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Characterizing Spatiotemporal Complex Patterns from Entropy Measures
Version 1
: Received: 5 February 2024 / Approved: 6 February 2024 / Online: 6 February 2024 (13:38:50 CET)
A peer-reviewed article of this Preprint also exists.
Barauna, L.O.; Sautter, R.A.; Rosa, R.R.; Rempel, E.L.; Frery, A.C. Characterizing Complex Spatiotemporal Patterns from Entropy Measures. Entropy 2024, 26, 508. Barauna, L.O.; Sautter, R.A.; Rosa, R.R.; Rempel, E.L.; Frery, A.C. Characterizing Complex Spatiotemporal Patterns from Entropy Measures. Entropy 2024, 26, 508.
Abstract
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 to classify spatiotemporal processes based on entropy measurements. To test and validate the method, we selected four classes of similar processes related to the evolution of random patterns: dynamic colored noises ((i)~white and (ii)~red); (iii)~weak turbulence from reaction-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 ($S^p_H$) and a new approach based on Tsallis Spectral Permutation Entropy ($S^s_q$). Notably, our observations reveal the segregation of reaction terms in this $S^p_H \times S^s_q$ space, a result that identifies specific sectors for each class of dynamic process, and can be used to train machine learning models for automatic classification of complex spatiotemporal patterns.
Keywords
nonlinear dynamics, spatiotemporal patterns; turbulence; Shannon Entropy; Tsallis 16; entropy: gradient pattern analysis
Subject
Physical Sciences, Fluids and Plasmas Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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