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The Entropy Universe

Institute for Systems and Computer Engineering, Technology and Science (INESC-TEC), 4200-465 Porto, Portugal
Computer Science Department, Faculty of Sciences, University of Porto, 4169-007 Porto, Portugal
Centre for Health Technology and Services Research (CINTESIS), Faculty of Medicine University of Porto, 4200-450 Porto, Portugal
Department of Community Medicine, Information and Health Decision Sciences-MEDCIDS, Faculty of Medicine, University of Porto, 4200-450 Porto, Portugal
LASIGE, Faculdade de Ciências da Universidade de Lisboa, 1749-016 Lisboa, Portugal
Departamento de Informática, Faculdade de Ciências da Universidade de Lisboa, 1749-016 Lisboa, Portugal
Instituto de Telecomunicações, 1049-001 Lisboa, Portugal
Instituto Politécnico de Viana do Castelo, 4900-347 Viana do Castelo, Portugal
Author to whom correspondence should be addressed.
Academic Editor: Miguel Rubi
Entropy 2021, 23(2), 222;
Received: 15 January 2021 / Revised: 6 February 2021 / Accepted: 8 February 2021 / Published: 11 February 2021
(This article belongs to the Special Issue Review Papers for Entropy)
About 160 years ago, the concept of entropy was introduced in thermodynamics by Rudolf Clausius. Since then, it has been continually extended, interpreted, and applied by researchers in many scientific fields, such as general physics, information theory, chaos theory, data mining, and mathematical linguistics. This paper presents The Entropy Universe, which aims to review the many variants of entropies applied to time-series. The purpose is to answer research questions such as: How did each entropy emerge? What is the mathematical definition of each variant of entropy? How are entropies related to each other? What are the most applied scientific fields for each entropy? We describe in-depth the relationship between the most applied entropies in time-series for different scientific fields, establishing bases for researchers to properly choose the variant of entropy most suitable for their data. The number of citations over the past sixteen years of each paper proposing a new entropy was also accessed. The Shannon/differential, the Tsallis, the sample, the permutation, and the approximate entropies were the most cited ones. Based on the ten research areas with the most significant number of records obtained in the Web of Science and Scopus, the areas in which the entropies are more applied are computer science, physics, mathematics, and engineering. The universe of entropies is growing each day, either due to the introducing new variants either due to novel applications. Knowing each entropy’s strengths and of limitations is essential to ensure the proper improvement of this research field. View Full-Text
Keywords: entropy measures; information theory; time-series; application areas entropy measures; information theory; time-series; application areas
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MDPI and ACS Style

Ribeiro, M.; Henriques, T.; Castro, L.; Souto, A.; Antunes, L.; Costa-Santos, C.; Teixeira, A. The Entropy Universe. Entropy 2021, 23, 222.

AMA Style

Ribeiro M, Henriques T, Castro L, Souto A, Antunes L, Costa-Santos C, Teixeira A. The Entropy Universe. Entropy. 2021; 23(2):222.

Chicago/Turabian Style

Ribeiro, Maria, Teresa Henriques, Luísa Castro, André Souto, Luís Antunes, Cristina Costa-Santos, and Andreia Teixeira. 2021. "The Entropy Universe" Entropy 23, no. 2: 222.

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