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Quantum Dynamical Systems$
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Robert Alicki and Mark Fannes

Print publication date: 2001

Print ISBN-13: 9780198504009

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780198504009.001.0001

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Classical Dynamical Entropy

Classical Dynamical Entropy

(p.213) 11 Classical Dynamical Entropy
Quantum Dynamical Systems

Robert Alicki

Mark Fannes

Oxford University Press

This chapter applies the algebraic formalism to classical dynamical systems, in particular, the notion of dynamical entropy developed in the previous chapter in terms of operational partitions is equivalent to the standard Kolmogorov–Sinai invariant. A characterization of partitions that are sufficiently fine to reach the KS-invariant is given in terms of H-dense sub-algebras, and then is applied to unimodular orthonormal systems. The new formalism provides new techniques for computing the KS-entropy that is illustrated by the examples of expanding maps and Arnold cat maps.

Keywords:   KS-entropy, H-dense sub-algebra, unimodular orthonormal systems, KS-invariant, Arnold cat maps

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