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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 2445

Special Issue Editor


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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

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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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Published Papers (3 papers)

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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 198
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 904
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
Viewed by 666
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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