Universal Dynamical Response to Slow Driving in Chaotic Systems

Abstract

We propose a unified perspective on classical and quantum chaos based on the sensitivity of a system's stationary states to 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.

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BibTeX RIS

BibTeX

@misc{karve2026universal,
  title = {{Universal Dynamical Response to Slow Driving in Chaotic Systems}},
  author = {Nachiket Karve and Nathan Rose and David Campbell and Anatoli Polkovnikov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.23810},
  eprint = {2606.23810},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.23810},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Universal Dynamical Response to Slow Driving in Chaotic Systems
AU  - Nachiket Karve
AU  - Nathan Rose
AU  - David Campbell
AU  - Anatoli Polkovnikov
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2606.23810
UR  - https://arxiv.org/abs/2606.23810
AB  - We propose a unified perspective on classical and quantum chaos based on the sensitivity of a system's stationary states to 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.
ER  -

Abstract

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