# Characterizing Complex Spatiotemporal Patterns from Entropy Measures

## TL;DR

This paper introduces a new method to classify complex spatiotemporal patterns using entropy measures, which can help in automatically identifying different types of dynamic processes.

## Contribution

The novel contribution is a classification method using Shannon permutation entropy and Tsallis Spectral Permutation Entropy for spatiotemporal data.

## Key findings

- Shannon permutation entropy (SHp) and Tsallis Spectral Permutation Entropy (Sqs) show better combined performance in classifying spatiotemporal processes.
- The SHp×Sqs space reveals segregation of reaction terms, identifying specific sectors for each dynamic process class.
- This method can be used to train machine learning models for automatic classification of complex spatiotemporal patterns.

## 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 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×Sqs 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.