The renormalized entropy—an appropriate complexity measure?

Abstract We have studied the renormalized entropy Δ S in the framework of complexity measures. In opposite to other complexity measures, this Δ S is a relative measure, i.e. it is defined relative to a fixed basic state. To investigate its specific capabilities, Δ S has been applied to different dynamical regimes of the logistic map. We have found that the renormalized entropy clearly indicates all transitions: from periodic to chaotic behaviour as well as between different types of chaos, such as band-merging, intermittency or inner crises. Δ S also distinctly describes how additive noise changes the dynamics. Due to these outstanding properties we recommend Δ S for various fields of application.