Journal Description
Entropy
Entropy
is an international and interdisciplinary peer-reviewed open access journal of entropy and information studies, published monthly online by MDPI. The International Society for the Study of Information (IS4SI) and Spanish Society of Biomedical Engineering (SEIB) are affiliated with Entropy and their members receive a discount on the article processing charge.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), Inspec, PubMed, PMC, Astrophysics Data System, and other databases.
- Journal Rank: JCR - Q2 (Physics, Multidisciplinary) / CiteScore - Q1 (Mathematical Physics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 21.8 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the first half of 2025).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about Entropy.
- Companion journals for Entropy include: Foundations, Thermo and Complexities.
Impact Factor:
2.0 (2024);
5-Year Impact Factor:
2.2 (2024)
Latest Articles
Study on a Fault Diagnosis Method for Heterogeneous Chiller Units Based on Transfer Learning
Entropy 2025, 27(10), 1049; https://doi.org/10.3390/e27101049 (registering DOI) - 9 Oct 2025
Abstract
As the core refrigeration equipment in cooling systems, the operational state of chiller units is crucial for ship support, equipment cooling, and mission stability. However, because of their sensitivity and the complexity of operating environments, obtaining large volumes of complete, fault-labeled data is
[...] Read more.
As the core refrigeration equipment in cooling systems, the operational state of chiller units is crucial for ship support, equipment cooling, and mission stability. However, because of their sensitivity and the complexity of operating environments, obtaining large volumes of complete, fault-labeled data is difficult in practical engineering appli-cations. This limitation makes it challenging for traditional data-driven approaches to deliver accurate fault diagnoses. Furthermore, data collected from different devices or under varying operating conditions often differ significantly in both feature dimensions and distributions, i.e., data heterogeneity, which further complicates model transfer. To address these challenges, this study proposes a deep transfer learning–based fault di-agnosis method designed to leverage abundant knowledge from the source domain while adaptively learning features of the target domain. Given the persistent difficulties in collecting sufficient high-quality labeled fault data, traditional data-driven models continue to face restricted diagnostic performance on target equipment. At the same time, data heterogeneity across devices or operating conditions intensifies the challenge of cross-domain knowledge transfer. To overcome these issues, this study develops a heterogeneous transfer learning method that integrates a dual-channel autoencoder, domain adversarial training, and pseudo-label self-training. This combination enables precise small-sample knowledge transfer from the source to the target domain. Specifi-cally, the dual-channel autoencoder is first applied to align heterogeneous feature di-mensions. Then, a Gradient Reversal Layer (GRL) and a domain discriminator are in-troduced to extract domain-invariant features. In parallel, high-confidence pseu-do-labeled samples from the target domain are incorporated into joint training to im-prove generalization and robustness. Experimental results confirm that the method achieves high fault diagnosis accuracy in typical industrial application scenarios, ena-bling effective identification of common faults in various types of chiller units under conventional operating conditions, the proposed method achieves higher accuracy and F1-scores in multi-class fault diagnosis tasks compared with both traditional approaches and existing transfer learning methods. These findings provide a novel perspective for advancing the intelligent operation and maintenance of chiller units.
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Open AccessArticle
Unlocking Carbon Emissions and Total Factor Productivity Nexus: Causal Moderation of Ownership Structures via Entropy Methods in Chinese Enterprises
by
Ruize Cai, Jie You and Minho Kim
Entropy 2025, 27(10), 1048; https://doi.org/10.3390/e27101048 (registering DOI) - 9 Oct 2025
Abstract
Amidst global imperatives for environmental sustainability, this study investigates the nexus between carbon emissions reduction (CER), ownership structures, and total factor productivity (TFP) in Chinese enterprises—recognized as vital economic drivers facing carbon emissions pressures. Based on the theoretical frameworks of innovation offsets, agency
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Amidst global imperatives for environmental sustainability, this study investigates the nexus between carbon emissions reduction (CER), ownership structures, and total factor productivity (TFP) in Chinese enterprises—recognized as vital economic drivers facing carbon emissions pressures. Based on the theoretical frameworks of innovation offsets, agency cost theory, and upper echelons theory, with data from CSMAR (2009–2023), we proposed a positive effect of CER on TFP while examining the moderating roles of ownership structure metrics: chairman shareholding ratio, manager shareholding ratio, and ownership–control separation ratio. TFP estimation employed dual approaches: mean consolidation (TFP-Mean) and entropy weighting (TFP-Entropy) methods. The results confirmed CER exerts significantly positive impacts on TFP, with ownership structures demonstrating statistically significant yet directionally heterogeneous moderation effects. Heterogeneity analysis reveals heightened TFP sensitivity to carbon emission initiatives among private enterprises, foreign-owned enterprises, and small enterprises. Notably, the entropy weighting method exhibits substantial comparative advantages in TFP measurement. These findings underscore that advancing TFP necessitates simultaneously optimizing carbon emissions efficiency and ownership governance.
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(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance, and Management, 4th Edition)
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Applying Entropic Measures, Spectral Analysis, and EMD to Quantify Ion Channel Recordings: New Insights into Quercetin and Calcium Activation of BK Channels
by
Przemysław Borys, Paulina Trybek, Beata Dworakowska, Anna Sekrecka-Belniak, Michał Wojcik and Agata Wawrzkiewicz-Jałowiecka
Entropy 2025, 27(10), 1047; https://doi.org/10.3390/e27101047 (registering DOI) - 9 Oct 2025
Abstract
Understanding the functional modulation of ion channels by multiple activating substances is critical to grasping stimulus-specific gating mechanisms and possible synergistic or competitive interactions. This study investigates the activation of large-conductance, voltage- and Ca2+-activated potassium channels (BK) in the plasma membrane
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Understanding the functional modulation of ion channels by multiple activating substances is critical to grasping stimulus-specific gating mechanisms and possible synergistic or competitive interactions. This study investigates the activation of large-conductance, voltage- and Ca2+-activated potassium channels (BK) in the plasma membrane of human bronchial epithelial cells by Ca2+ and quercetin (Que), both individually and in combination. Patch-clamp recordings were analyzed using open state probability, dwell-time distributions, Shannon entropy, sample entropy, power spectral density (PSD), and empirical mode decomposition (EMD). Our results reveal concentration-dependent alterations in gating kinetics, particularly at a low concentration of quercetin ([Que] = 10 μM) compared with [Que] = 100 μM, where some Que-related effects are strongly attenuated in the presence of Ca2+. We also identify specific frequency bands where oscillatory components are most sensitive to the considered stimuli. Our findings highlight the complex reciprocal interplay between Ca2+ and Que in modulating BK channel function, and demonstrate the interpretative power of entropic and signal-decomposition approaches in characterizing stimulus-specific gating dynamics.
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(This article belongs to the Special Issue Mathematical Modeling for Ion Channels)
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Hypergraph Semi-Supervised Contrastive Learning for Hyperedge Prediction Based on Enhanced Attention Aggregator
by
Hanyu Xie, Changjian Song, Hao Shao and Lunwen Wang
Entropy 2025, 27(10), 1046; https://doi.org/10.3390/e27101046 - 8 Oct 2025
Abstract
Hyperedge prediction is crucial for uncovering higher-order relationships in complex systems but faces core challenges, including unmodeled node influence heterogeneity, overlooked hyperedge order effects, and data sparsity. This paper proposes Order propagation Fusion Self-supervised learning for Hyperedge prediction (OFSH) to address these issues.
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Hyperedge prediction is crucial for uncovering higher-order relationships in complex systems but faces core challenges, including unmodeled node influence heterogeneity, overlooked hyperedge order effects, and data sparsity. This paper proposes Order propagation Fusion Self-supervised learning for Hyperedge prediction (OFSH) to address these issues. OFSH introduces a hyperedge order propagation mechanism that dynamically learns node importance weights and groups neighbor hyperedges by order, applying max–min pooling to amplify feature distinctions. To mitigate data sparsity, OFSH incorporates a key node-guided augmentation strategy with adaptive masking, preserving core high-order semantics. It identifies topological hub nodes based on their comprehensive influence and employs adaptive masking probabilities to generate augmented views preserving core high-order semantics. Finally, a triadic contrastive loss is employed to maximize cross-view consistency and capture invariant semantic information under perturbations. Extensive experiments on five public real-world hypergraph datasets demonstrate significant improvements over state-of-the-art methods in AUROC and AP.
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(This article belongs to the Section Complexity)
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Balanced-BiEGCN: A Bidirectional EvolveGCN with a Class-Balanced Learning Network for Dynamic Anomaly Detection in Bitcoin
by
Bo Xiao and Wei Yin
Entropy 2025, 27(10), 1045; https://doi.org/10.3390/e27101045 - 8 Oct 2025
Abstract
Bitcoin transaction anomaly detection is essential for maintaining financial market stability. A significant challenge is capturing the dynamically evolving transaction patterns within transaction networks. Dynamic graph models are effective for characterizing the temporal evolution of transaction systems. However, current methods struggle to mine
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Bitcoin transaction anomaly detection is essential for maintaining financial market stability. A significant challenge is capturing the dynamically evolving transaction patterns within transaction networks. Dynamic graph models are effective for characterizing the temporal evolution of transaction systems. However, current methods struggle to mine long-range temporal dependencies and address the class imbalance caused by the scarcity of abnormal samples. To address these issues, we propose a novel approach, the Bidirectional EvolveGCN with Class-Balanced Learning Network (Balanced-BiEGCN), for Bitcoin transaction anomaly detection. This model integrates two key components: (1) a bidirectional temporal feature fusion mechanism (Bi-EvolveGCN) that enhances the capture of long-range temporal dependencies and (2) a Sample Class Transformation (CSCT) classifier that generates difficult-to-distinguish abnormal samples to balance the positive and negative class distribution. The generation of these samples is guided by two loss functions: the adjacency distance adaptive loss function and the symmetric space adjustment loss function, which optimize the spatial distribution and confusion of abnormal samples. Experimental results on the Elliptic dataset demonstrate that Balanced-BiEGCN outperforms existing baseline methods in anomaly detection.
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(This article belongs to the Section Complexity)
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EEG Complexity Analysis of Psychogenic Non-Epileptic and Epileptic Seizures Using Entropy and Machine Learning
by
Hesam Shokouh Alaei, Samaneh Kouchaki, Mahinda Yogarajah and Daniel Abasolo
Entropy 2025, 27(10), 1044; https://doi.org/10.3390/e27101044 - 7 Oct 2025
Abstract
Psychogenic non-epileptic seizures (PNES) are often misdiagnosed as epileptic seizures (ES), leading to inappropriate treatment and delayed psychological care. To address this challenge, we analysed electroencephalogram (EEG) data from 74 patients (46 PNES, 28 ES) using one-minute preictal and interictal recordings per subject.
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Psychogenic non-epileptic seizures (PNES) are often misdiagnosed as epileptic seizures (ES), leading to inappropriate treatment and delayed psychological care. To address this challenge, we analysed electroencephalogram (EEG) data from 74 patients (46 PNES, 28 ES) using one-minute preictal and interictal recordings per subject. Nine entropy measures (Sample, Fuzzy, Permutation, Dispersion, Conditional, Phase, Spectral, Rényi, and Wavelet entropy) were evaluated individually to classify PNES from ES using k-nearest neighbours, Naïve Bayes, linear discriminant analysis, logistic regression, support vector machine, random forest, multilayer perceptron, and XGBoost within a leave-one-subject-out cross-validation framework. In addition, a dynamic state, defined as the entropy difference between interictal and preictal periods, was examined. Sample, Fuzzy, Conditional, and Dispersion entropy were higher in PNES than in ES during interictal recordings (not significant), but significantly lower in the preictal (p < 0.05) and dynamic states (p < 0.01). Spatial mapping and permutation-based importance analyses highlighted O1, O2, T5, F7, and Pz as key discriminative channels. Classification performance peaked in the dynamic state, with Fuzzy entropy and support vector machine achieving the best results (balanced accuracy = 72.4%, F1 score = 77.8%, sensitivity = 74.5%, specificity = 70.4%). These results demonstrate the potential of entropy features for differentiating PNES from ES.
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(This article belongs to the Special Issue Entropy Analysis of ECG and EEG Signals)
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Counting Cosmic Cycles: Past Big Crunches, Future Recurrence Limits, and the Age of the Quantum Memory Matrix Universe
by
Florian Neukart, Eike Marx and Valerii Vinokur
Entropy 2025, 27(10), 1043; https://doi.org/10.3390/e27101043 - 7 Oct 2025
Abstract
We present a quantitative theory of contraction and expansion cycles within the Quantum Memory Matrix (QMM) cosmology. In this framework, spacetime consists of finite-capacity Hilbert cells that store quantum information. Each non-singular bounce adds a fixed increment of imprint entropy, defined as the
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We present a quantitative theory of contraction and expansion cycles within the Quantum Memory Matrix (QMM) cosmology. In this framework, spacetime consists of finite-capacity Hilbert cells that store quantum information. Each non-singular bounce adds a fixed increment of imprint entropy, defined as the cumulative quantum information written irreversibly into the matrix and distinct from coarse-grained thermodynamic entropy, thereby providing an intrinsic, monotonic cycle counter. By calibrating the geometry–information duality, inferring today’s cumulative imprint from CMB, BAO, chronometer, and large-scale-structure constraints, and integrating the modified Friedmann equations with imprint back-reaction, we find that the Universe has already completed cycles. The finite Hilbert capacity enforces an absolute ceiling: propagating the holographic write rate and accounting for instability channels implies only additional cycles before saturation halts further bounces. Integrating Kodama-vector proper time across all completed cycles yields a total cumulative age , compared to the of the current expansion usually described by CDM. The framework makes concrete, testable predictions: an enhanced faint-end UV luminosity function at observable with JWST, a stochastic gravitational-wave background with scaling in the LISA band from primordial black-hole mergers, and a nanohertz background with slope accessible to pulsar-timing arrays. These signatures provide near-term opportunities to confirm, refine, or falsify the cyclical QMM chronology.
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(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology, 4th Edition)
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Secure Virtual Network Provisioning over Key Programmable Optical Networks
by
Xiaoyu Wang, Hao Jiang, Jianwei Li and Zhonghua Liang
Entropy 2025, 27(10), 1042; https://doi.org/10.3390/e27101042 - 7 Oct 2025
Abstract
Virtual networks have emerged as a promising solution for enabling diverse users to efficiently share bandwidth resources over optical network infrastructures. Despite the invention of various schemes aimed at ensuring secure isolation among virtual networks, the security of data transfer in virtual networks
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Virtual networks have emerged as a promising solution for enabling diverse users to efficiently share bandwidth resources over optical network infrastructures. Despite the invention of various schemes aimed at ensuring secure isolation among virtual networks, the security of data transfer in virtual networks remains a challenging problem. To address this challenge, the concept of evolving traditional optical networks into key programmable optical networks (KPONs) has been proposed. Inspired by this, this paper delves into the establishment of secure virtual networks over KPONs, in which the information-theoretically secure keys can be supplied for ensuring the information-theoretic security of data transfer within virtual networks. A layered architecture for secure virtual network provisioning over KPONs is proposed, which leverages software-defined networking to realize the programmable control of optical-layer resources. With this architecture, a heuristic algorithm, i.e., the key adaptation-based secure virtual network provisioning (KA-SVNP) algorithm, is designed to dynamically allocate key resources based on the adaption between the key supply and key demand. To evaluate the proposed solutions, an emulation testbed is established, achieving millisecond latencies for secure virtual network establishment and deletion. Moreover, numerical simulations indicate that the designed KA-SVNP algorithm performs superior to the benchmark algorithm in terms of the success probability of secure virtual network requests.
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(This article belongs to the Special Issue Secure Network Ecosystems in the Quantum Era)
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An Approximate Bayesian Approach to Optimal Input Signal Design for System Identification
by
Piotr Bania and Anna Wójcik
Entropy 2025, 27(10), 1041; https://doi.org/10.3390/e27101041 - 7 Oct 2025
Abstract
The design of informatively rich input signals is essential for accurate system identification, yet classical Fisher-information-based methods are inherently local and often inadequate in the presence of significant model uncertainty and non-linearity. This paper develops a Bayesian approach that uses the mutual information
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The design of informatively rich input signals is essential for accurate system identification, yet classical Fisher-information-based methods are inherently local and often inadequate in the presence of significant model uncertainty and non-linearity. This paper develops a Bayesian approach that uses the mutual information (MI) between observations and parameters as the utility function. To address the computational intractability of the MI, we maximize a tractable MI lower bound. The method is then applied to the design of an input signal for the identification of quasi-linear stochastic dynamical systems. Evaluating the MI lower bound requires the inversion of large covariance matrices whose dimensions scale with the number of data points N. To overcome this problem, an algorithm that reduces the dimension of the matrices to be inverted by a factor of N is developed, making the approach feasible for long experiments. The proposed Bayesian method is compared with the average D-optimal design method, a semi-Bayesian approach, and its advantages are demonstrated. The effectiveness of the proposed method is further illustrated through four examples, including atomic sensor models, where input signals that generate a large amount of MI are especially important for reducing the estimation error.
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(This article belongs to the Section Signal and Data Analysis)
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Thermoelectric Enhancement of Series-Connected Cross-Conjugated Molecular Junctions
by
Justin P. Bergfield
Entropy 2025, 27(10), 1040; https://doi.org/10.3390/e27101040 - 6 Oct 2025
Abstract
We investigate the thermoelectric response of single-molecule junctions composed of acyclic cross-conjugated molecules, including dendralene analogues and related iso-poly(diacetylene) (iso-PDA) motifs, in which node-possessing repeat units are connected in series. Using many-body quantum transport theory, we show that increasing the number of repeat
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We investigate the thermoelectric response of single-molecule junctions composed of acyclic cross-conjugated molecules, including dendralene analogues and related iso-poly(diacetylene) (iso-PDA) motifs, in which node-possessing repeat units are connected in series. Using many-body quantum transport theory, we show that increasing the number of repeat units leaves the fundamental gap essentially unchanged while giving rise to a split-node spectrum whose cumulative broadening dramatically enhances the thermopower. This form of quantum enhancement can exceed other interference-based mechanisms, such as the coalescence of nodes into a supernode, suggesting new opportunities for scalable quantum-interference–based materials. Although illustrated here with cross-conjugated systems, the underlying principles apply broadly to series-connected architectures hosting multiple interference nodes. Finally, we evaluate the scaling of the electronic figure of merit ZT and the maximum thermodynamic efficiency. Together, these results highlight the potential for split-node-based materials to realize quantum-enhanced thermoelectric response.
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(This article belongs to the Special Issue Thermodynamics at the Nanoscale)
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The Amount of Data Required to Recognize a Writer’s Style Is Consistent Across Different Languages of the World
by
Boris Ryabko, Nadezhda Savina, Yeshewas Getachew Lulu and Yunfei Han
Entropy 2025, 27(10), 1039; https://doi.org/10.3390/e27101039 - 4 Oct 2025
Abstract
In this paper, we apply an information-theoretic method proposed by Ryabko and Savina (therefore called the RS-method), based on the use of data compression, to recognize the individual author’s style of a writer across four languages from different language groups and families. In
[...] Read more.
In this paper, we apply an information-theoretic method proposed by Ryabko and Savina (therefore called the RS-method), based on the use of data compression, to recognize the individual author’s style of a writer across four languages from different language groups and families. In this paper, the presented method was used to study fiction texts in Russian (East Slavic group of languages of the Indo-European language family), Amharic (South Ethiosemitic group of the Semitic language family), Chinese (Sinitic group of the Sino-Tibetan language family) and English (West Germanic language group of the Indo-European language family). It was found that the amount of data necessary for recognizing an author’s style is almost the same for all four languages, i.e., the amount of data is invariant across different language groups. The results obtained are of interest to computer science, literary studies, linguistics and, in particular, computational linguistics.
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(This article belongs to the Section Information Theory, Probability and Statistics)
Open AccessArticle
Multiscale Permutation Time Irreversibility Analysis of MEG in Patients with Schizophrenia
by
Dengxuan Bai, Muxuan Xue, Yining Wang, Zhen Zhang, Xiaoli Chen, Wenpo Yao and Jun Wang
Entropy 2025, 27(10), 1038; https://doi.org/10.3390/e27101038 - 4 Oct 2025
Abstract
The use of questionnaire survey results as a clinical diagnostic method for schizophrenia lacks a certain degree of objectivity; thus, markers of schizophrenia in different brain signals have been widely investigated. The objective of this investigation was to explore potential markers of schizophrenia
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The use of questionnaire survey results as a clinical diagnostic method for schizophrenia lacks a certain degree of objectivity; thus, markers of schizophrenia in different brain signals have been widely investigated. The objective of this investigation was to explore potential markers of schizophrenia by investigating nonequilibrium features in magnetoencephalography (MEG) signals. We propose a new method to quantify the nonequilibrium features of MEG signals: the multiscale permutation time irreversibility (MsPTIRR) index. The results revealed that the MsPTIRR indices of the MEG recordings of patients with schizophrenia were significantly lower than those of the healthy controls (HCs). Moreover, the MsPTIRR indices of the MEG recordings of patients with schizophrenia and HCs differed significantly in the frontal, occipital, and temporal lobe regions. Furthermore, the MsPTIRR indices of the MEG recordings differed significantly between patients with schizophrenia and HCs in the , and bands. Abnormal nonequilibrium features mined in MEG recordings using the MsPTIRR index may be used as potential markers for schizophrenia, assisting in the clinical diagnosis of this disorder.
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(This article belongs to the Section Entropy and Biology)
Open AccessArticle
The Wave–Particle Dualism of Photons as Seen from an Informational Point of View
by
J. Gerhard Müller
Entropy 2025, 27(10), 1037; https://doi.org/10.3390/e27101037 - 3 Oct 2025
Abstract
This paper deals with J. A. Wheeler’s proposal that each piece of reality owes its existence to observation—an approach to physics, which implies that all physical entities at their bottom are informational in character. Focusing on the double-slit experiment with photons, which is
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This paper deals with J. A. Wheeler’s proposal that each piece of reality owes its existence to observation—an approach to physics, which implies that all physical entities at their bottom are informational in character. Focusing on the double-slit experiment with photons, which is the key evidence for the wave–particle dualism of photons, this paper follows Wheeler’s observational approach and interprets this experiment as a question posed to nature. Considering how the enquiry regarding the wave–particle duality of photons is answered by nature, it is shown that experimental questions are being answered by nature in the form of spatiotemporal patterns of elementary observations (EOs) which are binary pieces of information, produced by the dissipation of energy. Working through this line of thought, Wheeler’s statements of “binary information gain”, “observer participance” and the “impossibility of continuum idealizations of physical laws” are elucidated and connections to the Landauer Principle are made.
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(This article belongs to the Special Issue The Landauer Principle in Physics, Biophysics, Engineering and Computer Science: From Foundations of Thermodynamics to Computer Engineering)
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A Dissipative Phenomenon: The Mechanical Model of the Cosmological Axion Influence
by
Ferenc Márkus and Katalin Gambár
Entropy 2025, 27(10), 1036; https://doi.org/10.3390/e27101036 - 2 Oct 2025
Abstract
The appearance of a negative mass term in the classical, non-relativistic Klein–Gordon equation deduced from mechanical interactions describes a repulsive interaction. In the case of a traveling wave, this results in an increase in amplitude and a decrease in the wave propagation velocity.
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The appearance of a negative mass term in the classical, non-relativistic Klein–Gordon equation deduced from mechanical interactions describes a repulsive interaction. In the case of a traveling wave, this results in an increase in amplitude and a decrease in the wave propagation velocity. Since this leads to dissipation, it is a symmetry-breaking phenomenon. After the repulsive interaction is eliminated, the system evolves towards the original state. Given that the interactions within the system are conservative, it would be assumed that even the original state is restored. The analysis to be presented shows that a wave with a lower angular frequency than the original one is transformed back to a slightly larger amplitude. This description is a suitable model of the axion effect, during which an electromagnetic wave interacts with a repulsive field and becomes of a continuously lower frequency.
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(This article belongs to the Special Issue Dissipative Physical Dynamics)
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Research on the Consensus Convergence Rate of Multi-Agent Systems Based on Hermitian Kirchhoff Index Measurement
by
He Deng and Tingzeng Wu
Entropy 2025, 27(10), 1035; https://doi.org/10.3390/e27101035 - 2 Oct 2025
Abstract
Multi-agent systems (MAS) typically model interaction topologies using directed or undirected graphs when analyzing consensus convergence rates. However, as system complexity increases, purely directed or undirected networks may be insufficient to capture interaction heterogeneity. This paper adopts hybrid networks as interaction topology to
[...] Read more.
Multi-agent systems (MAS) typically model interaction topologies using directed or undirected graphs when analyzing consensus convergence rates. However, as system complexity increases, purely directed or undirected networks may be insufficient to capture interaction heterogeneity. This paper adopts hybrid networks as interaction topology to investigate strategies for improving consensus convergence rates. We propose the Hermitian Kirchhoff index, a novel metric based on resistance distance, to quantify the consensus convergence rates and establish its theoretical justification. We then examine how adding or removing edges/arcs affects the Hermitian Kirchhoff index, employing first-order eigenvalue perturbation analysis to relate these changes to algebraic connectivity and its associated eigenvectors. Numerical simulations corroborate the theoretical findings and demonstrate the effectiveness of the proposed approach.
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(This article belongs to the Section Complexity)
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A Two-Step Machine Learning Approach Integrating GNSS-Derived PWV for Improved Precipitation Forecasting
by
Laura Profetto, Andrea Antonini, Luca Fibbi, Alberto Ortolani and Giovanna Maria Dimitri
Entropy 2025, 27(10), 1034; https://doi.org/10.3390/e27101034 - 2 Oct 2025
Abstract
Global Navigation Satellite System (GNSS) meteorology has emerged as a valuable tool for atmospheric monitoring, providing high-resolution, near-real-time data that can significantly improve precipitation nowcasting. This study aims to enhance short-term precipitation forecasting by integrating GNSS-derived Precipitable Water Vapor (PWV)—a key indicator of
[...] Read more.
Global Navigation Satellite System (GNSS) meteorology has emerged as a valuable tool for atmospheric monitoring, providing high-resolution, near-real-time data that can significantly improve precipitation nowcasting. This study aims to enhance short-term precipitation forecasting by integrating GNSS-derived Precipitable Water Vapor (PWV)—a key indicator of atmospheric moisture—with traditional meteorological observations. A novel two-step machine learning framework is proposed that combines a Random Forest (RF) model and a Long Short-Term Memory (LSTM) neural network. The RF model first estimates current precipitation based on PWV, surface weather parameters, and auxiliary atmospheric variables. Then, the LSTM network leverages temporal dependencies within the data to predict precipitation for the subsequent hour. This hybrid method capitalizes on the RF’s ability to model complex nonlinear relationships and the LSTM’s strength in handling time series data. The results demonstrate that the proposed approach improves forecasting accuracy, particularly during extreme weather events such as intense rainfall and thunderstorms, outperforming conventional models. By integrating GNSS meteorology with advanced machine learning techniques, this study offers a promising tool for meteorological services, early warning systems, and disaster risk management. The findings highlight the potential of GNSS-based nowcasting for real-time decision-making in weather-sensitive applications.
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(This article belongs to the Special Issue Entropy in Machine Learning Applications, 2nd Edition)
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Security, Privacy, and Linear Function Retrieval in Combinatorial Multi-Access Coded Caching with Private Caches
by
Mallikharjuna Chinnapadamala and B. Sundar Rajan
Entropy 2025, 27(10), 1033; https://doi.org/10.3390/e27101033 - 1 Oct 2025
Abstract
We consider combinatorial multi-access coded caching with private caches, where users are connected to two types of caches: private caches and multi-access caches. Each user has its own private cache, while multi-access caches are connected in the same way as caches are connected
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We consider combinatorial multi-access coded caching with private caches, where users are connected to two types of caches: private caches and multi-access caches. Each user has its own private cache, while multi-access caches are connected in the same way as caches are connected in a combinatorial topology. A scheme is proposed that satisfies the following three requirements simultaneously: (a) Linear Function Retrieval (LFR), (b) content security against an eavesdropper, and (c) demand privacy against a colluding set of users. It is shown that the private caches included in this work enable the proposed scheme to provide privacy against colluding users. For the same rate, our scheme requires less total memory accessed by each user and less total system memory than the existing scheme for multi-access combinatorial topology (no private caches) in the literature. We derive a cut-set lower bound and prove optimality when . For , we show a constant gap of 5 under certain conditions. Finally, the proposed scheme is extended to a more general setup where different users are connected to different numbers of multi-access caches, and multiple users are connected to the same subset of multi-access caches.
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(This article belongs to the Special Issue Information and Coding Theory for Distributed Learning, Storage, Scheduling, and Security)
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Security of Quantum Key Distribution with One-Time-Pad-Protected Error Correction and Its Performance Benefits
by
Roman Novak
Entropy 2025, 27(10), 1032; https://doi.org/10.3390/e27101032 - 1 Oct 2025
Abstract
In quantum key distribution (QKD), public discussion over the authenticated classical channel inevitably leaks information about the raw key to a potential adversary, which must later be mitigated by privacy amplification. To limit this leakage, a one-time pad (OTP) has been proposed to
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In quantum key distribution (QKD), public discussion over the authenticated classical channel inevitably leaks information about the raw key to a potential adversary, which must later be mitigated by privacy amplification. To limit this leakage, a one-time pad (OTP) has been proposed to protect message exchanges in various settings. Building on the security proof of Tomamichel and Leverrier, which is based on a non-asymptotic framework and considers the effects of finite resources, we extend the analysis to the OTP-protected scheme. We show that when the OTP key is drawn from the entropy pool of the same QKD session, the achievable quantum key rate is identical to that of the reference protocol with unprotected error-correction exchange. This equivalence holds for a fixed security level, defined via the diamond distance between the real and ideal protocols modeled as completely positive trace-preserving maps. At the same time, the proposed approach reduces the computational requirements: for non-interactive low-density parity-check codes, the encoding problem size is reduced by the square of the syndrome length, while privacy amplification requires less compression. The technique preserves security, avoids the use of QKD keys between sessions, and has the potential to improve performance.
Full article
(This article belongs to the Section Quantum Information)
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Open AccessArticle
Efficient Algorithms for Permutation Arrays from Permutation Polynomials
by
Sergey Bereg, Brian Malouf, Linda Morales and Ivan Hal Sudborough
Entropy 2025, 27(10), 1031; https://doi.org/10.3390/e27101031 - 1 Oct 2025
Abstract
We develop algorithms for computing permutation polynomials (PPs) using normalization, so-called F-maps and G-maps, and the Hermite criterion. This allows for a more efficient computation of PPs for larger degrees and for larger finite fields. We use this to improve some lower bounds
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We develop algorithms for computing permutation polynomials (PPs) using normalization, so-called F-maps and G-maps, and the Hermite criterion. This allows for a more efficient computation of PPs for larger degrees and for larger finite fields. We use this to improve some lower bounds for , the maximum number of permutations on n symbols with a pairwise Hamming distance of D.
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(This article belongs to the Special Issue Discrete Math in Coding Theory, 2nd Edition)
Open AccessArticle
Enhance the Performance of Expectation Propagation Detection in Spatially Correlated Massive MIMO Channels via DFT Precoding
by
Huaicheng Luo, Jia Tang, Zeliang Ou, Yitong Liu and Hongwen Yang
Entropy 2025, 27(10), 1030; https://doi.org/10.3390/e27101030 - 1 Oct 2025
Abstract
Expectation Propagation (EP) has emerged as a promising detection algorithm for large-scale multiple-input multiple-output (MIMO) systems owing to its excellent performance and practical complexity. However, transmit antenna correlation significantly degrades the performance of EP detection, especially when the number of transmit and receive
[...] Read more.
Expectation Propagation (EP) has emerged as a promising detection algorithm for large-scale multiple-input multiple-output (MIMO) systems owing to its excellent performance and practical complexity. However, transmit antenna correlation significantly degrades the performance of EP detection, especially when the number of transmit and receive antennas is equal and high-order modulation is adopted. Based on the fact that the eigenvector matrix of the channel transmit correlation matrix approaches asymptotically to a discrete Fourier transform (DFT) matrix, a DFT precoder is proposed to effectively eliminate transmit antenna correlation. Simulation results demonstrate that for high-order, high-dimensional massive MIMO systems with strong transmit antenna correlation, employing the proposed DFT precoding can significantly accelerate the convergence of the EP algorithm and reduce the detection error rate.
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(This article belongs to the Special Issue Next-Generation Multiple Access for Future Wireless Communications)
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