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Entropy
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Entropy-Based Time Series Analysis: Theory and Applications
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Entropy-Based Time Series Analysis: Theory and Applications

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: 31 March 2026 | Viewed by 4307

Special Issue Editor

Dr. Felipe Olivares

E-Mail Website
Guest Editor
Institute for Cross-Disciplinary Physics and Complex Systems (CSIC-UIB), Campus UIB, 07122 Palma, Spain
Interests: time series analysis; permutation entropy; ordinal patterns; multifractality; long-range correlations; complexity measures; data analysis; nonlinear dynamics

Special Issue Information

Dear Colleagues,

Understanding complexity in empirical time series has become a crucial area of research across various scientific domains. Unlike traditional statistical measures, which focus on central tendency or variance, entropy-based approaches—alongside fractality and nonlinear dynamic methods—uncover deeper insights into the intrinsic structure of data. Entropy-based methodologies can be broadly categorized into two main types: structural entropy, which examines power distribution across frequency components, and dynamical entropy, which evaluates the evolution of similarity between inner patterns in data dynamics. While these techniques have been widely applied in various scientific disciplines, including finance, physiology, climate, and engineering, there is still room for further development and applications.

The distinct analytical approaches of structural and dynamical entropies suggest that integrating them may lead to a richer understanding of time series complexity. Additionally, opportunities exist for hybrid methods that combine entropy with fractal analysis or nonlinear dynamic techniques, as well as advancements in entropy computation, to handle large-scale datasets and finite-size matters efficiently. We also encourage contributions that apply these methodologies to real-world and socio-technical datasets.

This Special Issue aims to showcase original papers and comprehensive reviews focused on innovative and enhanced entropy-based techniques for time series analysis, including theoretical studies and multidisciplinary applications. We invite researchers to submit work that pushes the boundaries of knowledge and drives discoveries in this evolving field.

Dr. Felipe Olivares
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • structural entropies
  • dynamical entropies
  • multiscale entropy
  • ordinal patterns-based entropies
  • entropy as a complexity measure
  • signal classification
  • signal segmentation and spike detection
  • multivariate time series analysis
  • real-world and socio-technical applications
  • interdisciplinary applications

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

23 pages, 7685 KB  
Article
Literal Pattern Analysis of Texts Written with the Multiple Form of Characters: A Comparative Study of the Human and Machine Styles
by Kazuya Hayata
Entropy 2026, 28(1), 36; https://doi.org/10.3390/e28010036 - 27 Dec 2025
Viewed by 342
Abstract
Aside from languages having no form of written expression, it is usually the case with every language on this planet that texts are written in a single character. But every rule has its exceptions. A very rare exception is Japanese, the texts of [...] Read more.
Aside from languages having no form of written expression, it is usually the case with every language on this planet that texts are written in a single character. But every rule has its exceptions. A very rare exception is Japanese, the texts of which are written in the three kinds of characters. In European languages, no one can find a text written in a mixture of the Latin, Cyrillic, and Greek alphabets. For several Japanese texts currently available, we conduct a quantitative analysis of how the three characters are mixed using a methodology based on a binary pattern approach to the sequence that has been generated by a procedure. Specifically, we consider two different texts in the former and present constitutions as well as a famous American story that has been translated at least 13 times into Japanese. For the latter, a comparison is made among the human translations and four machine translations by DeepL and Google Translate. As metrics of divergence and diversity, the Hellinger distance, chi-square value, normalized Shannon entropy, and Simpson’s diversity index are employed. Numerical results suggest that in terms of the entropy, the 17 translations consist of three clusters, and that overall, the machine-translated texts exhibit entropy higher than the human translations. The finding suggests that the present method can provide a tool useful for stylometry and author attribution. Finally, through comparison with the diversity index, capabilities of the entropic measure are confirmed. Lastly, in addition to the abovementioned texts, applicability to the Japanese version of the periodic table of elements is investigated. Full article
(This article belongs to the Special Issue Entropy-Based Time Series Analysis: Theory and Applications)
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22 pages, 8479 KB  
Article
Coal-Free Zone Genesis and Logging Response Characterization Using a Multi-Curve Signal Analysis Framework
by Xiao Yang, Yanrong Chen, Longqing Shi, Xingyue Qu and Song Fu
Entropy 2025, 27(12), 1183; https://doi.org/10.3390/e27121183 - 21 Nov 2025
Viewed by 398
Abstract
Coal-free zones, particularly scouring zones, reduce recoverable reserves and increase water inrush risk in coal mining. Existing sedimentological, geophysical, and geostatistical methods are often constrained by coring conditions, lithological interpretation accuracy, and geological complexity. Given that well log signals provide the most continuous [...] Read more.
Coal-free zones, particularly scouring zones, reduce recoverable reserves and increase water inrush risk in coal mining. Existing sedimentological, geophysical, and geostatistical methods are often constrained by coring conditions, lithological interpretation accuracy, and geological complexity. Given that well log signals provide the most continuous carriers of geological information, this study integrates Singular Spectrum Analysis (SSA), Maximum Entropy Spectral Analysis (MESA), and Integrated Prediction Error Filter Analysis (INPEFA) to establish a multi-curve framework for analyzing the genesis and logging responses of coal-free zones. A two-stage SSA workflow was applied for noise reduction, and a Trend–Fluctuation Composite (TFC) curve was constructed to enhance depositional rhythm detection. The minimum singular value order (N), naturally derived from SSA-decomposed INPEFA curves, emerged as a quantitative indicator of mine water inrush risk. The results indicate that coal-free zones resulted from inhibited peat-swamp development followed by fluvial scouring and are characterized by dense inflection points and frequent cyclic fluctuations in TFC curves, together with the absence of low anomalies in natural gamma-ray logs. By integrating multi-curve logs, core data, and in-mine three-dimensional direct-current resistivity surveys, the genetic mechanisms and boundaries of coal-free zones were effectively delineated. The proposed framework enhances logging-based stratigraphic interpretation and provides practical support for working face layout and mine water hazard prevention. Full article
(This article belongs to the Special Issue Entropy-Based Time Series Analysis: Theory and Applications)
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21 pages, 599 KB  
Article
Healthcare Expenditure and COVID-19 in Europe: Correlation, Entropy, and Functional Data Analysis-Based Prediction of Hospitalizations and ICU Admissions
by Patrycja Hęćka, Wiktor Ejsmont and Marek Biernacki
Entropy 2025, 27(9), 962; https://doi.org/10.3390/e27090962 - 16 Sep 2025
Viewed by 1400
Abstract
This article aims to analyze the correlation between healthcare expenditure per capita in 2021 and the sum of the number of hospitalized patients, ICU admissions, confirmed COVID-19 cases, and deaths in a selected period of time. The analysis covers 2017 (before the pandemic), [...] Read more.
This article aims to analyze the correlation between healthcare expenditure per capita in 2021 and the sum of the number of hospitalized patients, ICU admissions, confirmed COVID-19 cases, and deaths in a selected period of time. The analysis covers 2017 (before the pandemic), 2021 (during the pandemic), and 2022/2023 (the initial post-pandemic recovery period). To assess the variability and stability of pandemic dynamics across countries, we compute Shannon entropy for hospitalization and ICU admission data. Additionally, we examine functional data on hospitalizations, ICU patients, confirmed cases, and deaths during a selected period of the COVID-19 pandemic in several European countries. To achieve this, we transform the data into smooth functions and apply principal component analysis along with a multiple function-on-function linear regression model to predict the number of hospitalizations and ICU patients. Full article
(This article belongs to the Special Issue Entropy-Based Time Series Analysis: Theory and Applications)
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21 pages, 6576 KB  
Article
Fault Diagnosis of Planetary Gearboxes Based on LSTM Improved via Feature Extraction Using VMD, Fusion Entropy, and Random Forest
by Xin Xia, Haoyu Sun and Aiguo Wang
Entropy 2025, 27(9), 956; https://doi.org/10.3390/e27090956 - 14 Sep 2025
Cited by 2 | Viewed by 974
Abstract
Extracting effective fault features from the complex vibration signals of planetary gearboxes is the key to conducting efficient fault diagnosis, and it involves signal processing, feature extraction, and feature selection. In this paper, a novel feature extraction method is proposed using variational mode [...] Read more.
Extracting effective fault features from the complex vibration signals of planetary gearboxes is the key to conducting efficient fault diagnosis, and it involves signal processing, feature extraction, and feature selection. In this paper, a novel feature extraction method is proposed using variational mode decomposition (VMD), fusion entropy, and random forest (RF). Firstly, VMD is employed to process the nonlinear and non-stationary signals of planetary gearboxes, which can effectively address the issues of signal modulation and mode mixing. Additionally, a fusion entropy that incorporates various refined composite multi-scale entropies is proposed; it fully utilizes the signal characteristics reflected by various entropies as features for fault diagnosis. Then, RF is adopted to calculate the importance of each feature, and appropriate features are selected to form a fault diagnosis vector, aiming to solve the problems of feature redundancy and interference in fusion entropy. Finally, long short-term memory (LSTM) is used for fault classification. The experimental results demonstrate that the proposed fusion entropy achieves higher accuracy compared with a single entropy value. The RF-based feature selection can also reduce interference and improve diagnostic efficiency. The proposed fault diagnosis method exhibits high fault diagnosis accuracy under different rotational speeds and environmental noise conditions. Full article
(This article belongs to the Special Issue Entropy-Based Time Series Analysis: Theory and Applications)
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