Speed-Fisher Information: Chaos and Irreversibility in Classical and Quantum Dynamics
cond-mat.stat-mech, nlin.CD, quant-ph
Submitted: 2026-09-28
Updated: 2026-09-28
Comments: 23 pages, 10 figures
License: http://creativecommons.org/licenses/by/4.0/
The gist: We propose a unified perspective on classical and quantum chaos based on the sensitivity of a system's stationary states to slow driving.
Terminology
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
Sources
- Gradient of the Adiabatic Gauge Potential in Classical Systems
- Hilbert space geometry and quantum chaos
- Multipartite entanglement and high precision metrology
- Fidelity approach to quantum phase transitions
- Universal Dynamical Response to Slow Driving in Chaotic Systems
- Confined and deconfined chaos in classical spin systems
- Sensitivity to perturbations in the three-dimensional Anderson model
- Temperature and integrability-breaking correspondence via adiabatic transformations
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