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Chaos forgets and remembers: Measuring information creation, destruction, and storage
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https://doi.org/10.1016/j.physleta.2014.05.014Abstract
The hallmark of deterministic chaos is that it creates information - the rate being given by the Kolmogorov-Sinai metric entropy. Since its introduction half a century ago, the metric entropy has been used as a unitary quantity to measure a system's intrinsic unpredictability. Here, we show that it naturally decomposes into two structurally meaningful components: A portion of the created information - the ephemeral information - is forgotten and a portion - the bound information - is remembered. The bound information is a new kind of intrinsic computation that differs fundamentally from information creation: it measures the rate of active information storage. We show that it can be directly and accurately calculated via symbolic dynamics, revealing a hitherto unknown richness in how dynamical systems compute. © 2014 Elsevier B.V.
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