Information, complexity and entropy: a new approach to theory and measurement methods

TL;DR

This paper introduces new computable definitions of information and complexity related to dynamical systems, enabling practical measurement of chaos and entropy through data compression, applicable to single orbits and experimental data.

Contribution

It proposes a novel, computable approach to defining and measuring information, complexity, and entropy, connecting them with Kolmogorov-Sinai entropy and applicable to real data.

Findings

New computable definitions of information and complexity.

Methods to measure chaos using data compression algorithms.

Ability to analyze chaotic behavior even with zero entropy.

Abstract

In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have the following features and motivations: -we give a new computable definition of information and complexity which allows to give a computable characterization of the K-S entropy; -these definitions make sense even for a single orbit and can be measured by suitable data compression algorithms; hence they can be used in simulations and in the analysis of experimental data; -the asymptotic behavior of these quantities allows to compute not only the Kolmogorov-Sinai entropy but also other quantities which give a measure of the chaotic behavior of a dynamical system even in the case of null entropy.