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arXiv · 1008.2419

Complexity and non-separability of classical Liouvillian dynamics

Tomaz Prosen
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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.

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Tomaz Prosen. 2011-02-01. Complexity and non-separability of classical Liouvillian dynamics. https://doi.org/10.1103/physreve.83.031124

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