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Optimal transition in underdamped systems with memory

T0 review · 1 major / 1 minor · reviewed 2026-06-28 · grok-4.3

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Pith's one-line read Inertia breaks time-reversal symmetry so forward and backward optimal protocols differ in underdamped systems with memory.

desk verdict Inertia plus memory breaks time-reversal symmetry in optimal finite-time control, but the claim that asymmetry alone governs the strategy rests on examined kernels without a general argument. read the letter →

arxiv 2605.30897 v1 pith:OOHIZAKY submitted 2026-05-29 physics.bio-ph

Tianyu Luo , Yunxin Zhang This is my paper · ORCID
classification physics.bio-ph
keywords optimalcontrolunderdampeddynamicsmemorykernelnonequilibriumsteadystatestime-reversalsymmetryharmonictrapfinite-timetransitionsinertia
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 examines optimal finite-time transitions between nonequilibrium steady states for an underdamped particle in a moving harmonic trap subject to general memory kernels. It establishes that particle inertia qualitatively changes the control problem once memory is present, breaking time-reversal symmetry and making the optimal forward and backward protocols distinct. The asymmetry itself, not the precise shape of any particular kernel, sets the structure of the optimal strategy. This framework applies to nanoscale devices such as nanomechanical resonators and biomolecular systems where both inertia and frequency-dependent friction matter.

What carries the argument

Underdamped Langevin equation with general memory kernel for a particle in a moving harmonic trap, used to derive optimal protocols analytically and computationally between nonequilibrium steady states.

What would settle it

Numerical or experimental observation that optimal forward and backward protocols remain symmetric in an underdamped particle with memory friction would falsify the claim that inertia breaks the symmetry.

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Extended reading notes

Core claim

In underdamped dynamics with memory kernels, optimal protocols for transitions between nonequilibrium steady states break time-reversal symmetry due to inertia, rendering forward and backward protocols distinct; across examined kernels, the asymmetry governs the structure of the optimal strategy rather than the kernel's detailed form.

Load-bearing premise

The system is accurately modeled as an underdamped particle in a moving harmonic trap whose friction follows a general memory kernel, and optimal protocols between nonequilibrium steady states can be found analytically and computationally in this model.

Editorial extensions

If this is right

  • Optimal protocols for forward and backward transitions are fundamentally distinct.
  • The structure of the optimal strategy is governed by dynamical asymmetry rather than the detailed form of the memory kernel.
  • Inertia qualitatively alters optimal control compared with the overdamped case once memory is present.
  • The results supply a unified framework for optimal control in underdamped systems with memory.

Reading between the lines

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

  • Control algorithms for nanomechanical resonators may require separate forward and backward protocols to achieve minimal dissipation.
  • The same asymmetry could appear in quantum Brownian motion settings where memory kernels arise from coupling to a bath.
  • Experiments that vary trap stiffness while keeping memory fixed could isolate whether asymmetry dominates over kernel details.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 1 minor

Summary. The manuscript analytically and computationally examines optimal finite-time transitions between nonequilibrium steady states for an underdamped particle in a moving harmonic trap subject to general memory kernels. It claims that inertia qualitatively alters optimal control relative to the overdamped limit by breaking time-reversal symmetry (making forward and backward protocols distinct) and that, across the kernels examined, this asymmetry rather than kernel details governs the structure of the optimal strategy, providing a unified framework for such systems.

Significance. If the central claims hold, the work extends optimal-control results to underdamped regimes with memory, relevant to nanomechanical resonators, biomolecular dynamics, and quantum Brownian motion. The reported dominance of asymmetry over kernel form, if general, would simplify protocol design; the combination of analytical and computational methods is a positive feature.

major comments (1)
  1. [Abstract] Abstract: the statement that 'across the memory-kernel types examined, the asymmetry, rather than the detailed form of the kernel, governs the structure of the optimal strategy' is qualified to the kernels studied. No general argument is supplied showing why underdamped inertia renders kernel details irrelevant (e.g., via symmetry properties independent of positive-definiteness or monotonicity), leaving open whether the observed structure is an artifact of the specific kernels chosen rather than a universal consequence of time-reversal symmetry breaking.
minor comments (1)
  1. The abstract states that the investigation is both analytical and computational yet supplies no equations, derivations, or data; the full manuscript must include explicit expressions for the optimal protocols and the memory kernels used to allow verification of the asymmetry claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that 'across the memory-kernel types examined, the asymmetry, rather than the detailed form of the kernel, governs the structure of the optimal strategy' is qualified to the kernels studied. No general argument is supplied showing why underdamped inertia renders kernel details irrelevant (e.g., via symmetry properties independent of positive-definiteness or monotonicity), leaving open whether the observed structure is an artifact of the specific kernels chosen rather than a universal consequence of time-reversal symmetry breaking.

    Authors: We agree that our abstract statement is explicitly limited to the kernels examined and that no general proof is given showing that inertia renders kernel details irrelevant for arbitrary kernels (independent of properties such as positive-definiteness or monotonicity). The observed dominance of asymmetry is an empirical finding from the analytical and numerical results for the specific kernels we studied. While the breaking of time-reversal symmetry by inertia is a general feature of the underdamped dynamics, we do not claim or demonstrate that this necessarily makes kernel details irrelevant beyond the cases considered. We have revised the abstract and discussion to further clarify the scope of the claim and to note that a general argument would be a valuable direction for future work. revision: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: derivation from model equations is self-contained

full rationale

The abstract and provided text describe an analytical and computational investigation of optimal protocols derived directly from the underdamped Langevin equation with general memory kernels. No load-bearing step reduces a claimed prediction or uniqueness result to a fitted parameter, self-citation, or ansatz by construction. The finding that asymmetry (rather than kernel details) governs the strategy is presented as an outcome of the examined cases within the model, without evidence of the enumerated circular patterns. The work is therefore scored as self-contained against external benchmarks.

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

Only the abstract is available; no explicit free parameters, invented entities, or additional axioms beyond the standard underdamped model with memory are stated.

assumptions (1)
  • domain assumption Dynamics follow underdamped Langevin equation with general memory kernel in a moving harmonic trap
    Standard modeling choice for systems with inertia and frequency-dependent friction invoked throughout the abstract

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Cite this review

Pith. "Pith review of Optimal transition in underdamped systems with memory." pith.science (2026). https://pith.science/paper/OOHIZAKY

@misc{pith2026260530897,
  author       = {Pith},
  title        = {Pith review of: Optimal transition in underdamped systems with memory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OOHIZAKY}},
  note         = {Machine review of arXiv:2605.30897}
}
read the original abstract

Optimal finite-time control is essential for energy-efficient operation of nanoscale devices. While existing work has largely focused on transitions between equilibrium states in overdamped systems, many settings of practical interest -- including nanomechanical resonators, biomolecular conformational dynamics, and quantum Brownian motion -- are governed by underdamped dynamics where both particle inertia and frequency-dependent friction (memory) play a non-negligible role. In this study, we analytically and computationally investigate optimal transitions between nonequilibrium steady states (NESS) for an underdamped particle in a moving harmonic trap with general memory kernels. We find that inertia qualitatively alters optimal control in the presence of memory. Compared to the overdamped case, underdamped dynamics break the time-reversal symmetry, making the forward and backward optimal protocols fundamentally distinct. Across the memory-kernel types examined, the asymmetry, rather than the detailed form of the kernel, governs the structure of the optimal strategy. These results offer a unified framework for optimal control in underdamped systems with memory.

Figures

Figures reproduced from arXiv: 2605.30897 by the authors.

Figure 1
Figure 1. FIG. 1. Optimal finite-time NESS transition for the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Optimal finite-time NESS transition for the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Optimal finite-time NESS transition for the power [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Reference graph

Works this paper leans on

24 extracted references · 1 canonical work pages

  1. [1]

    Optimal transition in underdamped systems with memory

    are all governed by underdamped dynamics in which particle inertia is non-negligible and frequency-dependent friction (memory) is ubiquitous. Critically, velocity is an independent dynamical variable that is odd under time reversal, breaking the forward–backward protocol sym- metry that constrains the overdamped case. The mem- ory kernel varies qualitativ...

    work page Pith review arXiv 2026

  2. [2]

    Schmiedl and U

    T. Schmiedl and U. Seifert, Optimal finite-time pro- cesses in stochastic thermodynamics, Phys. Rev. Lett. 98, 108301 (2007)

    2007

  3. [3]

    Seifert, Stochastic thermodynamics, fluctuation the - orems and molecular machines, Rep

    U. Seifert, Stochastic thermodynamics, fluctuation the - orems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012)

    2012

  4. [4]

    Bechhoefer, Feedback for physicists: A tutorial essa y on control, Rev

    J. Bechhoefer, Feedback for physicists: A tutorial essa y on control, Rev. Mod. Phys. 77, 783 (2005)

    2005

  5. [5]

    Jarzynski, Nonequilibrium equality for free energy d if- ferences, Phys

    C. Jarzynski, Nonequilibrium equality for free energy d if- ferences, Phys. Rev. Lett. 78, 2690 (1997)

    1997

  6. [6]

    Aurell, C

    E. Aurell, C. Mej ´ ıa-Monasterio, and P. Muratore- Ginanneschi, Optimal protocols and optimal transport in stochastic thermodynamics, Phys. Rev. Lett. 106, 250601 (2011)

    2011

  7. [7]

    S. A. M. Loos, S. Monter, F. Ginot, and C. Bechinger, Universal symmetry of optimal control at the microscale, Phys. Rev. X 14, 021032 (2024)

    2024

  8. [8]

    Toyabe, T

    S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, and M. Sano, Experimental demonstration of information- to-energy conversion and validation of the generalized Jarzynski equality, Nat. Phys. 6, 988 (2010)

    2010

Show all 24 references
  1. [9]

    J¨ ulicher, A

    F. J¨ ulicher, A. Ajdari, and J. Prost, Modeling molecula r motors, Rev. Mod. Phys. 69, 1269 (1997)

    1997

  2. [10]

    Hatano and S.-i

    T. Hatano and S.-i. Sasa, Steady-state thermodynamics of Langevin systems, Phys. Rev. Lett. 86, 3463 (2001)

    2001

  3. [11]

    Oono and M

    Y. Oono and M. Paniconi, Steady state thermodynamics, Prog. Theor. Phys. Suppl. 130, 29 (1998)

    1998

  4. [12]

    P. R. Zulkowski, D. A. Sivak, and M. R. DeWeese, Opti- mal control of transitions between nonequilibrium steady states, PLoS ONE 8, e82754 (2013)

    2013

  5. [13]

    Monter, S

    S. Monter, S. A. M. Loos, and C. Bechinger, Optimal transitions between nonequilibrium steady states, Proc. Natl. Acad. Sci. USA 122, e2510654122 (2025)

    2025

  6. [14]

    K. L. Ekinci and M. L. Roukes, Nanoelectromechanical systems, Rev. Sci. Instrum. 76, 061101 (2005)

    2005

  7. [15]

    Gieseler, B

    J. Gieseler, B. Deutsch, R. Quidant, and L. Novotn´ y, Subkelvin parametric feedback cooling of a laser-trapped nanoparticle, Phys. Rev. Lett. 109, 103603 (2012)

    2012

  8. [16]

    H¨ anggi, P

    P. H¨ anggi, P. Talkner, and M. Borkovec, Reaction-rate theory: fifty years after Kramers, Rev. Mod. Phys. 62, 251 (1990)

    1990

  9. [17]

    A. O. Caldeira and A. J. Leggett, Quantum tunnelling in a dissipative system, Ann. Phys. 149, 374 (1983)

    1983

  10. [18]

    Ginot, J

    F. Ginot, J. Caspers, M. Kr¨ uger, and C. Bechinger, Re- coil experiments determine the eigenmodes of viscoelastic fluids, New J. Phys. 24, 123013 (2022)

    2022

  11. [19]

    Kupferman, Fractional kinetics in Kac–Zwanzig heat bath models, J

    R. Kupferman, Fractional kinetics in Kac–Zwanzig heat bath models, J. Stat. Phys. 114, 291 (2004)

    2004

  12. [20]

    Zwanzig, Nonequilibrium Statistical Mechanics (Ox- ford University Press, New York, 2001)

    R. Zwanzig, Nonequilibrium Statistical Mechanics (Ox- ford University Press, New York, 2001)

    2001

  13. [21]

    Mori, A continued-fraction representation of the ti me- correlation function, Prog

    H. Mori, A continued-fraction representation of the ti me- correlation function, Prog. Theor. Phys. 34, 399 (1965)

    1965

  14. [22]

    (2026), see Supplemental Material at [URL will be in- serted by publisher] for details of the numerical optimiza- tion procedure, Markovian embedding, Euler–Lagrange derivation, excess work proofs, overdamped limit, and continued-fraction representation

    2026

  15. [23]

    Bradbury, R

    J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. Van- derPlas, S. Wanderman-Milne, and Q. Zhang, JAX: com- posable transformations of Python+NumPy programs (2018)

    2018

  16. [24]

    M. C. Engel, J. A. Smith, and M. P. Brenner, Optimal control of nonequilibrium systems through automatic dif- ferentiation, Phys. Rev. X 13, 041032 (2023)

    2023

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