{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T04:19:53Z","timestamp":1778645993641,"version":"3.51.4"},"reference-count":111,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2012,8,23]],"date-time":"2012-08-23T00:00:00Z","timestamp":1345680000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems.<\/jats:p>","DOI":"10.3390\/e14081553","type":"journal-article","created":{"date-parts":[[2012,8,23]],"date-time":"2012-08-23T11:05:47Z","timestamp":1345719947000},"page":"1553-1577","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":569,"title":["Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5839-0393","authenticated-orcid":false,"given":"Massimiliano","family":"Zanin","sequence":"first","affiliation":[{"name":"Centre for Biomedical Technology, Polytechnic University of Madrid, Pozuelo de Alarc\u00f3n, 28223 Madrid, Spain"},{"name":"Faculdade de Ci\u00eancias e Tecnologia, Departamento de Engenharia Electrot\u00e9cnica, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal"},{"name":"Innaxis Foundation & Research Institute Jos\u00e9 Ortega y Gasset 20, 28006 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luciano","family":"Zunino","sequence":"additional","affiliation":[{"name":"Centro de Investigaciones \u00d3pticas (CONICET La Plata - CIC) C.C. 3, 1897 Gonnet, Argentina"},{"name":"Departamento de Ciencias B\u00e1sicas, Facultad de Ingenier\u00eda, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Osvaldo A.","family":"Rosso","sequence":"additional","affiliation":[{"name":"LaCCAN\/CPMAT - Instituto de Computa\u00e7\u00e3o, Universidade Federal de Alagoas, BR 104 Norte km 97, 57072-970 Macei\u00f3, Alagoas, Brazil"},{"name":"Laboratorio de Sistemas Complejos, Facultad de Ingenier\u00eda, Universidad de Buenos Aires, 1063 Av. Paseo Col\u00f3n 840, Ciudad Aut\u00f3noma de Buenos Aires, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Papo","sequence":"additional","affiliation":[{"name":"Centre for Biomedical Technology, Polytechnic University of Madrid, Pozuelo de Alarc\u00f3n, 28223 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gray, R.M. (1990). 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