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arxiv: 2605.23585 · v1 · pith:HNIMWHGHnew · submitted 2026-05-22 · 🪐 quant-ph

Probing Chaos and Criticality with Observational Entropy and Finite-Resolution Measurements

J. Bharathi Kannan , Sreeram PG , M.S. Santhanam This is my paper

Pith reviewed 2026-05-25 04:26 UTC · model grok-4.3

classification 🪐 quant-ph
keywords observational entropyquantum chaoscriticalityAubry-Andre modelkicked rotorLyapunov exponentfinite-resolution measurementsEhrenfest time
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The pith

Observational entropy from finite-resolution measurements diagnoses quantum chaos and criticality.

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

This paper shows that observational entropy computed from coarse-grained measurement outcomes supplies a single practical quantity for locating both critical points and the onset of chaos in quantum systems. Derivatives of this entropy correctly identify the metal-insulator crossover in the Aubry-Andre model and the breakup of regular tori in the kicked rotor once resolution passes a modest threshold. In fully chaotic regimes the entropy grows linearly inside the Ehrenfest time and its slope supplies an observable Lyapunov exponent that, after a Pretty Good Measurement correction to the Husimi distribution, matches the classical value. If the claim holds, experimenters gain an accessible route to these diagnostics without requiring complete state tomography.

Core claim

Observational entropy defined directly from finite-resolution measurement outcomes provides a unified framework for quantifying chaos and probing criticality. Derivatives of OE accurately diagnose the insulator-metal crossover in the Aubry-Andre model and the destruction of KAM tori in the Kicked Rotor, with critical points converging to exact theoretical values above a resolution threshold. In chaotic regimes, OE grows linearly within the Ehrenfest time, and its slope defines an observable Lyapunov exponent that, after a Pretty Good Measurement correction to the Husimi distribution, reproduces the classical Lyapunov exponent in both standard and singular kicked rotors.

What carries the argument

Observational entropy, the entropy computed from the probability distribution over finite-resolution measurement outcomes.

Load-bearing premise

That the Pretty Good Measurement correction to the Husimi distribution yields an entropy production rate that quantitatively equals the classical Lyapunov exponent, and that OE derivatives converge to exact critical values once resolution exceeds a finite threshold.

What would settle it

Measure the slope of observational entropy in a kicked rotor whose classical Lyapunov exponent is known; if the corrected rate deviates from that value, or if OE-derived critical points fail to approach the theoretical location as resolution is increased, the central claim is falsified.

Figures

Figures reproduced from arXiv: 2605.23585 by J. Bharathi Kannan, M.S. Santhanam, Sreeram PG.

Figure 1
Figure 1. Figure 1: FIG. 1. Top: Schematic of measuring observational en [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Observational entropy growth and extracted Lya [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Effect of finite measurement statistics on the PGM [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

Coarse-grained measurements offer a scalable alternative to full state tomography for characterizing complex quantum dynamics. We show that observational entropy (OE), an information-theoretic entropy defined directly from finite-resolution measurement outcomes, provides a unified and experimentally accessible framework for quantifying chaos and probing criticality. From probing the insulator-metal crossover in the Aubry-Andre model to tracking the gradual destruction of Kolmogorov-Arnold-Moser tori in the Kicked Rotor, derivatives of OE provide an accurate and unified diagnostic of probing these transitions. In both cases, the critical points extracted from dynamical evolution and eigenstate analyses converge to the exact theoretical values once the observational resolution exceeds a finite threshold. In the chaotic limit, OE exhibits a linear behavior within the Ehrenfest time regime, and its slope defines an observable Lyapunov exponent. Using a Pretty Good Measurement correction to the Husimi phase-space distribution, this entropy-production rate quantitatively reproduces the classical Lyapunov exponent in both the standard and singular kicked rotors. Our results establish OE as a compact information-theoretic bridge between classical instability, quantum criticality, and realistic finite-resolution measurements.

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 claims that observational entropy (OE), defined from finite-resolution measurement outcomes, supplies a unified, experimentally accessible diagnostic for quantum criticality and chaos. Derivatives of OE identify the insulator-metal crossover in the Aubry-André model and the destruction of KAM tori in the kicked rotor, with extracted critical points converging to exact theoretical values above a finite observational-resolution threshold. In the chaotic regime, OE grows linearly inside the Ehrenfest time; its slope is interpreted as an observable Lyapunov exponent that, after a Pretty Good Measurement (PGM) correction is applied to the Husimi distribution, quantitatively reproduces the classical Lyapunov exponent for both the standard and singular kicked rotors.

Significance. If the quantitative claims hold, the work supplies a compact information-theoretic bridge between classical instability, quantum phase transitions, and realistic finite-resolution measurements. The approach is directly relevant to quantum simulators and avoids full state tomography. The use of a standard PGM correction to recover the classical Lyapunov exponent is noted as a strength when the raw OE already yields a close slope; the unified treatment across criticality and chaos is potentially useful if the resolution-threshold convergence is robust.

major comments (2)
  1. [Abstract and §4] Abstract and §4 (kicked-rotor analysis): the central claim that the OE entropy-production rate 'quantitatively reproduces the classical Lyapunov exponent' is achieved only after the PGM correction to the Husimi distribution. The manuscript must explicitly compare the raw OE slope (without PGM) to the corrected slope and to the classical value; without this comparison it remains unclear whether the correction is an essential auxiliary step whose form depends on resolution or singularity, which is load-bearing for the assertion that OE itself supplies the unified diagnostic.
  2. [§3] §3 (Aubry-André eigenstate and dynamical analyses): the statement that critical points extracted from OE derivatives 'converge to the exact theoretical values once the observational resolution exceeds a finite threshold' is central to the criticality claim. The text should report the numerical threshold value, the functional form of the convergence, and the residual error at that threshold for both the dynamical and eigenstate routes.
minor comments (2)
  1. Notation for the observational resolution parameter is introduced without a dedicated symbol table; a short table listing all resolution-related symbols and their physical meaning would improve readability.
  2. Figure captions for the OE time series in the chaotic regime should state the precise Ehrenfest-time window used for the linear fit and the number of disorder realizations averaged.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation and the recommendation of minor revision. The comments are helpful for improving the clarity of our claims regarding observational entropy. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and §4] Abstract and §4 (kicked-rotor analysis): the central claim that the OE entropy-production rate 'quantitatively reproduces the classical Lyapunov exponent' is achieved only after the PGM correction to the Husimi distribution. The manuscript must explicitly compare the raw OE slope (without PGM) to the corrected slope and to the classical value; without this comparison it remains unclear whether the correction is an essential auxiliary step whose form depends on resolution or singularity, which is load-bearing for the assertion that OE itself supplies the unified diagnostic.

    Authors: We agree that an explicit comparison is valuable for transparency. The manuscript already states that quantitative reproduction of the classical Lyapunov exponent requires the PGM correction to the Husimi distribution. In the revision we will add a direct comparison in §4 (including a new panel or table) of the raw OE slope, the PGM-corrected slope, and the classical value for both the standard and singular kicked rotors across a range of resolutions. This will show that the raw slope is already close but the correction yields quantitative agreement, and we will discuss its resolution dependence. revision: yes

  2. Referee: [§3] §3 (Aubry-André eigenstate and dynamical analyses): the statement that critical points extracted from OE derivatives 'converge to the exact theoretical values once the observational resolution exceeds a finite threshold' is central to the criticality claim. The text should report the numerical threshold value, the functional form of the convergence, and the residual error at that threshold for both the dynamical and eigenstate routes.

    Authors: We will incorporate the requested quantitative details. In the revised §3 we will state the specific numerical threshold (minimal resolution/binning) at which convergence is observed, describe the functional form of the approach to the exact critical value (e.g., scaling with resolution), and report the residual errors for both the eigenstate and dynamical routes in the Aubry-André model. These values are directly obtainable from the existing numerical data. revision: yes

Circularity Check

0 steps flagged

No significant circularity; OE definition and Lyapunov slope are independent of inputs

full rationale

The paper defines observational entropy directly from finite-resolution measurement outcomes and shows linear behavior in the Ehrenfest regime whose slope is presented as defining an observable Lyapunov exponent. The PGM correction to the Husimi distribution is invoked as an auxiliary standard tool to achieve quantitative match with classical values, but the abstract and provided text give no equation or self-citation that reduces this slope or the critical-point extraction to a fitted parameter or prior result by construction. Critical points are stated to converge to exact theoretical values once resolution exceeds a threshold, indicating an independent check rather than tautology. No load-bearing self-citation chain or ansatz smuggling is exhibited in the given material. The derivation chain remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on the definition of observational entropy from finite-resolution outcomes and the validity of the Pretty Good Measurement correction for phase-space distributions; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Observational entropy is defined directly from finite-resolution measurement outcomes
    Core definition invoked for all applications in the abstract.

pith-pipeline@v0.9.0 · 5722 in / 1133 out tokens · 19311 ms · 2026-05-25T04:26:09.759286+00:00 · methodology

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