Analytical results in calculating the entropy of recurrence microstates

Felipe Eduardo Lopes da Cruz, João Vitor Vieira Flauzino, Sergio Roberto Lopes and Thiago de Lima Prado

Physica A: Statistical Mechanics and its Applications, 2024, vol. 638, issue C

Abstract: Since the development of recurrence plots (RP) and recurrence quantification analysis (RQA), there has been a growing interest in many areas in studying physical systems using recursion techniques. In particular, as part of the RQAs, we observed the development of the concept of recurrence microstates, defined as small blocks obtained from a recurrence graph. It can be shown that some other RQAs can be calculated as a function of recurrence microstates, and the probabilities of occurrences of these microstates can define an information entropy, the so-called entropy of recurrence microstates. It was also observed that recurrence microstates and recurrence entropy can distinguish between correlated and uncorrelated stochastic and deterministic states, due to their symmetry properties. In this paper we propose analytical expressions for calculating the entropy of recurrence microstates, avoiding the need to sample a large set of recurrence microstates. The results can be particularly important in quantifying small amounts of data, where significant sampling of microstates may not be possible. In this paper we propose analytical expressions to compute the entropy of recurrence microstates avoiding the need to sample a large set of recurrence microstates. We show that our results are accurate for cases where the probability distribution function is known. For other situations, the results can be calculated approximately. Another important fact is that the approximate results can be generalized to any size of microstate, making them a powerful tool for calculating the entropy of recurrence. Our approximate methods allow us to know what these properties are and how to exploit this quantifier in the best possible way, with minimal memory usage. Finally, we show that our analytical results are in remarkable agreement with numerical simulations.

Keywords: Recurrence analysis; Recurrence entropy; Approximation method (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437124001377
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:638:y:2024:i:c:s0378437124001377

DOI: 10.1016/j.physa.2024.129629

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().