Amigó, José M.Dale, RobertoTempesta, Piergiulio2023-06-222023-06-222022-111054-150010.1063/5.0113335https://hdl.handle.net/20.500.14352/72811© American Institute of Physics 2022 We are very grateful to our reviewers for their comments and suggestions, which have helped to improve the original version of our manuscript. J.M.A. and R.D. were financially supported by the Spanish Grant No. PID2019-108654GB-I00/AEI/10.13039/501100011033. J.M.A. was also supported by Generalitat Valenciana, Spain, Grant No. PROMETEO/2021/063. The research of P.T. has been supported by the Research Project No. PGC2018-094898-B-I00, Ministerio de Ciencia, Innovacion y Universidades and Agencia Estatal de Investigacion, Spain, and by the Severo Ochoa Programme for Centres of Excellence in R & D (No. CEX2019-000904-S), and Ministerio de Ciencia, Innovacion y Universidades y Agencia Estatal de Investigacion, Spain. P.T. is member of the Gruppo Nazionale di Fisica Matematica (GNFM).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.engjournal articlehttp://dx.doi.org/10.1063/5.0113335https://aip.scitation.org/open access51-73MapsFísica-Modelos matemáticosFísica matemática