Abstract
In this chapter, we consider systems with irregular dynamical behaviors that are stronger than ergodic. Namely, we consider dynamics described by measure preserving transformations that have the property of strong, or Hopf, mixing. Systems with mixing dynamics have entropies that are forever fixed by their mode of preparation. This is followed by a brief discussion of Kolmogorov systems in Section B. Section C discusses the behavior of temporal correlation between dynamical variables, showing that mixing is necessary and sufficient for the decay of temporal correlations to zero.
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© 1992 Springer Science+Business Media New York
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Mackey, M.C. (1992). Mixing. In: Time’s Arrow: The Origins of Thermodynamic Behavior. Springer Study Edition. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9524-9_5
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DOI: https://doi.org/10.1007/978-1-4613-9524-9_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94093-9
Online ISBN: 978-1-4613-9524-9
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