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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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Dynamical Entropy

Dynamical Entropy

Chapter:
(p.186) 10 Dynamical Entropy
Source:
Quantum Dynamical Systems
Author(s):

Robert Alicki

Mark Fannes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198504009.003.0010

A non-zero Kolmogrov–Sinai entropy for a classical dynamical system is a signature of dynamical instability. This chapter presents an approach to quantifying randomizing dynamical behaviour in deterministic quantum systems based on a spin chain model. The starting point is an operational partition that is refined in the course of time. To each partition corresponds a correlation matrix and the dynamics lead eventually to a shift-invariant state on a quantum spin chain with its associated entropy. General properties and bounds are proved, which allow for the computation of the entropy in a number of simple model systems such as finite systems, shift dynamics on a quantum spin chain, free shifts, and Powers–Price shifts.

Keywords:   dynamical entropy, quantum dynamical entropy, operational partition, quantum shift, free shift, Powers-Price shift

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