pith. sign in

arxiv: 2606.05904 · v1 · pith:VM56GBADnew · submitted 2026-06-04 · 🪐 quant-ph

Non-equilibrium quantum thermodynamics of a memory-bearing open-system process

Biagio G. Banigi , Eric Lutz , Mauro Paternostro This is my paper

Pith reviewed 2026-06-28 01:06 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum thermodynamicsmemory effectsnon-Markovian dynamicstwo-level systemopen quantum systemsentropy production
0
0 comments X

The pith

A finite composite environment produces memory effects that change work, heat, and entropy production in a driven two-level quantum system.

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

The paper shows that memory effects arise in the dynamics of a driven two-level system coupled to a composite environment. These effects, due to the environment's finiteness, influence the system's work, heat, and entropy production. The study examines how driving, dissipation, and memory interact to shape the thermodynamic response. This matters because it extends quantum thermodynamics analysis past the common Markovian approximation to cases with memory.

Core claim

Memory effects emerge in the dynamics of a driven two-level system interacting with a composite environment. These effects influence work, heat and entropy production. The interplay between driving, dissipation and memory effects from the finiteness of the environment shapes the thermodynamic response of the system.

What carries the argument

The driven two-level system coupled to a finite composite environment, which generates memory effects in the open-system dynamics that affect thermodynamic quantities.

If this is right

  • Thermodynamic quantities like work and heat are modified by memory effects.
  • Entropy production analysis requires accounting for non-Markovian dynamics.
  • The system response depends on the interplay of driving and dissipation with memory.

Where Pith is reading between the lines

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

  • Similar memory effects could appear in other open quantum systems with finite baths.
  • This could lead to new ways to control thermodynamic processes by engineering environment size.
  • Testable predictions for entropy production in finite versus infinite bath limits.

Load-bearing premise

The finiteness of the composite environment is what produces the memory effects that shape the thermodynamic response.

What would settle it

A numerical simulation or experiment showing no difference in work, heat, and entropy production between finite and infinite environment cases would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.05904 by Biagio G. Banigi, Eric Lutz, Mauro Paternostro.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of the open system process described in Sec. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: with the harmonic oscillator. The inclusion of the bath, instead, produces further effects of dissipation and decoherence in the dynamics of the two-level system. Indeed, the inversion of populations between the qubit’s states |e⟩ and |g⟩, described from the plot in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Panel [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Time evolution of the entropy production rate [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Time evolution of entropy production rate [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Temporal behavior of the populations (panels [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
read the original abstract

We show the emergence of memory effects in the dynamics of a driven two-level system interacting with a composite environment, and analyze their influence on work, heat and entropy production. We further investigate how the interplay between driving, dissipation and memory effects, stemming from the finiteness of the environment, shapes the thermodynamic response of the system, thus providing insight into quantum thermodynamics beyond the Markovian approximation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper examines the dynamics of a driven two-level system coupled to a finite composite environment. It reports the emergence of memory effects arising from the environment's finiteness and analyzes their effects on work, heat, and entropy production, exploring the interplay of driving, dissipation, and non-Markovianity in shaping the system's thermodynamic response beyond the Markovian limit.

Significance. If the central results hold after addressing controls, the work would contribute to quantum thermodynamics by linking finite-environment memory effects to thermodynamic quantities in a driven open system. This could offer concrete insight into non-Markovian regimes, provided the attribution to finiteness is rigorously isolated.

major comments (1)
  1. [Model description and results sections] The central claim ties memory effects and their thermodynamic consequences explicitly to the finiteness of the composite environment (abstract; model description). However, no control comparison to the infinite-bath limit is presented (e.g., by increasing the number of discrete modes while holding the spectral density fixed). Without this or an equivalent analytic argument, alternative sources of non-Markovianity (structured spectral density, initial correlations, or the particular composite construction) cannot be ruled out, undermining the attribution that is load-bearing for the thermodynamic analysis.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive criticism. We address the major comment below and outline the revisions we plan to make to strengthen the manuscript.

read point-by-point responses

  1. Referee: The central claim ties memory effects and their thermodynamic consequences explicitly to the finiteness of the composite environment (abstract; model description). However, no control comparison to the infinite-bath limit is presented (e.g., by increasing the number of discrete modes while holding the spectral density fixed). Without this or an equivalent analytic argument, alternative sources of non-Markovianity (structured spectral density, initial correlations, or the particular composite construction) cannot be ruled out, undermining the attribution that is load-bearing for the thermodynamic analysis.

    Authors: We agree that a direct control comparison to the infinite-bath limit would strengthen the attribution of memory effects specifically to the finiteness of the environment. In the revised manuscript, we will include additional numerical simulations in which the number of discrete modes is systematically increased while the spectral density is held fixed, demonstrating convergence toward the Markovian limit. This will help isolate the contribution of finiteness and address potential alternative sources of non-Markovianity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against external benchmarks

full rationale

The provided abstract and model description frame memory effects as arising from the explicit assumption of a finite composite environment, with thermodynamic quantities (work, heat, entropy production) analyzed as consequences. No equations, self-citations, or fitted parameters are quoted that reduce any prediction to its own inputs by construction. The central claim is an assumption about environment size rather than a self-definitional loop or renamed known result. Absent any load-bearing step that collapses to a fit or prior self-citation chain, the paper's derivation chain is independent and externally falsifiable via comparison to infinite-bath limits.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields minimal ledger; the sole domain assumption is that finite environment size produces memory.

axioms (1)
  • domain assumption Memory effects stem from the finiteness of the environment
    Abstract explicitly attributes memory to finiteness of the composite environment.

pith-pipeline@v0.9.1-grok · 5581 in / 997 out tokens · 37645 ms · 2026-06-28T01:06:06.100683+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

34 extracted references

  1. [1]

    (11) and Eq

    Work and heat We start by adapting Eq. (11) and Eq. (12) to our case, leading to the two differential equations ˙W(t) =−λω D sin(ωDt)[ρ eg (t) +ρ ge(t)] +iλω D cos(ωDt)[ρ eg (t)−ρ ge(t)],(17) ˙Q(t) =2[Γ 2(t)ρ gg (t)−Γ 1(t)ρ ee(t)].(18) The solutions of these equations are shown, respectively, in Fig. 4(a)and Fig. 4(b). From here, we notice that the work o...

  2. [2]

    symmetry

    Entropy production and entropy production rate We proceed similarly with the analysis of the entropy pro- duction Σ(t), which takes into account the amount of entropy generated by the qubit during the interaction with the environ- ment, and its rate of change, σΣ(t). The entropy production Σ(t)can be cast as Σ(t) =S(t)−β(t)Q(t),(19) where ∆S(t) =S(t)−S(0)...

  3. [3]

    Breuer, E.-M

    H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini, Colloquium: Non-Markovian dynamics in open quantum systems, Rev. Mod. Phys.88, 021002 (2016)

    2016

  4. [4]

    Lindblad, On the generators of quantum dynamical semi- groups, Commun

    G. Lindblad, On the generators of quantum dynamical semi- groups, Commun. Math. Phys.48, 119 (1976)

    1976

  5. [5]

    Gorini, A

    V . Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N-level systems, J. Math. Phys. 8 17, 821 (1976)

    1976

  6. [6]

    H. P. Breuer and F. Petruccione,The Theory of Open Quantum Systems(Oxford University Press, Oxford, UK, 2002)

    2002

  7. [7]

    Zicari, M

    G. Zicari, M. Brunelli, and M. Paternostro, Assessing the role of initial correlations in the entropy production rate for nonequilib- rium harmonic dynamics, Phys. Rev. Res.2, 043006 (2020)

    2020

  8. [8]

    Breuer, E.-M

    H.-P. Breuer, E.-M. Laine, and J. Piilo, Measure for the degree of non-Markovian behavior of quantum processes in open systems, Phys. Rev. Lett.103, 210401 (2009)

    2009

  9. [9]

    Rivas, S

    Á. Rivas, S. F. Huelga, and M. B. Plenio, Quantum non- Markovianity: characterization, quantification and detection, Reports on Progress in Physics77, 094001 (2014)

    2014

  10. [10]

    de Vega and D

    I. de Vega and D. Alonso, Dynamics of non-Markovian open quantum systems, Rev. Mod. Phys.89, 015001 (2017)

    2017

  11. [11]

    Binder, L

    F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, Fundamental Theories of Physics, V ol. 195 (Springer, 2018)

    2018

  12. [12]

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

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

    1978

  13. [13]

    Marcantoni, S

    S. Marcantoni, S. Alipour, F. Benatti, R. Floreanini, and A. T. Rezakhani, Entropy production and non-Markovian dynamical maps, Sci. Rep.7, 12447 (2017)

    2017

  14. [14]

    Popovic, B

    M. Popovic, B. Vacchini, and S. Campbell, Entropy production and correlations in a controlled non-Markovian setting, Phys. Rev. A98, 012130 (2018)

    2018

  15. [15]

    Strasberg and M

    P. Strasberg and M. Esposito, Non-Markovianity and negative entropy production rates, Phys. Rev. E99, 012120 (2019)

    2019

  16. [16]

    Dann, Interplay between external driving, dissipation and collective effects in the Markovian and non-Markovian regimes, Quantum9, 1740 (2025)

    R. Dann, Interplay between external driving, dissipation and collective effects in the Markovian and non-Markovian regimes, Quantum9, 1740 (2025)

    2025

  17. [17]

    Follia, B

    P. Follia, B. Vacchini, and H.-P. Breuer, Control of memory effects in a spin-boson system by periodic driving (2025), arXiv:2510.25875 [quant-ph]

    arXiv 2025

  18. [18]

    I. A. Picatoste, A. Colla, and H.-P. Breuer, Dynamically emer- gent quantum thermodynamics: Non-Markovian Otto cycle, Phys. Rev. Res.6, 013258 (2024)

    2024

  19. [19]

    Abah and M

    O. Abah and M. Paternostro, Implications of non-Markovian dynamics on information-driven engine, Journal of Physics Com- munications4, 085016 (2020)

    2020

  20. [20]

    Deffner and E

    S. Deffner and E. Lutz, Nonequilibrium entropy production for open quantum systems, Phys. Rev. Lett.107, 140404 (2011)

    2011

  21. [21]

    Spohn and J

    H. Spohn and J. L. Lebowitz,Irreversible Thermodynamics for Quantum Systems Weakly Coupled to Thermal Reservoirs, Advances in Chemical Physics (John Wiley & Sons, Ltd, 1978)

    1978

  22. [22]

    Lindblad,Non-Equilibrium Entropy and Irreversibility, Math- ematical Physics Studies, V ol

    G. Lindblad,Non-Equilibrium Entropy and Irreversibility, Math- ematical Physics Studies, V ol. 5 (Springer Dordrecht, 1983)

    1983

  23. [23]

    Raimond and S

    J.-M. Raimond and S. Haroche,Exploring the Quantum(Oxford University Press, Oxford, UK, 2006)

    2006

  24. [24]

    Denzler, J

    T. Denzler, J. F. G. Santos, E. Lutz, and R. M. Serra, Nonequi- librium fluctuations of a quantum heat engine, Quantum Science and Technology9, 045017 (2024)

    2024

  25. [25]

    J. P. S. Peterson, T. B. Batalhão, M. Herrera, A. M. Souza, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, Experimental characterization of a spin quantum heat engine, Phys. Rev. Lett. 123, 240601 (2019)

    2019

  26. [26]

    Andersson, J

    E. Andersson, J. D. Cresser, and M. J. W. Hall, Finding the Kraus decomposition from a master equation and vice versa, Journal of Modern Optics54, 1695 (2007)

    2007

  27. [27]

    M. B. Ruskai, Beyond Strong Subadditivity? Improved Bounds on the Contraction of Generalized Relative Entropy, Reviews in Mathematical Physics6, 1147 (1994)

    1994

  28. [28]

    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)

    1979

  29. [29]

    Gemmer, M

    J. Gemmer, M. Michel, and G. Mahler,Quantum Thermodynam- ics: Emergence of Thermodynamic Behavior Within Composite Quantum Systems(Springer Berlin Heidelberg, Berlin, Heidel- berg, 2009)

    2009

  30. [30]

    Rivas, Quantum thermodynamics in the refined weak cou- pling limit, Entropy21, 725 (2019)

    Á. Rivas, Quantum thermodynamics in the refined weak cou- pling limit, Entropy21, 725 (2019)

    2019

  31. [31]

    Esposito, K

    M. Esposito, K. Lindenberg, and C. Van den Broeck, Entropy production as correlation between system and reservoir, New Journal of Physics12, 013013 (2010)

    2010

  32. [32]

    Deffner and S

    S. Deffner and S. Campbell,Quantum Thermodynamics(Morgan & Claypool Publishers, San Rafael, CA, USA, 2019)

    2019

  33. [33]

    M. J. W. Hall, J. D. Cresser, L. Li, and E. Andersson, Canon- ical form of master equations and characterization of non- Markovianity, Phys. Rev. A89, 042120 (2014). Appendix A: Quantum dynamical map and master equation Here we show a detailed derivation of the master equation for the qubit interacting only with the harmonic oscillator. To this end, we ma...

    2014

  34. [34]

    The Hamiltonian H(t) in Eq

    The jump operators Li are found through the relation Li = ∑ j Pji Bj,(A13) with Pji being the elements of a passage matrix made up of the normalized eigenvectors of subA′(t). The Hamiltonian H(t) in Eq. (A12) is a Lamb-shift-like term given by H(t) = κ†(t)−κ(t) 2i withκ(t) = 1√ 2 ∑ i A′ i0(t)B i. (A14) An explicit calculation leads us to γ1(t) =− µ(t) +ν(...