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PreprintCC BY 4.0arXiv

Speed-Fisher Information: Chaos and Irreversibility in Classical and Quantum Dynamics

  • Nachiket Karve
  • Nathan Rose
  • David Campbell
  • Anatoli Polkovnikov
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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. Additionally, we identify a quantum regime at times shorter than the Planckian timescale, in which the speed-Fisher information exhibits a uniquely quantum scaling. We illustrate this framework with simple classical and quantum examples

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Cite

BibTeXRIS
BibTeX
@misc{karve2026speedfisher,
  title = {{Speed-Fisher Information: Chaos and Irreversibility in Classical and Quantum Dynamics}},
  author = {Nachiket Karve and Nathan Rose and David Campbell and Anatoli Polkovnikov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35687},
  eprint = {2609.35687},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35687},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Speed-Fisher Information: Chaos and Irreversibility in Classical and Quantum Dynamics
AU  - Nachiket Karve
AU  - Nathan Rose
AU  - David Campbell
AU  - Anatoli Polkovnikov
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35687
UR  - https://arxiv.org/abs/2609.35687
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. Additionally, we identify a quantum regime at times shorter than the Planckian timescale, in which the speed-Fisher information exhibits a uniquely quantum scaling. We illustrate this framework with simple classical and quantum examples
ER  -