Next Article in Journal
Computational Complexity Reduction of Neural Networks of Brain Tumor Image Segmentation by Introducing Fermi–Dirac Correction Functions
Next Article in Special Issue
Three-Factor Kinetic Equation of Catalyst Deactivation
Previous Article in Journal
Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics
Previous Article in Special Issue
An Optimality Summary: Secret Key Agreement with Physical Unclonable Functions
Review

The Entropy Universe

1
Institute for Systems and Computer Engineering, Technology and Science (INESC-TEC), 4200-465 Porto, Portugal
2
Computer Science Department, Faculty of Sciences, University of Porto, 4169-007 Porto, Portugal
3
Centre for Health Technology and Services Research (CINTESIS), Faculty of Medicine University of Porto, 4200-450 Porto, Portugal
4
Department of Community Medicine, Information and Health Decision Sciences-MEDCIDS, Faculty of Medicine, University of Porto, 4200-450 Porto, Portugal
5
LASIGE, Faculdade de Ciências da Universidade de Lisboa, 1749-016 Lisboa, Portugal
6
Departamento de Informática, Faculdade de Ciências da Universidade de Lisboa, 1749-016 Lisboa, Portugal
7
Instituto de Telecomunicações, 1049-001 Lisboa, Portugal
8
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; https://doi.org/10.3390/e23020222
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
Show Figures

Figure 1

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. https://doi.org/10.3390/e23020222

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. https://doi.org/10.3390/e23020222

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. https://doi.org/10.3390/e23020222

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop