title: Complexity and nonseparability 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 a stricter criterion of complexity than Kolmogorov-Sinai entropy, namely it requires that the dynamics be exponentially unstable, nonlinear, and non-Markovian.
authors.affiliation: Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia.
authors.forename: Tomaž
authors.initials: T
authors.lastname: Prosen
mesh_terms: D000465:Algorithms; D019277:Entropy; D005583:Fourier Analysis; D008390:Markov Chains; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D010825:Physics / Q000379:methods*; D011789:Quantum Theory; D013816:Thermodynamics