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

Highlights: • Kolmogorov–Sinai entropy measures information creation in dynamical systems. • It decomposes into information remembered (bound) and that forgotten (ephemeral). • Thus chaotic dynamical systems compute: they actively store and destroy information. • This is easily estimated and, in many cases, analytically computed. • Decomposition illustrated for the Logistic, Tent, and Lozi discrete-time maps. - 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