Chaos forgets and remembers: Measuring information creation, destruction, and storage

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. (C) 2014 Elsevier B.V. All rights reserved.