Santa Fe Institute

SFI Working Paper Abstract

Title: Chaos Forgets and Remembers: Measuring Information Creation, Destruction, and Storage
Author(s): Ryan G. James, Korana Burke, James P. Crutchfield
Files: [pdf]
Paper #: 13-10-030
Date: Oct. 2, 2013
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 fundamen- tally 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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