Complexity and non-separability of classical Liouvillian dynamics

Details Complexity and non-separability of classical Liouvillian dynamics Complexity and non-separability of classical Liouvillian dynamics

2010-08-14

arxiv.org/abs/1008.2419v2

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

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.

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