{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:10:30Z","timestamp":1760145030391,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T00:00:00Z","timestamp":1718150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FAPESP","award":["2021\/15114-8","306920\/2020-4"],"award-info":[{"award-number":["2021\/15114-8","306920\/2020-4"]}]},{"name":"Federal Brazilian Agency-CAPES","award":["2021\/15114-8","306920\/2020-4"],"award-info":[{"award-number":["2021\/15114-8","306920\/2020-4"]}]},{"name":"CNPq (Brazil)","award":["2021\/15114-8","306920\/2020-4"],"award-info":[{"award-number":["2021\/15114-8","306920\/2020-4"]}]},{"name":"Council of Australian University Librarians (CAUL) Consortium","award":["2021\/15114-8","306920\/2020-4"],"award-info":[{"award-number":["2021\/15114-8","306920\/2020-4"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method for classifying spatiotemporal processes based on entropy measurements. To test and validate the method, we selected five classes of similar processes related to the evolution of random patterns: (i) white noise; (ii) red noise; (iii) weak turbulence from reaction to diffusion; (iv) hydrodynamic fully developed turbulence; and (v) plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon permutation entropy (SHp) and a new approach based on Tsallis Spectral Permutation Entropy (Sqs). Notably, our observations reveal the segregation of reaction terms in this SHp\u00d7Sqs space, a result that identifies specific sectors for each class of dynamic process, and it can be used to train machine learning models for the automatic classification of complex spatiotemporal patterns.<\/jats:p>","DOI":"10.3390\/e26060508","type":"journal-article","created":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T06:47:30Z","timestamp":1718174850000},"page":"508","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Characterizing Complex Spatiotemporal Patterns from Entropy Measures"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5214-2399","authenticated-orcid":false,"given":"Luan Orion","family":"Barauna","sequence":"first","affiliation":[{"name":"Applied Computing Graduate Program (CAP), National Institute for Space Research, Av. dos Astronautas, 1.758, Jardim da Granja, S\u00e3o Jos\u00e9 dos Campos 12227-010, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8318-4068","authenticated-orcid":false,"given":"Rubens Andreas","family":"Sautter","sequence":"additional","affiliation":[{"name":"Applied Computing Graduate Program (CAP), National Institute for Space Research, Av. dos Astronautas, 1.758, Jardim da Granja, S\u00e3o Jos\u00e9 dos Campos 12227-010, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2962-4322","authenticated-orcid":false,"given":"Reinaldo Roberto","family":"Rosa","sequence":"additional","affiliation":[{"name":"Applied Computing Graduate Program (CAP), National Institute for Space Research, Av. dos Astronautas, 1.758, Jardim da Granja, S\u00e3o Jos\u00e9 dos Campos 12227-010, SP, Brazil"},{"name":"Laboratory for Computing and Applied Math, National Institute for Space Research, Av. dos Astronautas, 1.758, Jardim da Granja, S\u00e3o Jos\u00e9 dos Campos 12227-010, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4971-5854","authenticated-orcid":false,"given":"Erico Luiz","family":"Rempel","sequence":"additional","affiliation":[{"name":"Mathematics Department, Aeronautics Institute of Technology, Pra\u00e7a Marechal Eduardo Gomes, 50, Vila das Ac\u00e1cias, S\u00e3o Jos\u00e9 dos Campos 12228-900, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8002-5341","authenticated-orcid":false,"given":"Alejandro C.","family":"Frery","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1284458","DOI":"10.3389\/fcpxs.2023.1284458","article-title":"When may a system be referred to as complex? An entropic perspective","volume":"1","author":"Tsallis","year":"2023","journal-title":"Front. Complex Syst."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhang, A., Yang, B., and Huang, L. (2008, January 27\u201330). Feature Extraction of EEG Signals Using Power Spectral Entropy. Proceedings of the International Conference on BioMedical Engineering and Informatics, Sanya, China.","DOI":"10.1109\/BMEI.2008.254"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Raja Abdullah, R.S.A., Saleh, N.L., Syed Abdul Rahman, S.M., Zamri, N.S., and Abdul Rashid, N.E. (2019). 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