Chaos forgets and remembers: Measuring information creation,destruction, and storage |
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Institution: | 1. Complexity Sciences Center and Physics Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA;2. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA |
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Abstract: | 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. |
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Keywords: | Chaos Entropy rate Bound information Shannon information measures Information diagram Discrete-time maps |
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