arxiv: 2604.18439 · v1 · submitted 2026-04-20 · 🪐 quant-ph · physics.class-ph

Recognition: unknown

Classical counterparts of shortcuts to adiabaticity in nonlinear dissipative Lagrangian systems

Jincheng Shi , Yicheng Pan , Yue Ban , Xi Chen

Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:08 UTC · model grok-4.3

classification 🪐 quant-ph physics.class-ph

keywords shortcuts to adiabaticityclassical Lagrangian systemsinverse engineeringRayleigh dissipationgeometric couplingresidual energymanipulator dynamicsdissipative systems

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The pith

Shortcuts to adiabaticity from quantum dynamics extend to classical nonlinear dissipative Lagrangian systems via inverse engineering of trajectories.

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

This paper shows that shortcuts to adiabaticity, originally developed for rapid quantum state changes with suppressed excitations, can be realized in classical mechanical systems described by nonlinear Lagrangian dynamics with dissipation. Using a coupled r-θ manipulator as the model, the authors apply inverse engineering to the Euler-Lagrange equations that include a Rayleigh dissipation term, deriving the required force and torque from trajectories prescribed to be stationary at both endpoints. The work quantifies how the nonlinear geometric coupling between coordinates amplifies timing errors and residual energy. Comparisons are made to actuator-limited time-optimal solutions and PID tracking to illustrate trade-offs in smoothness, speed, and robustness, and a single mid-course measurement correction is proposed to handle early deviations while keeping inputs smooth.

Core claim

In the coupled r-θ manipulator, inverse engineering of the Euler-Lagrange equations with Rayleigh dissipation, achieved by prescribing endpoint-stationary trajectories, generates explicit force and torque profiles that suppress residual energy after rapid transformations, while geometric coupling is shown to increase sensitivity to timing inaccuracies, and a mid-course measurement correction is introduced to mitigate early errors.

What carries the argument

Inverse engineering of the Euler-Lagrange equations with Rayleigh dissipation by prescribing endpoint-stationary trajectories in the nonlinear coupled r-θ manipulator model.

Load-bearing premise

That endpoint-stationary trajectories can be prescribed to produce well-defined force and torque profiles that suppress residual energy without additional unstated constraints on system parameters or dissipation strength.

What would settle it

Applying the inverse-engineered force and torque profiles to a physical coupled r-θ manipulator and measuring whether the final residual kinetic energy is substantially lower than that from a direct fast ramp under identical dissipation conditions.

Figures

Figures reproduced from arXiv: 2604.18439 by Jincheng Shi, Xi Chen, Yicheng Pan, Yue Ban.

**Figure 2.** Figure 2: FIG. 2. (a) Angular coordinate [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Relative error RE of the final mechanical energy as a function [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. The evolutions of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. (a) [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

read the original abstract

Shortcuts to adiabaticity (STA) were first developed in quantum dynamics to realize rapid transformations with suppressed residual excitations. Here we show how the same idea can be implemented in classical nonlinear dissipative Lagrangian systems. Using a coupled $r$-$\theta$ manipulator as an illustrative model, we perform inverse engineering on the Euler-Lagrange equations with Rayleigh dissipation by prescribing endpoint-stationary trajectories, obtaining the corresponding force and torque profiles and quantifying how geometric coupling amplifies errors and residual energy. We further compare smooth STA protocols with actuator-bounded time-optimal solutions and with proportional-integral-derivative tracking, which highlights a trade-off among smoothness, speed, and robustness. Finally, we introduce a single-shot correction based on one mid-course measurement to reduce the effect of early deviations while keeping the inputs nearly smooth. These results provide a practical bridge between quantum STA concepts and their classical counterparts.

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.

Desk Editor's Note private letter to a colleague

This paper transfers STA inverse engineering to classical nonlinear dissipative Lagrangians on a specific r-θ manipulator, with comparisons and a mid-course fix, but adds no broad new mechanics.

read the letter

The core move is taking the quantum STA trick of prescribing endpoint-stationary trajectories and applying it to the Euler-Lagrange equations plus Rayleigh dissipation on a coupled manipulator. They derive the required force and torque profiles, quantify how the geometric coupling boosts residual energy, and test a single mid-course measurement correction that keeps inputs smooth while cutting early deviations. They also run comparisons against time-optimal bounded controls and PID tracking to show the usual smoothness-speed-robustness trade-offs. That combination on a nonlinear dissipative example is the new piece; earlier classical STA work stayed simpler or lossless. The derivations follow standard forms without obvious circularity or invented constraints, and the stress-test finds no internal contradictions in the numerics or solvability assumptions. The correction is presented as optional rather than a hidden fix. The main limitation is scope. Everything is demonstrated on one manipulator geometry, so the error-amplification numbers and residual-energy gains are tied to that setup and its parameter range. Without the actual plots or error bars in front of me it is hard to judge how large the practical improvement is, but the abstract and stress-test description suggest the claims rest on concrete simulations rather than hand-waving. No load-bearing fitting or parameter tuning is flagged as a problem. This is useful reading for control engineers or roboticists who already work with Lagrangian models and want a quantum-inspired shortcut for fast, low-residual trajectories in dissipative hardware. A theorist looking for new general principles in classical mechanics will not find them here. I would send it to peer review because the example is carried through with explicit comparisons and the correction method is a concrete addition worth checking in detail, even if the revisions will likely ask for more general discussion or additional models.

Referee Report

0 major / 3 minor

Summary. The paper extends shortcuts to adiabaticity (STA) concepts from quantum dynamics to classical nonlinear dissipative Lagrangian systems. It uses inverse engineering on the Euler-Lagrange equations with Rayleigh dissipation for a coupled r-θ manipulator model, by prescribing endpoint-stationary trajectories to derive the required force and torque inputs. The work quantifies geometric coupling effects on error amplification and residual energy, compares smooth STA protocols against actuator-bounded time-optimal and PID tracking solutions, and proposes an optional single-shot mid-course correction based on one measurement to improve robustness while preserving smoothness.

Significance. If the derivations and simulations hold, the manuscript provides a concrete bridge from quantum STA techniques to classical control of nonlinear dissipative systems, with explicit trade-off analysis among smoothness, speed, and robustness. The use of a specific manipulator example, quantification of coupling-induced errors, and the mid-course correction add practical utility for mechanical and robotic applications where rapid low-excitation transitions are needed.

minor comments (3)

The abstract and introduction would benefit from a brief statement of the specific residual-energy metric used (e.g., kinetic plus potential energy at final time) and how it is computed from the numerical trajectories.
In the section comparing STA, time-optimal, and PID protocols, the actuator bounds and dissipation coefficients should be stated explicitly so that the reported speed-robustness trade-off can be reproduced.
The single-shot correction is presented as optional; a short discussion of the measurement noise level at which the correction itself begins to increase residual energy would strengthen the robustness claim.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our work, for recognizing its potential as a bridge between quantum STA methods and classical nonlinear dissipative control, and for recommending minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper applies standard inverse engineering to the Euler-Lagrange equations augmented with Rayleigh dissipation by directly prescribing endpoint-stationary trajectories for the coupled r-θ manipulator model. Force and torque profiles are obtained by solving the resulting differential equations for the controls, with subsequent quantification of geometric coupling effects and numerical comparisons to time-optimal and PID baselines. No equations reduce by construction to redefinitions of the input trajectories, no fitted parameters are relabeled as predictions, and no load-bearing self-citations or uniqueness theorems imported from prior author work are invoked to justify the central results. The approach remains self-contained against the standard Lagrangian formalism and external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated beyond the standard use of Euler-Lagrange equations and Rayleigh dissipation, which are treated as background knowledge.

pith-pipeline@v0.9.0 · 5447 in / 1211 out tokens · 36457 ms · 2026-05-10T04:08:41.653595+00:00 · methodology

discussion (0)

Reference graph

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consistent with Eq. (14). The motion first accelerates at the maximal admissible acceleration until the velocity bound is reached, then evolves with a coasting phase, and finally de- celerates to satisfy the endpoint conditions. The correspond- ingτ(t) andf(t) are obtained by inverse substitution into the equations of motion. Because the two coordinates m...
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As a benchmark for feedback stabilization, we intro- duce a proportional-integral-derivative (PID) tracking scheme [52]

PID tracking The results above highlight a generic limitation of open- loop protocols in coupled nonlinear dynamics: performance degrades in the presence of model mismatch and disturbances because deviations cannot be corrected once the evolution starts. As a benchmark for feedback stabilization, we intro- duce a proportional-integral-derivative (PID) tra...
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Single-shot corrected STA Continuous feedback can strongly improve robustness but requires high-rate sensing and real-time computation and typ- 0.0 0.2 0.4 0.6 0.8 1.0 t / tf 0 10 20 30 40 ( ) (a) 0.0 0.2 0.4 0.6 0.8 1.0 t / tf 1.0 1.5 2.0 2.5 3.0 3.5 4.0 r (m) (b) 0.0 0.2 0.4 0.6 0.8 1.0 t / tf 400 200 0 200 (kg m2 s 2) and f (N) (c)difference of differe...

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