Chaos Forgets and Remembers: Measuring Information Creation, Destruction, and Storage

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.

5 pages, 4 figures; supplemental: 2 pages, 4 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/chaos_anatomy.htm

References in corpus (3)

• Time's Barbed Arrow: Irreversibility, Crypticity, and Stored Information
• Anatomy of a Bit: Information in a Time Series Observation
• Prediction, Retrodiction, and The Amount of Information Stored in the Present

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• The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications
• Irreversibility of symbolic time series: a cautionary tale