2013/09/30 by Ryan G. James, Korana Burke, James P. Crutchfield · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #cond-mat.stat-mech #cs.IT #math.DS #math.IT #nlin.CD
paper · pdf · doi:10.1016/j.physleta.2014.05.014
5 pages, 4 figures; supplemental: 2 pages, 4 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/chaos_anatomy.htm
arxiv created 2013/12/17 · arxiv updated 2015/06/17
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.