pith. sign in

arxiv: 2510.12599 · v1 · pith:ZWJBVUYKnew · submitted 2025-10-14 · ❄️ cond-mat.stat-mech · cond-mat.quant-gas· quant-ph

Quantum thermodynamics of Gross-Pitaevskii qubits

Sebastian Deffner This is my paper

Pith reviewed 2026-05-21 21:15 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.quant-gasquant-ph
keywords quantum thermodynamicsGross-Pitaevskii equationquantum Otto enginenonlinear qubitsthermodynamic equilibriumquantum heat engine
0
0 comments X

The pith

Nonlinear Gross-Pitaevskii qubits enable quantum Otto engines with higher efficiency than linear designs.

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

The paper builds a thermodynamic description for qubits whose evolution follows the nonlinear Gross-Pitaevskii equation. It first identifies the equilibrium states that serve as hot and cold reservoirs for these systems. With this foundation the work shows that Otto cycles using the nonlinear qubits reach higher efficiency than cycles using ordinary linear qubits, both when the engine runs ideally and when it is tuned for maximum power. The nonlinear dynamics are presented as an effective model for correlated many-body systems, so the efficiency gain supplies a new route to quantum thermodynamic advantage.

Core claim

Quantum Otto engines that operate with nonlinear qubits significantly outperform linear engines, with higher efficiency for ideal cycles as well as at maximum power.

What carries the argument

The thermodynamic equilibrium state identified for nonlinear qubits governed by the Gross-Pitaevskii equation, which supplies well-defined hot and cold reservoirs together with the work and heat exchanges in an Otto cycle.

If this is right

  • Nonlinear engines reach higher efficiency both in the ideal-cycle limit and at the point of maximum power.
  • The nonlinear Gross-Pitaevskii description functions as an effective model of a correlated, complex quantum many-body system.
  • The results supply a concrete design route for quantum heat engines that achieve higher performance without relying solely on quantum correlations.

Where Pith is reading between the lines

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

  • The same equilibrium-state construction might be applied to other nonlinear Schrödinger-type models to test whether efficiency gains appear more broadly.
  • Realization in a trapped Bose-Einstein condensate could provide a direct experimental check of the predicted efficiency advantage.
  • Nonlinearities could be combined with entanglement or coherence to explore additive resources for thermodynamic tasks.

Load-bearing premise

A proper thermodynamic equilibrium state exists and can be identified for nonlinear qubits described by the Gross-Pitaevskii equation, allowing well-defined hot and cold reservoirs and work strokes.

What would settle it

A side-by-side numerical or experimental comparison of the work output and efficiency of an Otto cycle realized with a Gross-Pitaevskii nonlinear qubit versus the same cycle realized with a linear qubit, under matched temperatures and cycle times.

Figures

Figures reproduced from arXiv: 2510.12599 by Sebastian Deffner.

Figure 1
Figure 1. Figure 1: FIG. 1. Internal energy ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Internal energy ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Efficiency of the ideal Otto cycle ( [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Efficiency at maximum power of the endoreversible [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Difference in efficiency at maximum power of the [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

What are the resources that can be leveraged for a thermodynamic device to exhibit genuine quantum advantage? Typically, the answer to this question is sought in quantum correlations. In the present work, we show that quantum Otto engines that operate with nonlinear qubits significantly outperform linear engines. To this end, we develop a comprehensive thermodynamic description of nonlinear qubits starting with identifying the proper thermodynamic equilibrium state. We then show that for ideal cycles as well as at maximum power the efficiency of the nonlinear engine is significantly higher. Interestingly, nonlinear dynamics can be thought of as an effective description of a correlated, complex quantum many body system. Hence, our findings corroborate common wisdom, while at the same time propose a new design of more efficient quantum engines.

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

2 major / 2 minor

Summary. The manuscript develops a thermodynamic description of nonlinear qubits governed by the Gross-Pitaevskii equation. It identifies a suitable equilibrium state, constructs quantum Otto cycles with hot and cold reservoirs, and reports that the resulting nonlinear engines achieve significantly higher efficiency than linear qubit engines, both for ideal cycles and when optimized for maximum power. Nonlinearity is interpreted as an effective description of correlated many-body systems.

Significance. If the equilibrium-state construction is internally consistent and recovers the standard Gibbs state in the linear limit, the result would indicate that nonlinearity itself can serve as a resource for thermodynamic quantum advantage, offering a concrete design principle for more efficient quantum heat engines and supporting the broader intuition that complexity enhances performance.

major comments (2)
  1. [equilibrium state definition] Section on equilibrium state identification (around the definition following the Gross-Pitaevskii Hamiltonian): the construction must be shown to reduce exactly to the thermal Gibbs state when the nonlinear coefficient vanishes; without this explicit limit, the subsequent efficiency comparisons to linear engines rest on an unverified foundation.
  2. [cycle construction] Otto cycle stroke definitions and first-law accounting: it is unclear how work and heat are partitioned during the nonlinear evolution strokes, particularly whether the nonlinear term contributes to heat or work in a manner consistent with the standard thermodynamic identity dU = đQ + đW.
minor comments (2)
  1. [figures] Figure captions should explicitly state the value of the nonlinearity parameter used in each panel to allow direct comparison with the linear case.
  2. [notation] Notation for the effective temperature and chemical potential in the nonlinear equilibrium state should be introduced with a clear relation to the linear-case expressions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment in turn below, indicating the revisions we intend to implement.

read point-by-point responses

  1. Referee: Section on equilibrium state identification (around the definition following the Gross-Pitaevskii Hamiltonian): the construction must be shown to reduce exactly to the thermal Gibbs state when the nonlinear coefficient vanishes; without this explicit limit, the subsequent efficiency comparisons to linear engines rest on an unverified foundation.

    Authors: We agree that an explicit demonstration of the linear limit is necessary to place the equilibrium-state construction on firm ground. Our equilibrium state is defined via entropy maximization subject to the mean energy constraint obtained from the full Gross-Pitaevskii Hamiltonian. Setting the nonlinearity coefficient to zero recovers the linear Hamiltonian, and the same maximization procedure then yields the standard Gibbs state. In the revised manuscript we will insert a short analytic calculation (new paragraph plus appendix) that explicitly takes this limit, shows the partition function reduces to the usual trace, and confirms that the density matrix becomes exp(−βH_linear)/Z. revision: yes

  2. Referee: Otto cycle stroke definitions and first-law accounting: it is unclear how work and heat are partitioned during the nonlinear evolution strokes, particularly whether the nonlinear term contributes to heat or work in a manner consistent with the standard thermodynamic identity dU = đQ + đW.

    Authors: We thank the referee for highlighting the need for transparent thermodynamic accounting. Because the nonlinear term belongs to the system Hamiltonian, its contribution to the instantaneous energy is included in the internal energy U. During the isentropic strokes the evolution is closed (no reservoir coupling), so dU is entirely work; during the isochoric strokes the parameter is fixed and energy exchange with the reservoir is heat. We define the infinitesimal work as the expectation value of the partial derivative of the Hamiltonian with respect to the control parameter (including the nonlinear term) and heat as the remainder, thereby preserving dU = đQ + đW. In the revision we will add explicit expressions for đW and đQ along each stroke and verify the first-law balance numerically for a representative cycle. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper develops a thermodynamic description for nonlinear qubits by first identifying an equilibrium state for the Gross-Pitaevskii equation, then compares Otto engine efficiencies to the linear case. No quoted equations or steps reduce the efficiency advantage or equilibrium identification to a fitted parameter, self-referential definition, or self-citation chain by construction. The central claims rest on the model's dynamics and numerical/analytic results rather than tautological renaming or imported uniqueness theorems. The derivation is self-contained against the stated assumptions, with the equilibrium state serving as an input rather than an output forced by the target efficiencies.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields limited visibility into parameters or axioms; the central claim rests on the existence of a thermodynamic equilibrium state for the nonlinear system, which is stated but not derived in the provided text.

axioms (1)
  • domain assumption Nonlinear qubits possess a well-defined thermodynamic equilibrium state that can be used to define hot and cold reservoirs.
    Explicitly invoked as the starting point for the thermodynamic description in the abstract.

pith-pipeline@v0.9.0 · 5642 in / 1199 out tokens · 38640 ms · 2026-05-21T21:15:25.509644+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

64 extracted references · 64 canonical work pages

  1. [1]

    Campbell, D

    D. Campbell, D. Farmer, J. Crutchfield, and E. Jen, Ex- perimental mathematics: the role of computation in non- linear science, Commun. ACM28, 374 (1985)

    work page 1985

  2. [2]

    T. F. Jordan, Why quantum dynamics is linear, J. Phys.: Conf. Ser.196, 012010 (2009)

    work page 2009

  3. [3]

    R. L. Walsworth, I. F. Silvera, E. M. Mattison, and R. F. C. Vessot, Test of the linearity of quantum mechan- ics in an atomic system with a hydrogen maser, Phys. Rev. Lett.64, 2599 (1990)

    work page 1990

  4. [4]

    P. K. Majumder, B. J. Venema, S. K. Lamoreaux, B. R. Heckel, and E. N. Fortson, Test of the linearity of quan- tum mechanics in optically pumped 201Hg, Phys. Rev. Lett.65, 2931 (1990)

    work page 1990

  5. [5]

    Forstner, M

    S. Forstner, M. Zych, S. Basiri-Esfahani, K. E. Khosla, and W. P. Bowen, Nanomechanical test of quantum lin- earity, Optica7, 1427 (2020)

    work page 2020

  6. [6]

    DalFavero, A

    B. DalFavero, A. Meill, D. A. Meyer, T. G. Wong, and J. P. Wrubel, Constant-time quantum search with a many-body quantum system, Phys. Rev. A110, 052411 (2024)

    work page 2024

  7. [7]

    E. P. Gross, Structure of a quantized vortex in boson systems, Nuovo Cim.20, 454 (1961)

    work page 1961

  8. [8]

    L. P. Pitaevskii, Vortex lines in an imperfect Bose gas, Sov. J. Exp. Theor. Phys.13, 451 (1961)

    work page 1961

  9. [9]

    Rand,Nonlinear and Quantum Optics using the den- sity matrix(Oxford University Press, 2010)

    S. Rand,Nonlinear and Quantum Optics using the den- sity matrix(Oxford University Press, 2010)

    work page 2010

  10. [10]

    M. S. Ruderman, Propagation of solitons of the Deriva- tive Nonlinear Schr¨ odinger equation in a plasma with fluctuating density, Phys. Plasmas9, 2940 (2002)

    work page 2002

  11. [11]

    Soler, Classical, stable, nonlinear spinor field with positive rest energy, Phys

    M. Soler, Classical, stable, nonlinear spinor field with positive rest energy, Phys. Rev. D1, 2766 (1970)

    work page 1970

  12. [12]

    Cooper, A

    F. Cooper, A. Khare, B. Mihaila, and A. Saxena, Soli- tary waves in the nonlinear dirac equation with arbitrary nonlinearity, Phys. Rev. E82, 036604 (2010)

    work page 2010

  13. [13]

    F. G. Mertens, N. R. Quintero, F. Cooper, A. Khare, and A. Saxena, Nonlinear dirac equation solitary waves in external fields, Phys. Rev. E86, 046602 (2012)

    work page 2012

  14. [14]

    E. B. Kolomeisky, T. J. Newman, J. P. Straley, and X. Qi, Low-dimensional bose liquids: Beyond the gross- pitaevskii approximation, Phys. Rev. Lett.85, 1146 (2000)

    work page 2000

  15. [15]

    D. A. Meyer and T. G. Wong, Quantum search with gen- eral nonlinearities, Phys. Rev. A89, 012312 (2014)

    work page 2014

  16. [16]

    A. M. Childs and J. Young, Optimal state discrimination and unstructured search in nonlinear quantum mechan- ics, Phys. Rev. A93, 022314 (2016). 8

    work page 2016

  17. [17]

    Zhang, C

    X. Zhang, C. Wang, J. Ma, and G. Ren, Control and syn- chronization in nonlinear circuits by using a thermistor, Mod. Phys. Lett. B34, 2050267 (2020)

    work page 2020

  18. [18]

    Shen, W.-K

    Y. Shen, W.-K. Mok, C. Noh, A. Q. Liu, L.-C. Kwek, W. Fan, and A. Chia, Quantum synchronization effects induced by strong nonlinearities, Phys. Rev. A107, 053713 (2023)

    work page 2023

  19. [19]

    de Lacy, L

    K. de Lacy, L. Noakes, J. Twamley, and J. B. Wang, Controlled quantum search, Quantum Inf. Process.17, 266 (2018)

    work page 2018

  20. [20]

    Chiew, K

    M. Chiew, K. de Lacy, C. H. Yu, S. Marsh, and J. B. Wang, Graph comparison via nonlinear quantum search, Quantum Inf. Process.18, 302 (2019)

    work page 2019

  21. [21]

    Holmes, N

    Z. Holmes, N. J. Coble, A. T. Sornborger, and Y. Sub- asi, Nonlinear transformations in quantum computation, Phys. Rev. Res.5, 013105 (2023)

    work page 2023

  22. [22]

    M. R. Geller, Nonlinear and non-cp gates for bloch vector amplification, Commun. Theor. Phys.75, 105102 (2023)

    work page 2023

  23. [23]

    M. R. Geller, Fast quantum state discrimination with nonlinear positive trace-preserving channels, Adv. Quan- tum Technol.6, 2200156 (2023)

    work page 2023

  24. [24]

    Deiml and D

    M. Deiml and D. Peterseim, Nonlinear quantum computing by amplified encodings, arXiv preprint arXiv:2411.16435 (2024)

    work page arXiv 2024

  25. [25]

    Byrnes, D

    T. Byrnes, D. Rosseau, M. Khosla, A. Pyrkov, A. Thomasen, T. Mukai, S. Koyama, A. Abdelrahman, and E. Ilo-Okeke, Macroscopic quantum information pro- cessing using spin coherent states, Opt. Commun.337, 102 (2015)

    work page 2015

  26. [26]

    S. Xu, J. Schmiedmayer, and B. C. Sanders, Nonlinear quantum gates for a bose-einstein condensate, Phys. Rev. Res.4, 023071 (2022)

    work page 2022

  27. [27]

    M. R. Geller, Protocol for nonlinear state discrimina- tion in rotating condensate, Adv. Quantum Technol.7, 2300431 (2024)

    work page 2024

  28. [28]

    Großardt

    A. Großardt, Nonlinear-ancilla aided quantum algo- rithm for nonlinear schr¨ odinger equations, arXiv preprint arXiv:2403.10102 (2024)

    work page arXiv 2024

  29. [29]

    M. R. Geller, Proposal for a lorenz qubit, Sci. Rep.13, 14106 (2023)

    work page 2023

  30. [30]

    K´ alm´ an and T

    O. K´ alm´ an and T. Kiss, Quantum state matching of qubits via measurement-induced nonlinear transforma- tions, Phys. Rev. A97, 032125 (2018)

    work page 2018

  31. [31]

    Sakaguchi, S

    A. Sakaguchi, S. Konno, F. Hanamura, W. Asavanant, K. Takase, H. Ogawa, P. Marek, R. Filip, J.-i. Yoshikawa, E. Huntington, H. Yonezawa, and A. Furusawa, Non- linear feedforward enabling quantum computation, Nat. Commun.14, 3817 (2023)

    work page 2023

  32. [32]

    L. Yang, Z. Wen-Hong, Z. Cun-Lin, and L. Gui-Lu, Quantum computation with nonlinear optics, Commun. Theor. Phys.49, 107 (2008)

    work page 2008

  33. [33]

    D. E. Chang, V. Vuleti´ c, and M. D. Lukin, Quantum nonlinear optics — photon by photon, Nat. Photon.8, 685 (2014)

    work page 2014

  34. [34]

    B. Gu, C. Zhao, A. Baev, K.-T. Yong, S. Wen, and P. N. Prasad, Molecular nonlinear optics: recent advances and applications, Adv. Opt. Photon.8, 328 (2016)

    work page 2016

  35. [35]

    Scala, D

    F. Scala, D. Nigro, and D. Gerace, Deterministic entan- gling gates with nonlinear quantum photonic interferom- eters, Commun. Phys.7, 118 (2024)

    work page 2024

  36. [36]

    del Campo, Probing quantum speed limits with ultra- cold gases, Phys

    A. del Campo, Probing quantum speed limits with ultra- cold gases, Phys. Rev. Lett.126, 180603 (2021)

    work page 2021

  37. [37]

    Deffner, Nonlinear speed-ups in ultracold quantum gases, EPL (Europhys

    S. Deffner, Nonlinear speed-ups in ultracold quantum gases, EPL (Europhys. Lett.)140, 48001 (2022)

    work page 2022

  38. [38]

    Beau and A

    M. Beau and A. del Campo, Nonlinear quantum metrol- ogy of many-body open systems, Phys. Rev. Lett.119, 010403 (2017)

    work page 2017

  39. [39]

    Deffner, Towards enhanced precision in thermometry with nonlinear qubits, Quantum Sci

    S. Deffner, Towards enhanced precision in thermometry with nonlinear qubits, Quantum Sci. Technol.10, 025009 (2025)

    work page 2025

  40. [40]

    Deffner, C

    S. Deffner, C. Jarzynski, and A. del Campo, Classical and quantum shortcuts to adiabaticity for scale-invariant driving, Phys. Rev. X4, 021013 (2014)

    work page 2014

  41. [41]

    X. Chen, Y. Ban, and G. C. Hegerfeldt, Time-optimal quantum control of nonlinear two-level systems, Phys. Rev. A94, 023624 (2016)

    work page 2016

  42. [42]

    J.-J. Zhu, X. Chen, H.-R. Jauslin, and S. Gu´ erin, Robust control of unstable nonlinear quantum systems, Phys. Rev. A102, 052203 (2020)

    work page 2020

  43. [43]

    Zhu and X

    J.-J. Zhu and X. Chen, Fast-forward scaling of atom- molecule conversion in bose-einstein condensates, Phys. Rev. A103, 023307 (2021)

    work page 2021

  44. [44]

    J.-j. Zhu, K. Liu, X. Chen, and S. Gu´ erin, Optimal con- trol and ultimate bounds of 1:2 nonlinear quantum sys- tems, Phys. Rev. A108, 042610 (2023)

    work page 2023

  45. [45]

    Deffner and S

    S. Deffner and S. Campbell, Suppressing excitations in the nonlinear landau-zener model, EPL (Europhys. Lett.) 151, 58001 (2025)

    work page 2025

  46. [46]

    (13) impliesβ=∂S/∂E, which is identical to the thermodynamic definition of temperature [47]

    Note that Eq. (13) impliesβ=∂S/∂E, which is identical to the thermodynamic definition of temperature [47]

    work page

  47. [47]

    H. B. Callen,Thermodynamics and an introduction to thermostatistics(Wiley, New York, USA, 1985)

    work page 1985

  48. [48]

    Deffner and S

    S. Deffner and S. Campbell,Quantum Thermodynamics (Morgan & Claypool Publishers, 2019)

    work page 2019

  49. [49]

    Campbell, I

    S. Campbell, I. D’Amico, M. A. Ciampini,et al., Roadmap on quantum thermodynamics, arXiv preprint arXiv:2504.20145 (2025)

    work page arXiv 2025

  50. [50]

    H. T. Quan, Y.-x. Liu, C. P. Sun, and F. Nori, Quantum thermodynamic cycles and quantum heat engines, Phys. Rev. E76, 031105 (2007)

    work page 2007

  51. [51]

    Smith, P

    Z. Smith, P. S. Pal, and S. Deffner, Endoreversible otto engines at maximal power, J. Non-Equilib. Thermodyn. 45, 305 (2020)

    work page 2020

  52. [52]

    O. Abah, J. Roßnagel, G. Jacob, S. Deffner, F. Schmidt- Kaler, K. Singer, and E. Lutz, Single-ion heat engine at maximum power, Phys. Rev. Lett.109, 203006 (2012)

    work page 2012

  53. [53]

    Deffner, Efficiency of harmonic quantum otto engines at maximal power, Entropy20, 875 (2018)

    S. Deffner, Efficiency of harmonic quantum otto engines at maximal power, Entropy20, 875 (2018)

    work page 2018

  54. [54]

    N. M. Myers and S. Deffner, Bosons outperform fermions: The thermodynamic advantage of symmetry, Phys. Rev. E101, 012110 (2020)

    work page 2020

  55. [55]

    N. M. Myers and S. Deffner, Thermodynamics of statis- tical anyons, PRX Quantum2, 040312 (2021)

    work page 2021

  56. [56]

    N. M. Myers, O. Abah, and S. Deffner, Quantum otto engines at relativistic energies, New J. Phys.23, 105001 (2021)

    work page 2021

  57. [57]

    K. H. Hoffmann, J. M. Burzler, and S. Schubert, En- doreversible thermodynamics, J. Non-Equilib. Thermo- dyn.22, 311 (1997)

    work page 1997

  58. [58]

    F. L. Curzon and B. Ahlborn, Efficiency of a Carnot en- gine at maximum power output, Am. J. Phys.43, 22 (1975)

    work page 1975

  59. [59]

    E. E. Ferketic and S. Deffner, Boosting thermodynamic performance by bending space-time, EPL (Europhys. Lett.)141, 19001 (2023)

    work page 2023

  60. [60]

    N. M. Myers, J. McCready, and S. Deffner, Quantum heat engines with singular interactions, Symmetry13, 978 (2021). 9

    work page 2021

  61. [61]

    N. M. Myers, F. J. Pe˜ na, O. Negrete, P. Vargas, G. De Chiara, and S. Deffner, Boosting engine perfor- mance with bose–einstein condensation, New J. Phys.24, 025001 (2022)

    work page 2022

  62. [62]

    N. M. Myers, F. J. Pe˜ na, N. Cort´ es, and P. Vargas, Mul- tilayer graphene as an endoreversible otto engine, Nano- materials13, 1548 (2023)

    work page 2023

  63. [63]

    F. J. Pe˜ na, N. M. Myers, D. ´Ordenes, F. Albarr´ an- Arriagada, and P. Vargas, Enhanced efficiency at maxi- mum power in a fock–darwin model quantum dot engine, Entropy25, 518 (2023)

    work page 2023

  64. [64]

    Behrendt and S

    G. Behrendt and S. Deffner, Endoreversible stirling cy- cles: Plasma engines at maximal power, Entropy27, 807 (2025)

    work page 2025