3):032106, 2020

    2020

  28. [36]

    A brief introduction to observational entropy.Foundationsof Physics, 51(5):101, 2021

    Dominik Šafránek, Anthony Aguirre, Joseph Schindler, and JM Deutsch. A brief introduction to observational entropy.Foundationsof Physics, 51(5):101, 2021

    2021

  29. [37]

    First and second law of quantum thermodynamics: A consistent derivation based on a microscopic definition of entropy.PRX Quantum, 2(3):030202, 2021

    Philipp Strasberg and Andreas Winter. First and second law of quantum thermodynamics: A consistent derivation based on a microscopic definition of entropy.PRX Quantum, 2(3):030202, 2021

    2021

  30. [38]

    Entropy production as change in observational entropy

    Philipp Strasberg. Entropy production as change in observational entropy. 8 2020

    2020

  31. [39]

    Observational entropy, coarse- grained states, and the petz recovery map: Information-theoretic properties and bounds.New Journal of Physics, 25(5):053002, 2023

    Francesco Buscemi, Joseph Schindler, and Dominik Šafránek. Observational entropy, coarse- grained states, and the petz recovery map: Information-theoretic properties and bounds.New Journal of Physics, 25(5):053002, 2023

    2023

  32. [40]

    Comparative microscopic study of entropies and their production

    Philipp Strasberg and Joseph Schindler. Comparative microscopic study of entropies and their production. SciPost Phys., 17(5):143, 2024

    2024

  33. [41]

    Joseph Schindler, Philipp Strasberg, Niklas Galke, Andreas Winter, and Michael G. Jabbour. Unification of observational entropy with maximum entropy principles. 3 2025

    2025

  34. [42]

    Coarse-grained quantum thermodynam- ics: Observation-dependent quantities, observation-independent laws.PhysicalReview Research, 8(2):023284, 2026

    Giulia Rubino, Časlav Brukner, and Gonzalo Manzano. Coarse-grained quantum thermodynam- ics: Observation-dependent quantities, observation-independent laws.PhysicalReview Research, 8(2):023284, 2026

    2026

  35. [43]

    Informationtheoryandstatisticalmechanics

    EdwinT.Jaynes. Informationtheoryandstatisticalmechanics. PhysicalReview, 106(4):620–630, 1957

    1957

  36. [44]

    General properties of entropy.Reviews of Modern Physics, 50(2):221–260, Apr 1978

    Alfred Wehrl. General properties of entropy.Reviews of Modern Physics, 50(2):221–260, Apr 1978

    1978

  37. [45]

    Sufficient subalgebras and the relative entropy of states of a von neumann algebra

    Dénes Petz. Sufficient subalgebras and the relative entropy of states of a von neumann algebra. Communications in Mathematical Physics, 105(1):123–131, 1986

    1986

  38. [46]

    Sufficiency of channels over von neumann algebras

    Dénes Petz. Sufficiency of channels over von neumann algebras. The Quarterly Journal of Mathematics, 39(1):97–108, 1988

    1988

  39. [47]

    Brief overview of the petz recovery map and its applications, 2023

    Owen Santoso. Brief overview of the petz recovery map and its applications, 2023. PHYS 213 final paper

    2023

  40. [48]

    Hamed Mohammady

    Cyril Elouard and M. Hamed Mohammady. Work, heat and entropy production along quantum trajectories. In Felix Binder, Luis A. Correa, Christian Gogolin, Janet Anders, and Gerardo Adesso, editors, Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, volu...

    2018

  41. [49]

    Theory of Operator Algebras I, volume 124 of Encyclopaedia of Mathematical Sciences

    Masamichi Takesaki. Theory of Operator Algebras I, volume 124 of Encyclopaedia of Mathematical Sciences. Springer, reprint of the first 1979 edition edition, 2002

    1979

  42. [50]

    Kadison and John R

    Richard V. Kadison and John R. Ringrose.Fundamentalsof the Theory of Operator Algebras. Volume II: Advanced Theory, volume 100 ofPure and Applied Mathematics. Academic Press, Orlando, FL, 1986

    1986

  43. [51]

    Entropy of quantum states.Entropy, 23(6):645, 2021

    Paolo Facchi, Giovanni Gramegna, and Arturo Konderak. Entropy of quantum states.Entropy, 23(6):645, 2021

    2021

  44. [52]

    Completely positive maps and entropy inequalities

    Göran Lindblad. Completely positive maps and entropy inequalities. Communications in Mathematical Physics, 40:147–151, 1975

    1975

  45. [53]

    Entropyproductionforquantumdynamicalsemigroups

    HerbertSpohn. Entropyproductionforquantumdynamicalsemigroups. JournalofMathematical Physics, 19(5):1227–1230, May 1978

    1978

  46. [54]

    Sufficient subalgebras and the relative entropy of states of a von Neumann algebra

    Dénes Petz. Sufficient subalgebras and the relative entropy of states of a von Neumann algebra. Communications in Mathematical Physics, 105(1):123–131, March 1986

    1986

  47. [55]

    Landi and Mauro Paternostro

    Gabriel T. Landi and Mauro Paternostro. Irreversible entropy production: From classical to quantum. Reviews of Modern Physics, 93(3):035008, September 2021

    2021

  48. [56]

    Cambridge University Press, 2018

    John Watrous.The Theory of Quantum Information. Cambridge University Press, 2018

    2018

  49. [57]

    Fixed points of completely positive trace-preserving maps in infinite dimension

    Roderich Tumulka and Jonte Weixler. Fixed points of completely positive trace-preserving maps in infinite dimension. 2024

    2024

  50. [58]

    Non-Markovianity and negative entropy produc- tion rates

    Philipp Strasberg and Massimiliano Esposito. Non-Markovianity and negative entropy produc- tion rates. Physical Review E, 99(1):012120, January 2019

    2019

  51. [59]

    Thermodynamic roles of quantum environments: from heat baths to work reservoirs.Quantum Science and Technology, 10(1):015047, 2025

    Alessandra Colla and Heinz-Peter Breuer. Thermodynamic roles of quantum environments: from heat baths to work reservoirs.Quantum Science and Technology, 10(1):015047, 2025

    2025

  52. [60]

    Local approach to entropy production in the nonequilibrium dynamics of open quantum systems.ArXiv e-prints, March 2026

    Irene Ada Picatoste, Alessandra Colla, and Heinz-Peter Breuer. Local approach to entropy production in the nonequilibrium dynamics of open quantum systems.ArXiv e-prints, March 2026

    2026

  53. [61]

    Guillaume Theret, Dominique Sugny, and Camille L. Latune. Entropy production versus memory effects in two-level open quantum systems. 2026

    2026

  54. [62]

    Fluctuation theorem with information exchange: Role of correlations in stochastic thermodynamics.Physical Review Letters, 109(18):180602, 2012

    Takahiro Sagawa and Masahito Ueda. Fluctuation theorem with information exchange: Role of correlations in stochastic thermodynamics.Physical Review Letters, 109(18):180602, 2012

    2012

  55. [63]

    Role of mutual information in entropy production under information exchanges.New Journal of Physics, 15(12):125012, 2013

    Takahiro Sagawa and Masahito Ueda. Role of mutual information in entropy production under information exchanges.New Journal of Physics, 15(12):125012, 2013

    2013

  56. [64]

    Juan M. R. Parrondo, Jordan M. Horowitz, and Takahiro Sagawa. Thermodynamics of informa- tion. Nature Physics, 11(2):131–139, 2015

    2015

  57. [65]

    Entanglement and the thermodynamic arrow of time

    David Jennings and Terry Rudolph. Entanglement and the thermodynamic arrow of time. Physical Review E, 81(6):061130, June 2010. 77

    2010

  58. [66]

    Horowitz and Massimiliano Esposito

    Jordan M. Horowitz and Massimiliano Esposito. Thermodynamics with Continuous Information Flow. Physical Review X, 4(3):031015, July 2014

    2014

  59. [67]

    Extending the Laws of Thermodynamics for Arbi- trary Autonomous Quantum Systems.PRX Quantum, 4(2):020309, 2023

    Cyril Elouard and Camille Lombard Latune. Extending the Laws of Thermodynamics for Arbi- trary Autonomous Quantum Systems.PRX Quantum, 4(2):020309, 2023

    2023

  60. [68]

    Horowitz and Massimiliano Esposito

    Jordan M. Horowitz and Massimiliano Esposito. Thermodynamics with continuous information flow. Physical Review X, 4(3):031015, 2014

    2014

  61. [69]

    Nonequilibrium equalities in absolutely irre- versible processes

    Yûto Murashita, Ken Funo, and Masahito Ueda. Nonequilibrium equalities in absolutely irre- versible processes. Physical Review E, 90(4):042110, 2014

    2014

  62. [70]

    Quantum nonequilibrium equalities with abso- lute irreversibility.New Journal of Physics, 17(7):075005, 2015

    Ken Funo, Yûto Murashita, and Masahito Ueda. Quantum nonequilibrium equalities with abso- lute irreversibility.New Journal of Physics, 17(7):075005, 2015

    2015

  63. [71]

    Relaxation in a com- pletely integrable many-body quantum system: An ab initio study of the dynamics of the highly excited states

    Marcos Rigol, Vanja Dunjko, Vladimir Yurovsky, and Maxim Olshanii. Relaxation in a com- pletely integrable many-body quantum system: An ab initio study of the dynamics of the highly excited states. Physical Review Letters, 98(5):050405, 2007

    2007

  64. [72]

    Horowitz and Massimiliano Esposito

    Jordan M. Horowitz and Massimiliano Esposito. Work producing reservoirs: Stochastic thermo- dynamics with generalized Gibbs ensembles.Physical Review E, 94(2):020102, August 2016

    2016

  65. [73]

    Generalized gibbs ensemble in integrable lattice models.Journal of Statistical Mechanics: Theory and Experiment, 2016(6):064007, 2016

    Lev Vidmar and Marcos Rigol. Generalized gibbs ensemble in integrable lattice models.Journal of Statistical Mechanics: Theory and Experiment, 2016(6):064007, 2016

    2016

  66. [74]

    Enej Ilievski, Jacopo De Nardis, Bram Wouters, Jean-Sébastien Caux, Fabian H. L. Essler, and Tomaž Prosen. Complete generalized gibbs ensembles in an interacting theory.Physical Review Letters, 115(15):157201, 2015

    2015

  67. [75]

    Fabian H. L. Essler, Giuseppe Mussardo, and Milosz Panfil. Generalized gibbs ensembles for quantum field theories.Physical Review A, 91(5):051602, 2015

    2015

  68. [76]

    Squeezed thermal reservoir as a generalized equilibrium reservoir.Physical Review E, 98(4):042123, October 2018

    Gonzalo Manzano. Squeezed thermal reservoir as a generalized equilibrium reservoir.Physical Review E, 98(4):042123, October 2018

    2018

  69. [77]

    Kouhei Fukai, Yuji Nozawa, Koji Kawahara, and Tatsuhiko N. Ikeda. Noncommutative gen- eralized gibbs ensemble in isolated integrable quantum systems. Physical Review Research, 2(3):033403, 2020

    2020

  70. [78]

    Giuliano Benenti, Giulio Casati, Keiji Saito, and Robert S. Whitney. Fundamental aspects of steady-state conversion of heat to work at the nanoscale.Physics Reports, 694:1–124, June 2017

    2017

  71. [79]

    Fundamental work cost of quantum processes

    Philippe Faist and Renato Renner. Fundamental work cost of quantum processes. Physical Review X, 8(2):021011, 2018

    2018

  72. [80]

    Camati, Cyril Elouard, and Alexia Auffeves

    Samyak Pratyush Prasad, Maria Maffei, Patrice A. Camati, Cyril Elouard, and Alexia Auffeves. Thermodynamics of autonomous optical bloch equations.SciPost Physics, 20(4):112, 2026

    2026

  73. [81]

    Wiseman and Gerard J

    Howard M. Wiseman and Gerard J. Milburn.Quantum Measurement and Control. Cambridge University Press, Cambridge, England, UK, November 2009. 78

    2009

  74. [82]

    K. W. Murch, S. J. Weber, C. Macklin, and I. Siddiqi. Observing single quantum trajectories of a superconducting quantum bit.Nature, 502:211–214, October 2013

    2013

  75. [83]

    Campagne-Ibarcq, P

    P. Campagne-Ibarcq, P. Six, L. Bretheau, A. Sarlette, M. Mirrahimi, P. Rouchon, and B. Huard. Observing Quantum State Diffusion by Heterodyne Detection of Fluorescence.Physical Review X, 6(1):011002, January 2016

    2016

  76. [84]

    Observing and Verifying the Quantum Trajectory of a Mechanical Resonator.Physical Review Letters, 123(16):163601, October 2019

    Massimiliano Rossi, David Mason, Junxin Chen, and Albert Schliesser. Observing and Verifying the Quantum Trajectory of a Mechanical Resonator.Physical Review Letters, 123(16):163601, October 2019

    2019

  77. [85]

    Contextual Unification of Classical and Quan- tum Physics.Found

    Mathias Van Den Bossche and Philippe Grangier. Contextual Unification of Classical and Quan- tum Physics.Found. Phys., 53(2):45, 2023

    2023

  78. [86]

    Postulating the Unicity of the Macroscopic Physical World.Entropy, 25(12):1600, 2023

    Mathias Van Den Bossche and Philippe Grangier. Postulating the Unicity of the Macroscopic Physical World.Entropy, 25(12):1600, 2023

    2023

  79. [87]

    Revisiting quantum contextuality in an al- gebraic framework

    Mathias Van Den Bossche and Philippe Grangier. Revisiting quantum contextuality in an al- gebraic framework. In Journal of Physics: Conference Series, volume 2533, page 012008. IOP Publishing, 2023

    2023

  80. [88]

    Heading towards an algebraic heisenberg cut

    Mathias Van Den Bossche and Philippe Grangier. Heading towards an algebraic heisenberg cut. arXiv preprint, arXiv:2412.16574, 2024

    2024 arXiv

  81. [89]

    Aron C. Wall. Ten Proofs of the Generalized Second Law.JHEP, 06:021, 2009

    2009

  82. [90]

    Aron C. Wall. A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices. Phys. Rev. D, 85:104049, 2012. [Erratum: Phys.Rev.D 87, 069904 (2013)]

    2012

  83. [91]

    An algebra of observables for de Sitter space.JHEP, 02:082, 2023

    Venkatesa Chandrasekaran, Roberto Longo, Geoff Penington, and Edward Witten. An algebra of observables for de Sitter space.JHEP, 02:082, 2023

    2023

  84. [92]

    Large N algebras and gener- alized entropy.JHEP, 04:009, 2023

    Venkatesa Chandrasekaran, Geoff Penington, and Edward Witten. Large N algebras and gener- alized entropy.JHEP, 04:009, 2023

    2023

  85. [93]

    Generalized black hole entropy is von Neumann entropy.Phys

    Jonah Kudler-Flam, Samuel Leutheusser, and Gautam Satishchandran. Generalized black hole entropy is von Neumann entropy.Phys. Rev. D, 111(2):025013, 2025

    2025

  86. [94]

    Speranza

    Kristan Jensen, Jonathan Sorce, and Antony J. Speranza. Generalized entropy for general sub- regions in quantum gravity.JHEP, 12:020, 2023

    2023

  87. [95]

    Speranza

    Thomas Faulkner and Antony J. Speranza. Gravitational algebras and the generalized second law. JHEP, 11:099, 2024

    2024

  88. [96]

    Black hole thermodynamic potentials for asymptotic observers.Phys.Rev

    Antoine Rignon-Bret. Black hole thermodynamic potentials for asymptotic observers.Phys.Rev. D, 110(12):124002, 2024

    2024

  89. [97]

    Black hole thermodynamics at null infinity

    Antoine Rignon-Bret and Matthieu Vilatte. Black hole thermodynamics at null infinity. Part 1: Dual Generalized Second Law. 1 2026

    2026

  90. [98]

    Black hole thermodynamics at null infinity

    Antoine Rignon-Bret and Matthieu Vilatte. Black hole thermodynamics at null infinity. Part 2: Open systems, Markovian dynamics and work extraction from non-rotating black holes. 1 2026. 79

    2026

  91. [99]

    The classical limit of quantum mechanics through coarse-grained measurements.ArXiv e-prints, March 2025

    Fatemeh Bibak, Carlo Cepollaro, Nicolás Medina Sánchez, Borivoje Dakić, and Časlav Brukner. The classical limit of quantum mechanics through coarse-grained measurements.ArXiv e-prints, March 2025

    2025

  92. [100]

    Itano, D

    Wayne M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland. Quantum zeno effect. Physical Review A, 41(5):2295–2300, 1990

    1990

  93. [101]

    Quantum zeno dynamics: Mathematical and physical aspects

    Paolo Facchi and Saverio Pascazio. Quantum zeno dynamics: Mathematical and physical aspects. Journal of Physics A: Mathematical and Theoretical, 41(49):493001, 2008

    2008

  94. [102]

    Fewster and Kasia Rejzner

    Christopher J. Fewster and Kasia Rejzner. Algebraic quantum field theory – an introduction. Progress and Visions in Quantum Theory in View of Gravity, pages 125–189, 2020

    2020

  95. [103]

    Notes on some entanglement properties of quantum field theory

    Edward Witten. Notes on some entanglement properties of quantum field theory. 2018

    2018

  96. [104]

    Notes on the type classification of von Neumann algebras.Rev

    Jonathan Sorce. Notes on the type classification of von Neumann algebras.Rev. Math. Phys., 36(02):2430002, 2024

    2024

  97. [105]

    F. J. Murray and J. von Neumann. On rings of operators.Annals of Mathematics, 37(1):116–229, 1936

    1936

  98. [106]

    Von Neumann Algebras

    Jacques Dixmier. Von Neumann Algebras. North-Holland, 1981. 80

    1981

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