José María Amigó, Roberto Dale (Center of Operations Research, Miguel Hernández University of Elche) and Piergiulio Tempesta (Departamento de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid)
Abstract: This is a review of group entropy and its application to permutation complexity. Specifically, we revisit a new approach to the notion of complexity in the time series analysis based on both permutation entropy and group entropy. As a result, the permutation entropy rate can be extended from deterministic dynamics to random processes. More generally, our approach provides a unified framework to discuss chaotic and random behaviors.