Complexity and non-separability of classical Liouvillian dynamics

Abstract

We propose a simple complexity indicator of classical Liouvillian dynamics, namely the separability entropy, which determines the logarithm of an effective number of terms in a Schmidt decomposition of phase space density with respect to an arbitrary fixed product basis. We show that linear growth of separability entropy provides stricter criterion of complexity than Kolmogorov-Sinai entropy, namely it requires that dynamics is exponentially unstable, non-linear and non-markovian.

Revised version, 5 pages (RevTeX), with 6 pdf-figures

References in corpus (7)

• Entropy scaling and simulability by Matrix Product States
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• How complex is the quantum motion?
• Complexity of Quantum States and Reversibility of Quantum Motion
• On ergodic and mixing properties of the triangle map
• Phase-space characterization of complexity in quantum many-body dynamics
• Chaotic Diffusion on Periodic Orbits: The Perturbed Arnol'd Cat Map

Cited by in corpus (7)

• A Universal Operator Growth Hypothesis
• OTOC, complexity and entropy in bi-partite systems
• Classical Dynamics of Quantum Entanglement
• Complexity of quantum motion and quantum-classical correspondence: A phase-space approach
• Wigner separability entropy and complexity of quantum dynamics
• Quantum and classical complexity in coupled maps
• Entanglement dynamics and classical complexity