Speed limits on classical chaos
arXiv:2110.06993
Abstract
Uncertainty in the initial conditions of dynamical systems can cause exponentially fast divergence of trajectories, a signature of deterministic chaos. Here, we derive a classical uncertainty relation that sets a speed limit on the rates of local observables underlying this behavior. For systems with a time-invariant stability matrix, this general speed limit simplifies to classical analogues of the Mandelstam-Tamm versions of the time-energy uncertainty relation. This classical bound derives from our definition of Fisher information in terms of Lyapunov vectors on tangent space, analogous to the quantum Fisher information defined in terms of wavevectors on Hilbert space. This information measures fluctuations in local stability of the state space and sets a lower bound on the time of classical, dynamical systems to evolve between two distinguishable states. The bounds it sets apply to systems that are open or closed, conservative or dissipative, actively driven or passively evolving, and directly connect the geometries of phase space and information.
arXiv commentRevision in the main text and some new results added in supplementary material
References in corpus (15)
- Advances in Quantum Metrology
- Ultimate physical limits to computation
- Quantum speed limit for non-Markovian dynamics
- Speed Limit for Classical Stochastic Processes
- Fundamental Quantum Limit to Waveform Estimation
- Quantum Speed Limit is Not Quantum
- Uncertainty relations in stochastic processes: An information inequality approach
- Nonlinear quantum metrology of many-body open systems
- Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
- Quantum speed limits and the maximal rate of information production
- Probing Quantum Speed Limits with Ultracold Gases
- Critical fluctuations and slowing down of chaos
- Bounding generalized relative entropies: Nonasymptotic quantum speed limits
- Self-averaging fluctuations in the chaoticity of simple fluids
- Thermodynamic speed limits from the regression of information