Researchers have proposed a new metric, the “speed-Fisher information,” to unify the understanding of chaos in classical and quantum systems. This metric quantifies the sensitivity of a system's stationary states to slow driving and is directly related to irreversible entropy production. Chaotic dynamics manifest as a divergence of this speed-Fisher information with increasing protocol time, with the response controlled by the perturbation's low-frequency spectral weight.

This approach applies to both classical and quantum Hamiltonian systems and can be extended to non-Hamiltonian classical flows. The relevance of this metric lies in its ability to provide a unified framework for studying chaos across different domains of physics, addressing one of the fundamental questions in the dynamics of complex systems. Sensitivity to slow perturbations is a key characteristic distinguishing chaotic behavior from other types of dynamics.

Furthermore, the study identifies a unique quantum regime at timescales shorter than the Planckian time, where the speed-Fisher information exhibits a distinct quantum scaling. This finding suggests that the metric can be particularly useful for exploring the transition between quantum and classical dynamics and for understanding the limits of predictability in quantum systems. The authors illustrate their framework with simple classical and quantum examples, demonstrating the applicability and power of their new analytical tool.