The Entropy Universe

Abstract

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.

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

“…The nonlinear bilateral behavior is shown in this paper to be a necessary but not sufficient condition for finding a complex behavior when the transistor is modeled as a two port admittance parameter. Meanwhile, the study in [ 70 ] demonstrates an important research study related to entropy in which the origin and fundamentals of entropy are presented, explaining how the entropy concept is used in physics, information theory, chaos theory, and data mining, and providing researchers with important issues that can be selected to choose the right variant of entropy for their research study. In addition, the study in [ 71 ] shows a chaotic time delay signature suppression by frequency band extracting is investigated the time delay signature and entropy grow enhancement in a chaotic optical feedback semiconductor laser.…”

Estimation of different types of entropies for the Kumaraswamy distribution

“…• the Rényi, Havrda and Charvat, Arimoto and Tsallis entropy measures are decreasing when δ is increasing while the Awad and Alawneh1 entropy is increasing when δ is increasing, but the Awad and Alawneh2 entropy is decreasing and increasing when δ is increasing. Tables [5][6][7] show the values of the entropy of the Kumaraswamy distribution for a fixed value of b and different values for a and δ. In this setting,…”

“…Since that publication, many areas of study such as statistics, neurobiology, cryptography, bioinformatics, quantum computer science and linguistics, have developed various entropy-based measures. Modern and exhaustive reviews on the 'entropy universe' can be found in [2][3][4][5][6].…”

Entropy Optimization, Maxwell–Boltzmann, and Rayleigh Distributions

“…For γ = 0, the model in ( 9) is very useful in real multivariate reliability analysis; see [12,13]. The model in (10) for γ = 0 corresponds to a multivariate version of Student-t, Cauchy, multivariate F, and related distributions; see [14].…”

“…The concept of entropy is applied in general physics, information theory, chaos theory, time series, computer science, data mining, statistics, engineering, mathematical linguistics, stochastic processes, etc. An account of the entropic universe was given by [10], along with answers to the following questions: How different concepts of entropy arose, what the mathematical definitions of each entropy are, how entropies are related to each other, which entropy is appropriate in which areas of application, and their impacts on the scientific community. Hence, the present article does not attempt to repeat the answers to these questions again.…”