Steady-state coherence in multipartite quantum systems: its connection with thermodynamic quantities and impact on quantum thermal machines

Farzam Nosrati; Q. Y. Cai; Rosario Lo Franco; Rui Huang; Zhong-Xiao Man

REVIEW 3 major objections 5 minor 87 references

Steady-state coherence in multipartite quantum systems: its connection with thermodynamic quantities and impact on quantum thermal machines

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read In a two-bath quantum machine, the paper shows that steady-state coherence among particles sets which currents carry heat and work, and it writes down the exact combinations of coherence elements that control the work currents.

desk verdict Useful decomposition of coherence-class contributions to heat and work currents, but the cascaded model's missing 1/N normalization overreports currents and needs fixing before the model comparisons are trustworthy. read the letter →

arxiv 2502.03722 v1 pith:OAZA4DUR submitted 2025-02-06 quant-ph

Rui Huang , Q. Y. Cai , Farzam Nosrati , Rosario Lo Franco , Zhong-Xiao Man This is my paper · ORCID

classification quant-ph

keywords quantumthermodynamicscoherencethermalmachinecollisionmodelnon-localdissipationsteady-statecascadedsystem-bathinteractionworkandheatcurrents

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

This paper studies a quantum thermal machine built from two ensembles of two-level particles, each ensemble coupled to its own heat bath, and asks how steady-state quantum coherence among the particles shapes the machine's work and heat currents. The central claim is that once the system reaches its non-equilibrium steady state, the work and heat currents split into local and non-local parts, and each part is controlled by a specific kind of coherence: local work by coherence between particles in different baths, non-local work by both same-bath and cross-bath coherence, non-local heat by same-bath coherence, and local heat only by populations. The paper derives explicit formulas expressing these currents in terms of coherence quantities for two intrasystem interaction geometries, and shows numerically that the currents track these quantities as the frequency ratio is varied. With the same setup the machine can act as an accelerator, an engine, or a refrigerator depending on the ratio of the two transition frequencies. If correct, the work establishes a direct, quantitative bridge between steady-state coherence and thermodynamic output, offering a design handle for quantum thermal machines.

What carries the argument

The machinery is the collision-model master equation with non-local dissipation. When the $N$ particles of an ensemble collide with a common bath — all at once (common-bath model) or one after another (cascaded model) — the dissipators contain cross terms of the form $\sum_{n'\ne n}\gamma_{i,nn'}[\cdots]$ that generate coherences between particles sharing a bath. Work is defined through the time-dependent collision Hamiltonian $\hat{V}_{i,n}/\sqrt{\tau}$, and the assumption $[\sum_n H_{S_i,n}+H_{E_i},\sum_n V_{i,n}]=0$ makes the intrasystem coupling $\hat{H}_I$ the only source of work. The operator $\hat{F}_{i,n} = [\hat{H}_I,\hat{\sigma}^-_{i,n}]$ converts the interaction structure into the coherence combinations $C_{\rm loc}$ and $C_{\rm non\text{-}loc}$ that appear in the current formulas.

What would settle it

Simulate the exact finite-$\tau$ collision map for $N=2$ with $\hat{H}_I^{(2)}$, compute the work current by direct energy bookkeeping without taking $\tau\to 0$, and compare with the $\tau\to0$ predictions of Eqs. (36) and (38); visible disagreement that grows with the coupling strengths would falsify the claim that the listed coherence quantities fully determine the work currents.

Watch

Extended reading notes

Core claim

The paper's central discovery is a classification (its Table I) tying steady-state currents to the system's coherence structure: local heat is a functional of populations alone; non-local heat is driven by coherence between particles sharing the same bath; the local work current is a fixed linear combination of coherence elements across the two baths, e.g. $\dot{W}_{\rm loc}^{(2)} = -\frac12[\Omega_1\Gamma_{h1c1}\langle(\sigma^+_{h,1}\sigma^-_{c,1})_+\rangle + \Omega_2\Gamma_{h2c2}\langle(\sigma^+_{h,2}\sigma^-_{c,2})_+\rangle]$; and non-local work depends on three-body coherence correlators that mix one particle from one bath with two from the other. The same structure holds for the cascaded interaction, where the non-local terms involve only the later-colliding particles, reflecting the one-way influence of the cascade order. In all cases the paper supplies explicit 'coherence-related quantities' $C$ that, in the steady state, determine the work currents, and it verifies numerically that the currents track these quantities as the frequency ratio $\omega_h/\omega_c$ is varied.

Load-bearing premise

The argument rests on two unproved steps: that the coupling between system and bath conserves energy so all work is done by the internal interaction, and that certain oscillating cross-terms cancel in the steady-state limit; if either fails, the work formulas lose terms.

Editorial extensions

If this is right

In the steady state, work output is governed by coherence, not just by populations: tuning the intrasystem coupling constants $\Omega_n$ or the bath parameters entering $\Gamma$ changes the steady-state cross-bath coherences and hence the local work current.
A single physical setup covers all three thermal-machine functions — accelerator, engine, and refrigerator — with coefficients of performance fixed by $\omega_h$ and $\omega_c$; the choice of interaction geometry (common vs cascaded, first vs second interaction type) selects the best performer for a given function.
Non-local dissipation adds a non-local work channel that independent dissipation does not have, so machines exploiting common baths or cascaded couplings can outperform locally dissipative ones in some regimes, notably refrigerator cooling power for the first interaction type.
In the cascaded model, the one-way influence between sequentially colliding particles is visible in the non-local work and heat currents through coherence terms that involve only the later-colliding particle, giving an observable thermodynamic signature of the cascade order.

Reading between the lines

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

The classification in Table I should persist for larger $N$, with the coherence quantities becoming sums over all ordered pairs; the paper's formulas already display the $N=2$ building blocks.
Because the local work current is linear in cross-bath coherences, an external coherence-control protocol — for example a short pulse that prepares a target $C_{\rm loc}$ before the steady state is reestablished — could modulate power faster than changing bath temperatures.
A two-qubit experiment with collisional reservoirs could test the linear relation $\dot{W}_{\rm loc}\propto \sum_n \Omega_n \Gamma_n \,{\rm Re}\langle\sigma^+_{h,n}\sigma^-_{c,n}\rangle$ by performing full two-qubit state tomography at steady state; deviations at strong coupling would signal the dropped $\tau$-order terms.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. First, the paper genuinely advances the bookkeeping of steady-state quantum thermodynamics: it gives explicit formulas decomposing heat and work currents into local and non-local parts for two-ensemble machines with common or cascaded baths, and it classifies which coherence class controls which current (Table I). That goes beyond Ref. [35] and the authors' earlier common-bath and cascaded studies. The local parts match Ref. [35] in the appropriate limit, and the qualitative Table I is plausible.

Second, the cascaded model has a normalization problem that looks load-bearing. Eq. (13) says one full cycle of N sequential collisions advances the state by Nτ. Expanding U_N...U_1 with V scaled by 1/√τ produces a generator that should carry an explicit 1/N factor. No such factor appears in the dissipators (14)-(15) or in the current formulas (40)-(45). For N=2 the cascaded currents are inflated by a factor of two relative to the simultaneous model, directly biasing the comparisons in Figs. 2-4 and the conclusion that the optimal configuration depends on the regime.

The Appendix A issue flagged by the reader is real but smaller. The asserted relation <[H_tot,V_i,n]>=0 is not true per particle, because same-bath coherences contribute. However, the sum over n cancels, so the final currents in Sec. III.A are likely fine. That part is sloppy rather than fatal. What needs a real fix is the cascaded normalization.

A separate weakness: the numerics come from an unspecified solver, with no code or data, and a single operating point. That is hard to check or reuse.

This paper is for people working on steady-state quantum thermal machines with collective or cascaded dissipation. The qualitative message about which coherence controls which current is likely robust and worth keeping. The quantitative comparisons are not trustworthy until the cascaded QME is re-derived with the proper time normalization and checked against a direct finite-tau collision-model simulation. I would send it to peer review, because the decomposition framework is novel and important, but the referee should require that fix before acceptance.

Referee Report

3 major / 5 minor

Summary. The paper studies steady-state thermodynamics of two coupled ensembles of N two-level systems, each ensemble coupled to a thermal bath, with system-bath interactions either simultaneous (common bath) or sequential (cascaded). Using a collision-model master equation, the authors decompose work and heat currents into local and non-local parts. They find that local heat depends on populations, non-local heat on same-bath coherences, local work on cross-ensemble coherences, and non-local work on both, as summarized in Table I. Explicit coherence-related quantities are given for two intrasystem interaction types, and numerical results for N=2 show operation as refrigerator, engine, or accelerator in different frequency regimes.

Significance. If correct, the paper provides a concrete and falsifiable connection between steady-state quantum coherence and thermodynamic currents in a multipartite setting, extending the local-dissipation results of Ref. [35] to non-local and cascaded dissipation. The explicit analytic expressions, e.g., Eqs. (36)-(37) relating local work to cross-ensemble coherences, are useful and testable, and the comparison of six machine configurations is of practical interest. However, two load-bearing issues in the derivations currently compromise the quantitative claims: the cascaded-model time normalization appears to be missing a factor 1/N, and the τ→0 expansion in Appendix A relies on an unproved and individually false commutator relation. The qualitative classification may survive, but the numerical comparisons and the section IV conclusions as presented are not reliable until these points are fixed.

major comments (3)

[Sec. II.B and Sec. III.B, Eq. (13) and Eqs. (40)-(45)] The cascaded map in Eq. (13) advances the state by Nτ, as stated explicitly in the text, so the continuous-time limit should be lim_{τ→0}(ρ'_S - ρ_S)/(Nτ). The master equation presented after Eq. (13) and the heat/work currents in Eqs. (40)-(45) appear to divide by τ only, omitting the factor 1/N. For N=2, this overreports the cascaded currents by a factor of 2 relative to the simultaneous model. This affects the quantitative comparisons in Figs. 2-4 and the Sec. IV conclusion that the optimal configuration depends on the regime (for example, ˙Q_cas(2)_h > ˙Q_com(2)_h). The authors should re-derive the cascaded currents with explicit time normalization and update all affected numerical results.
[Appendix A, Eq. (A2)] The relation ⟨[H_tot,V_i,n]⟩=0 is not valid for each individual n. For n'≠n, the commutator [V_i,n',V_i,n] has nonzero expectation values in the thermal bath state, so the first-order term iτ⟨[H_tot,V_i,n]⟩ contains contributions of order √τ that can cancel only after summing over n. As written, the expansion also drops the [H0,[V_i,n',V_i,n]] contribution, which is of the same order as the retained term before the summation. The derivation should be restructured to take the sum over n before the τ→0 limit and to show the required cancellations explicitly; this is load-bearing for Eqs. (19)-(21).
[Appendix A, Eqs. (A6)-(A8)] The final expression in the appendix defines the non-local heat current with [V_i,n',[V_i,n,H_S+H_Ei]], whereas the main-text formula in Eq. (24) uses only [V_i,n',[V_i,n,H_Ei]]. These are not equivalent because [H_S,V_i,n] does not generally vanish. This inconsistency means the derivation in the appendix does not reproduce Eq. (26) or the classification in Table I. The appendix should be corrected to match the main text, or the main-text formula should be revised if the appendix expression is the intended one.

minor comments (5)

[Sec. III.C, Fig. 2 caption] The caption of Fig. 2(d) is garbled: the sentence containing 'we includes the curves regarding ...' and the comparison of C with eC needs to be rewritten for clarity.
[Sec. III.A.3, Eqs. (33), (35), (37), (39)] The coherence-related quantities C are defined from the same expectation values that appear in the corresponding work-current formulas, so the proportionality is exact by construction. The authors should state explicitly that these are algebraic decompositions rather than newly introduced independent measures, to avoid the appearance of circularity.
[General] Table I is stated for general N, but the explicit non-local work expressions are derived only for N=2. The authors should either provide the general-N expressions or explicitly state that the classification is established for N=2 and conjectured otherwise.
[Sec. II.B] There is a typo: 'illistrated' should be 'illustrated'.
[Data availability statement] The data availability statement is self-contradictory: it says the data cannot be made publicly available and also that the data are available upon reasonable request. Please clarify the actual policy.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the coherence dependence of the work/heat currents is derived from the model Hamiltonian; the C quantities are post-hoc shorthand, not fitted inputs or imported results.

full rationale

The derivation chain is self-contained and algebraic. Work and heat are defined from the collision-model energy balance (Eqs. 16-18), and the one-collision expansion in Appendix A produces the general currents (Eqs. 19-24). The specific formulas (25)-(28), (32), (34), (36), (38) and their cascaded analogues follow from inserting the explicit TLS-oscillator coupling V_i,n of Eq. (9) and the interaction Hamiltonians H_I of Eqs. (29) and (31); they are not assumptions. The coherence-related quantities C in Eqs. (33), (35), (37), (39), (46), and (47) are defined after the work expressions are obtained, as combinations of the same expectation values appearing in those expressions. This makes Fig. 2(c) a consistency check rather than an independent experimental confirmation, but it is not a case of fitting a parameter and calling it a prediction, nor is the work current defined as C. The claim that W is linked to coherence is a derived property of the model, not an input. There is no load-bearing self-citation: the comparison with Ref. [35] is an external benchmark for the local-work formula, and the in-group references (e.g., Refs. [43], [50], [80]) are contextual rather than premises. Two genuine correctness concerns should be noted separately, but neither is circular: Appendix A uses the relation <[H_tot,V_i,n]>=0 without proof, and the cascaded map of Eq. (13) advances the state by N tau while the continuous-time limit is taken as tau->0 without an explicit 1/N normalization in Eqs. (14)-(15) or (40)-(45). These are possible derivation gaps, not reductions of the conclusions to their own inputs.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The analytical heart of the paper (master equation, current decompositions, Table I classification) is parameter-free: the model Hamiltonian (1)-(2), (7)-(9) fixes everything. The C quantities are bookkeeping definitions. The fragility is in the derivation assumptions: the energy-conserving-coupling ansatz, the unproved <[H_tot, V]> = 0 relation, and the dropped same-order commutator terms. The single operating point used for all figures limits the scope of the machine-performance conclusions. No new physical entities are introduced.

free parameters (1)

operating point for Figs. 2-4 (g_h1 = g_c1 = 0.5w_c, g_h2 = g_c2 = 0.55w_c, Omega1 = Omega2 = 0.1w_c, Th = 2w_c, Tc =… = stated in figure captions
Hand-chosen, not fitted: the analytical claims are parameter-free, but the performance comparisons (which configuration wins as refrigerator, engine, or accelerator) are demonstrated at this single operating point with no sensitivity analysis, so the practical conclusions are examples, not theorems.

assumptions (4)

domain assumption Born-Markov / continuous-time limit of the collision model (tau -> 0 with first-order expansion) yields the Lindblad master equation (4)
Standard open-quantum-systems approximation invoked in Sec. II; the paper does not quantify the coupling strength or bath correlation time beyond the weak-coupling scaling.
domain assumption Energy-conserving system-bath coupling: [sum_n H_Si,n + H_Ei, sum_n V_i,n] = 0, so the work current is entirely due to the intrasystem interaction H_I
Stated in Sec. III; it is what makes the work/heat split (Eqs. 19-24) meaningful. Off-resonant couplings would change the definition of work.
ad hoc to paper The relation <[H_tot, V_i,n]> = 0 used in the Appendix A derivation of the work current
Asserted without proof below Eq. (A2); required for a finite work current in the tau -> 0 limit, but generically nonzero through same-ensemble cross terms [V_i,n', V_i,n] proportional to Im<sigma+_i,n' sigma-_i,n>.
ad hoc to paper Absence or cancellation of same-order commutator terms [H_I, [V_i,n, V_i,n']] in the tau -> 0 work-current expansion
The appendix keeps terms of type [V_tot, [V, H_I]] but drops [H_I, [V, V']], which is the same order and has nonzero three-body coherence expectations.

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Pith. "Pith review of Steady-state coherence in multipartite quantum systems: its connection with thermodynamic quantities and impact on quantum thermal machines." pith.science (2026). https://pith.science/paper/OAZA4DUR

@misc{pith2026250203722,
  author       = {Pith},
  title        = {Pith review of: Steady-state coherence in multipartite quantum systems: its connection with thermodynamic quantities and impact on quantum thermal machines},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OAZA4DUR}},
  note         = {Machine review of arXiv:2502.03722}
}

abstract

Understanding how coherence of quantum systems affects thermodynamic quantities, such as work and heat, is essential for harnessing quantumness effectively in thermal quantum technologies. Here, we study the unique contributions of quantum coherence among different subsystems of a multipartite system, specifically in non-equilibrium steady states, to work and heat currents. Our system comprises two coupled ensembles, each consisting of $N$ particles, interacting with two baths of different temperatures, respectively. The particles in an ensemble interact with their bath either simultaneously or sequentially, leading to non-local dissipation and enabling the decomposition of work and heat currents into local and non-local components.We find that the non-local heat current, as well as both the local and non-local work currents,are linked to the system quantum coherence. We provide explicit expressions of coherence-related quantities that determine the work currents under various intrasystem interactions.Our scheme is versatile, capable of functioning as a refrigerator, an engine, and an accelerator, with its performance being highly sensitive to the configuration settings. These findings establish a connection between thermodynamic quantities and quantum coherence, supplying valuable insights for the design of quantum thermal machines.

Figures

Figures reproduced from arXiv: 2502.03722 by the authors.

**Figure 2.** FIG. 2. (a) The local components of work currents, i.e., [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 4.** FIG. 4. Parametric plot of power [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

Figures from the paper (1 more)

**Figure 3.** Figure 3: FIG. 3. Work currents [PITH_FULL_IMAGE:figures/full_fig_p010_3.png]

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Z.-X. Man and Y .-J. Xia, “Smallest quantum thermal machine: The e ffect of strong coupling and distributed thermal tasks,” Phys. Rev. E 96, 012122 (2017)

2017
[37]

Coherence and decoherence in quan- tum absorption refrigerators,

M. Kilgour and D. Segal, “Coherence and decoherence in quan- tum absorption refrigerators,” Phys. Rev. E98, 012117 (2018)

2018
[38]

Thermodynamics of a con- tinuous quantum heat engine: Interplay between population and coherence,

P. Bayona-Pena and K. Takahashi, “Thermodynamics of a con- tinuous quantum heat engine: Interplay between population and coherence,” Phys. Rev. A104, 042203 (2021)

2021
[39]

Reconciliation of quantum lo- cal master equations with thermodynamics,

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

2018
[40]

How small can thermal machines be? the smallest possible refrigerator,

N. Linden, S. Popescu, and P. Skrzypczyk, “How small can thermal machines be? the smallest possible refrigerator,” Phys. Rev. Lett. 105, 130401 (2010)

2010
[41]

Boost- ing the performance of small autonomous refrigerators via com- mon environmental effects,

G. Manzano, G.-L. Giorgi, R. Fazio, and R. Zambrini, “Boost- ing the performance of small autonomous refrigerators via com- mon environmental effects,” New J. Phys. 21, 123026 (2019)

2019
[42]

Thermal rectification and heat amplification in a nonequilibrium v-type three-level system,

C. Wang, D. Xu, H. Liu, and X. Gao, “Thermal rectification and heat amplification in a nonequilibrium v-type three-level system,” Phys. Rev. E99, 042102 (2019)

2019
[43]

Thermal production, protection, and heat exchange of quantum coher- ences,

B. C ¸ akmak, A. Manatuly, and¨O. E. M¨ustecaplıo˘glu, “Thermal production, protection, and heat exchange of quantum coher- ences,” Phys. Rev. A96, 032117 (2017). 14

2017
[44]

Collective effects and quantum coherence in dissipative charging of quantum batter- ies,

Franco Mayo and Augusto J. Roncaglia, “Collective effects and quantum coherence in dissipative charging of quantum batter- ies,” Physical Review, A105, 062203 (2022)

2022
[45]

Heat transfer in trans- versely coupled qubits: optically controlled thermal modulator with common reservoirs,

Y . J. Yang, Y . Q Liu, and C. s. Yu, “Heat transfer in trans- versely coupled qubits: optically controlled thermal modulator with common reservoirs,” J. Phys. A 55, 395303 (2022)

2022
[46]

Common environmental effects on quantum thermal transistor,

Y .-Q. Liu, D.-H. Yu, and C.-S. Yu, “Common environmental effects on quantum thermal transistor,” Entropy 24, 32 (2022)

2022
[47]

Features of quantum thermodynamics induced by common environments based on collision model,

R. Huang, Z. X. Man, Y . J. Zhang, and Y . J. Xia, “Features of quantum thermodynamics induced by common environments based on collision model,” EPJ Quantum Technol.9, 28 (2022)

2022
[48]

Quantum thermal- ization of two coupled two-level systems in eigenstate and bare- state representations,

J.-Q. Liao, J.-F. Huang, and L.-M. Kuang, “Quantum thermal- ization of two coupled two-level systems in eigenstate and bare- state representations,” Phys. Rev. A83, 052110 (2011)

2011
[49]

Improving autonomous thermal entanglement generation using a common reservoir,

Z.-X. Man, A. Tavakoli, J. B. Brask, and Y .-J. Xia, “Improving autonomous thermal entanglement generation using a common reservoir,” Phys. Scr.94, 075101 (2019)

2019
[50]

Correlated versus uncorrelated noise acting on a quantum refrigerator,

B. Karimi and J. P. Pekola, “Correlated versus uncorrelated noise acting on a quantum refrigerator,” Phys. Rev. B 96, 115408 (2017)

2017
[51]

Master equations for corre- lated quantum channels,

V . Giovannetti and G. M. Palma, “Master equations for corre- lated quantum channels,” Phys. Rev. Lett.108, 040401 (2012)

2012
[52]

Landauer’s principle in multipartite open quan- tum system dynamics,

S. Lorenzo, R. McCloskey, F. Ciccarello, M. Paternostro, and G. M. Palma, “Landauer’s principle in multipartite open quan- tum system dynamics,” Phys. Rev. Lett.115, 120403 (2015)

2015
[53]

Heat flux and quantum correlations in dissipative cas- caded systems,

S. Lorenzo, A. Farace, F. Ciccarello, G. M. Palma, and V . Gio- vannetti, “Heat flux and quantum correlations in dissipative cas- caded systems,” Phys. Rev. A91, 022121 (2015)

2015
[54]

E ffects of one-way cor- relations on thermodynamics of a multipartite open quantum system,

Q. Zhang, Y .-J. Xia, and Z.-X. Man, “E ffects of one-way cor- relations on thermodynamics of a multipartite open quantum system,” Phys. Rev. A108, 062211 (2023)

2023
[55]

Thermodynamic deficiencies of some simple lindblad operators,

J. T. Stockburger and T. Motz, “Thermodynamic deficiencies of some simple lindblad operators,” Fortschr. Phys65, 1600067 (2016)

2016
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Adding dynamical generators in quantum master equations,

J. Kołody ´nski, J. B. Brask, M. Perarnau-Llobet, and B. Bylicka, “Adding dynamical generators in quantum master equations,” Phys. Rev. A 97, 062124 (2018)

2018
[57]

Testing the validity of the ‘lo- cal’ and ‘global’ gkls master equations on an exactly solvable model,

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
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Out-of- equilibrium open quantum systems: A comparison of approxi- mate quantum master equation approaches with exact results,

A. Purkayastha, A. Dhar, and M. Kulkarni, “Out-of- equilibrium open quantum systems: A comparison of approxi- mate quantum master equation approaches with exact results,” Phys. Rev. A 93, 062114 (2016)

2016
[59]

Modeling heat transport through completely posi- tive maps,

H. Wichterich, M. J. Henrich, H.-P. Breuer, J. Gemmer, and M. Michel, “Modeling heat transport through completely posi- tive maps,” Phys. Rev. E76, 031115 (2007)

2007
[60]

The local approach to quantum trans- port may violate the second law of thermodynamics,

A. Levy and R. Kosloff, “The local approach to quantum trans- port may violate the second law of thermodynamics,” EPL (Eu- rophysics Letters) 107, 20004 (2014)

2014
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Relaxation phenomena in spin and harmonic oscillator systems,

J. Rau, “Relaxation phenomena in spin and harmonic oscillator systems,” Phys. Rev.129, 1880 (1963)

1963
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Quantum collision models: Open system dynamics from re- peated interactions,

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

2022
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Collision models can e fficiently simulate any multipartite markovian quantum dynamics,

M. Cattaneo, G. De Chiara, S. Maniscalco, R. Zambrini, and G. L. Giorgi, “Collision models can e fficiently simulate any multipartite markovian quantum dynamics,” Phys. Rev. Lett. 126, 130403 (2021)

2021
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Thermalizing quantum machines: Dissipation and entangle- ment,

V . Scarani, M. Ziman, P.ˇStelmachoviˇc, N. Gisin, and V . Buˇzek, “Thermalizing quantum machines: Dissipation and entangle- ment,” Phys. Rev. Lett.88, 097905 (2002)

2002
[65]

All (qubit) decoherences: Complete characterization and physical implementation,

M. Ziman and V . Buˇzek, “All (qubit) decoherences: Complete characterization and physical implementation,” Phys. Rev. A 72, 022110 (2005)

2005
[66]

Reversible and irreversible dy- namics of a qubit interacting with a small environment,

G. Benenti and G. M. Palma, “Reversible and irreversible dy- namics of a qubit interacting with a small environment,” Phys. Rev. A 75, 052110 (2007)

2007
[67]

Relaxation due to random collisions with a many-qudit environment,

G. Gennaro, G. Benenti, and G. M. Palma, “Relaxation due to random collisions with a many-qudit environment,” Phys. Rev. A 79, 022105 (2009)

2009
[68]

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

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

2021
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Temperature effects on quantum non-Markovianity via collision models,

Z. X. Man, Y . J. Xia, and R. Lo Franco, “Temperature effects on quantum non-Markovianity via collision models,” Phys. Rev. A 97, 062104 (2018)

2018
[70]

Non-Markovianity in the collision model with environmental block,

J. Jin and C.-S. Yu, “Non-Markovianity in the collision model with environmental block,” New J. Phys. 20, 053026 (2018)

2018
[71]

The thermodynamic cost of driving quantum systems by their boundaries,

F. Barra, “The thermodynamic cost of driving quantum systems by their boundaries,” Sci. Rep. 5, 14873 (2015)

2015
[72]

Implications of non-markovian quantum dynamics for the landauer bound,

M. Pezzutto, M. Paternostro, and Y . Omar, “Implications of non-markovian quantum dynamics for the landauer bound,” New J. Phys. 18, 123018 (2016)

2016
[73]

Validity of the landauer principle and quantum memory e ffects via collisional models,

Z. X. Man, Y . J. Xia, and R. Lo Franco, “Validity of the landauer principle and quantum memory e ffects via collisional models,” Phys. Rev. A99, 042106 (2019)

2019
[74]

Non-Markovianity and the landauer principle in composite thermal environments,

Q. Zhang, Z. X. Man, and Y . J. Xia, “Non-Markovianity and the landauer principle in composite thermal environments,” Phys. Rev. A 103, 032201 (2021)

2021
[75]

Collisional quantum thermometry,

S. Seah, S. Nimmrichter, D. Grimmer, J. P. Santos, V . Scarani, and G. T. Landi, “Collisional quantum thermometry,” Phys. Rev. Lett. 123, 180602 (2019)

2019
[76]

Dissipative charging of a quantum battery,

F. Barra, “Dissipative charging of a quantum battery,” Phys. Rev. Lett. 122, 210601 (2019)

2019
[77]

Three-qubit refrigerator with two-body in- teractions,

A. Hewgill, J. O. Gonz ´alez, J. P. Palao, D. Alonso, A. Ferraro, and G. De Chiara, “Three-qubit refrigerator with two-body in- teractions,” Phys. Rev. E101, 012109 (2020)

2020
[78]

Quantum nonequilibrium steady states induced by repeated interactions,

D. Karevski and T. Platini, “Quantum nonequilibrium steady states induced by repeated interactions,” Phys. Rev. Lett. 102, 207207 (2009)

2009
[79]

Entropy production and asymptotic factorization via thermalization: A collisional model approach,

S. Cusumano, V . Cavina, M. Keck, A. De Pasquale, and V . Gio- vannetti, “Entropy production and asymptotic factorization via thermalization: A collisional model approach,” Phys. Rev. A 98, 032119 (2018)

2018
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Thermal- ization of finite many-body systems by a collision model,

O. Arısoy, S. Campbell, and ¨O. E. M ¨ustecaplıoˇglu, “Thermal- ization of finite many-body systems by a collision model,” En- tropy 21, 1182 (2019)

2019
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Multiatom quantum coherences in micromasers as fuel for thermal and nonthermal machines,

C. B. Da ˇg, W. Niedenzu, ¨O. E. M ¨ustecaplıoˇglu, and G. Kur- izki, “Multiatom quantum coherences in micromasers as fuel for thermal and nonthermal machines,” Entropy18, 244 (2016)

2016
[82]

Thermodynamics of weakly coherent collisional mod- els,

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

2019
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Ex- ploiting coherence for quantum thermodynamic advantage,

K. Hammam, H. Leitch, Y . Hassouni, and G. De Chiara, “Ex- ploiting coherence for quantum thermodynamic advantage,” New J. Phys. 24, 113053 (2022)

2022
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Heat fluxes in a two-qubit cascaded system due to coherences of a non-thermal bath,

Z. X. Man, Y . J. Xia, and N. B. An, “Heat fluxes in a two-qubit cascaded system due to coherences of a non-thermal bath,” J. Phys. B 53, 205505 (2020)

2020
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Quantum measurement cooling,

L. Bu ffoni, A. Solfanelli, P. Verrucchi, A. Cuccoli, and M. Campisi, “Quantum measurement cooling,” Phys. Rev. Lett. 122, 070603 (2019)

2019
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Nonadiabatic single-qubit quantum otto engine,

A. Solfanelli, M. Falsetti, and M. Campisi, “Nonadiabatic single-qubit quantum otto engine,” Phys. Rev. B 101, 054513 (2020)

2020
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Quantum advantage of thermal machines 15 with bose and fermi gases,

S. Sur and A. Ghosh, “Quantum advantage of thermal machines 15 with bose and fermi gases,” Entropy 25, 372 (2023)

2023

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

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Quan- tum thermal machine acting on a many-body quantum system: Role of correlations in thermodynamic tasks,

P. Doyeux, B. Leggio, R. Messina, and M. Antezza, “Quan- tum thermal machine acting on a many-body quantum system: Role of correlations in thermodynamic tasks,” Phys. Rev. E 93, 022134 (2016)

work page 2016

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Steady-state coherence in multipartite quantum systems: its connection with thermodynamic quantities and impact on quantum thermal machines

has prompted researchers to further explore the combi- nation of quantum mechanics and other traditional fields. In this context, quantum thermodynamics has attracted extensive studies, with the aim to exploit quantum advantage in ther- modynamic processes [2–7]. A topic of great interest is to use quantum resources to design quantum thermal machines (QTM...

work page Pith review arXiv 2025

[3] [2]

com” in the work current indicates that the ensemble parti- cles interact simultaneously with a “common

General formulations of work and heat currents We first establish the relevant thermodynamic quantities, namely work and heat currents, for the simultaneous system- bath interaction and decompose them into local and non-local parts (see Appendix A for details). By taking the limit ofτ→ 0, we obtain the work current ˙Wcom = lim τ→0 (∆W/τ) = ˙Wcom loc + ˙Wc...

[4] [3]

Specific model for the system and bath made up of TLSs and harmonic oscillators Returning to the situation where the system is composed of TLSs, the bath ancilla is an harmonic oscillator, and system- bath interactions are governed by the operator ˆVi,n of Eq. (9), the local and non-local heat currents become ˙Qcom(i) loc =ωi NX n=1 γ+ i,nn D ˆσ− i,n ˆσ+ ...

[5] [4]

Moreover, the interaction types between subsystems across the two ensembles in our setup are rich, whose e ffects on the work deserve a compre- hensive study

E ffects of intrasystem interactions on the work for two pairs of TLSs As discussed above, the intrasystem interactions play a cru- cial role on the work, which can be used as a control factor to enhance the performance of QTMs. Moreover, the interaction types between subsystems across the two ensembles in our setup are rich, whose e ffects on the work de...

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