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arxiv: 2606.23810 · v1 · pith:X465UXITnew · submitted 2026-06-22 · ❄️ cond-mat.stat-mech · nlin.CD· quant-ph

Universal Dynamical Response to Slow Driving in Chaotic Systems

Nachiket Karve , Nathan Rose , David Campbell , Anatoli Polkovnikov This is my paper

Pith reviewed 2026-06-26 06:13 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech nlin.CDquant-ph
keywords chaosslow drivingFisher informationentropy productiondynamical responseclassical quantum systemsnon-Hamiltonian flowsstationary state stability
0
0 comments X

The pith

Chaotic dynamics produces a divergence in speed-Fisher information as the driving protocol slows.

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

The paper establishes a unified view of chaos in classical and quantum systems by examining how stationary states respond to slow driving. It defines the speed-Fisher information as the susceptibility to the average speed of the protocol and shows that this quantity diverges with increasing protocol time precisely when the dynamics are chaotic. The divergence is controlled by the low-frequency spectral weight of the perturbation and is tied to irreversible entropy production. The same signature appears in non-Hamiltonian flows, offering a common diagnostic based on stability rather than trajectory divergence or level statistics.

Core claim

Chaotic dynamics manifests as a divergence of the speed-Fisher information with the protocol time, and this response is controlled by the perturbation's low-frequency spectral weight. The effect holds for classical and quantum Hamiltonian systems and extends naturally to non-Hamiltonian classical flows, with the divergence linked directly to irreversible entropy production.

What carries the argument

Speed-Fisher information, the susceptibility of the system to the average speed of the driving protocol, which probes stability of stationary states.

If this is right

  • Chaotic systems generate diverging irreversible entropy production under slower driving protocols.
  • The magnitude of the response is set by the low-frequency content of the perturbation spectrum.
  • Non-chaotic systems keep finite speed-Fisher information for arbitrarily long protocol times.
  • The same divergence criterion applies uniformly to classical Hamiltonian, quantum, and non-Hamiltonian flows.

Where Pith is reading between the lines

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

  • The measure could serve as a practical diagnostic in experiments where Lyapunov exponents or spectral statistics are difficult to access directly.
  • Links may exist between the low-frequency spectral weight and other chaos indicators such as level repulsion or out-of-time-order correlators.
  • The framework suggests testing whether many-body driven systems exhibit analogous divergences that mark chaotic phases or heating transitions.

Load-bearing premise

The speed-Fisher information acts as a faithful universal probe that distinguishes chaotic from non-chaotic behavior through the stability of stationary states.

What would settle it

A direct computation or simulation in a known chaotic system showing that speed-Fisher information remains finite and converges as protocol time approaches infinity would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.23810 by Anatoli Polkovnikov, David Campbell, Nachiket Karve, Nathan Rose.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) Slow, cyclic driving of a regular system. The [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) The thermodynamic drag, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (a) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (a) The thermodynamic drag, [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (a) Time evolution of a [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

We propose a unified perspective on classical and quantum chaos based on the stability of a system's stationary states under slow driving. We probe this sensitivity via the system's susceptibility to the average protocol speed, which we call the ``speed-Fisher information," and relate it to irreversible entropy production in the system. We show that chaotic dynamics manifests as a divergence of the speed-Fisher information with the protocol time, and that this response is controlled by the perturbation's low-frequency spectral weight. This approach to chaos applies to both classical and quantum Hamiltonian systems, and naturally extends to non-Hamiltonian classical flows. We illustrate this framework with simple classical and quantum examples, along with a non-Hamiltonian flow that qualitatively exhibits analogous low-frequency spectral behavior.

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

0 major / 2 minor

Summary. The paper proposes a unified perspective on classical and quantum chaos based on the stability of stationary states under slow driving. It introduces the speed-Fisher information as the system's susceptibility to average protocol speed, relates it to irreversible entropy production, and shows that chaotic dynamics produces a divergence of this quantity with protocol time controlled by the perturbation's low-frequency spectral weight. The framework is illustrated with simple classical Hamiltonian, quantum, and non-Hamiltonian examples.

Significance. If the derivations and relations hold, the work supplies a parameter-free diagnostic that unifies classical and quantum chaos detection and extends naturally to non-Hamiltonian flows. The explicit examples and concrete illustrations of the divergence provide falsifiable support for the central claim within the regimes examined.

minor comments (2)
  1. [Abstract] The abstract states that the approach 'naturally extends' to non-Hamiltonian flows, but the manuscript should clarify whether this extension relies on additional assumptions not required for the Hamiltonian cases.
  2. [Introduction] Notation for the speed-Fisher information and its relation to entropy production should be introduced with an explicit equation in the main text before the examples are presented.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, including the significance of the proposed framework and the recommendation for minor revision. We note that no specific major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The abstract and skeptic analysis indicate that the speed-Fisher information is introduced as a new susceptibility measure, explicitly related to entropy production, and then shown to diverge in chaotic regimes via concrete classical, quantum, and non-Hamiltonian examples. No equations or self-citations are visible that would reduce the central divergence claim to a fit, definition, or prior author result by construction. The argument relies on parameter-free relations and explicit illustrations that remain independent of the target result, making the derivation self-contained within the regimes examined.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Abstract-only; the framework introduces the speed-Fisher information as a new probe without specifying its derivation or external calibration. No free parameters or axioms are stated explicitly.

axioms (1)
  • domain assumption Stationary states exist and their stability under slow driving can be probed by a susceptibility to protocol speed.
    Invoked in the first sentence of the abstract as the basis for the unified perspective.
invented entities (1)
  • speed-Fisher information no independent evidence
    purpose: Quantify susceptibility to average protocol speed and serve as a chaos diagnostic linked to entropy production.
    New quantity defined in the abstract; no independent evidence or prior definition supplied.

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