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Complexity and nonseparability of classical Liouvillian dynamics

  • 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.

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Author details:Tomaz Prosen
DOI:https://doi.org/10.1103/PhysRevE.83.031124
ISSN:1539-3755
Title of parent work (English):Physical review : E, Statistical, nonlinear and soft matter physics
Publisher:American Physical Society
Place of publishing:College Park
Publication type:Article
Language:English
Year of first publication:2011
Publication year:2011
Release date:2017/03/26
Volume:83
Issue:3
Number of pages:5
Funding institution:Slovenian research agency [P1-0044, J1-2208]; Alexander von Humboldt Foundation
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer review:Referiert
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