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Entropy, Volume 27, Issue 6 (June 2025) – 91 articles

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24 pages, 9425 KiB  
Article
An Information Geometry-Based Track-Before-Detect Algorithm for Range-Azimuth Measurements in Radar Systems
by Jinguo Liu, Hao Wu, Zheng Yang, Xiaoqiang Hua and Yongqiang Cheng
Entropy 2025, 27(6), 637; https://doi.org/10.3390/e27060637 (registering DOI) - 14 Jun 2025
Abstract
The detection of weak moving targets in heterogeneous clutter backgrounds is a significant challenge in radar systems. In this paper, we propose a track-before-detect (TBD) method based on information geometry (IG) theory applied to range-azimuth measurements, which extends the IG detectors to multi-frame [...] Read more.
The detection of weak moving targets in heterogeneous clutter backgrounds is a significant challenge in radar systems. In this paper, we propose a track-before-detect (TBD) method based on information geometry (IG) theory applied to range-azimuth measurements, which extends the IG detectors to multi-frame detection through inter-frame information integration. The approach capitalizes on the distinctive benefits of the information geometry detection framework in scenarios with strong clutter, while enhancing the integration of information across multiple frames within the TBD approach. Specifically, target and clutter trajectories in multi-frame range-azimuth measurements are modeled on the Hermitian positive definite (HPD) and power spectrum (PS) manifolds. A scoring function based on information geometry, which uses Kullback–Leibler (KL) divergence as a geometric metric, is then devised to assess these motion trajectories. Moreover, this study devises a solution framework employing dynamic programming (DP) with constraints on state transitions, culminating in an integrated merit function. This algorithm identifies target trajectories by maximizing the integrated merit function. Experimental validation using real-recorded sea clutter datasets showcases the effectiveness of the proposed algorithm, yielding a minimum 3 dB enhancement in signal-to-clutter ratio (SCR) compared to traditional approaches. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
14 pages, 1641 KiB  
Article
Measurement-Induced Dynamical Quantum Thermalization
by Marvin Lenk, Sayak Biswas, Anna Posazhennikova and Johann Kroha
Entropy 2025, 27(6), 636; https://doi.org/10.3390/e27060636 (registering DOI) - 14 Jun 2025
Abstract
One of the fundamental problems of quantum statistical physics is how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here, we study, via explicit time evolution for the generic model system of [...] Read more.
One of the fundamental problems of quantum statistical physics is how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here, we study, via explicit time evolution for the generic model system of an interacting, trapped Bose gas with discrete single-particle levels, how the measurement of one or more observables subdivides the system into observed and non-observed Hilbert subspaces and the tracing over the non-measured quantum numbers defines an effective, thermodynamic bath, induces the entanglement of the observed Hilbert subspace with the bath, and leads to a bi-exponential approach of the entanglement entropy and of the measured observables to thermal equilibrium behavior as a function of time. We find this to be more generally fulfilled than in the scenario of the eigenstate thermalization hypothesis (ETH), namely for both local particle occupation numbers and non-local density correlation functions, and independent of the specific initial quantum state of the time evolution. Full article
(This article belongs to the Special Issue Non-Equilibrium Dynamics in Ultra-Cold Quantum Gases)
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37 pages, 12509 KiB  
Article
Modeling Stylized Facts in FX Markets with FINGAN-BiLSTM: A Deep Learning Approach to Financial Time Series
by Dong-Jun Kim, Do-Hyeon Kim and Sun-Yong Choi
Entropy 2025, 27(6), 635; https://doi.org/10.3390/e27060635 (registering DOI) - 14 Jun 2025
Abstract
We propose the financial generative adversarial network–bidirectional long short-term memory (FINGAN-BiLSTM) model to accurately reproduce the complex statistical properties and stylized facts, namely, heavy-tailed behavior, volatility clustering, and leverage effects observed in the log returns of the foreign exchange (FX) market. The proposed [...] Read more.
We propose the financial generative adversarial network–bidirectional long short-term memory (FINGAN-BiLSTM) model to accurately reproduce the complex statistical properties and stylized facts, namely, heavy-tailed behavior, volatility clustering, and leverage effects observed in the log returns of the foreign exchange (FX) market. The proposed model integrates a bidirectional LSTM (BiLSTM) into the conventional FINGAN framework so that the generator, discriminator, and predictor networks simultaneously incorporate both past and future information, thereby overcoming the information loss inherent in unidirectional LSTM architectures. Experimental results, assessed using metrics such as the Kolmogorov–Smirnov statistic, demonstrate that FINGAN-BiLSTM effectively mimics the distributional and dynamic patterns of actual FX data. In particular, the model significantly reduces the maximum cumulative distribution discrepancy in assets with high standard deviations and extreme values, such as the Canadian dollar (CAD) and the Mexican Peso (MXN), while precisely replicating dynamic features like volatility clustering and leverage effects, thereby outperforming conventional models. The findings suggest that the proposed deep learning–based forecasting model holds significant promise for practical applications in financial risk assessment, derivative pricing, and portfolio optimization, and they highlight the need for further research to enhance its generalization capabilities through the integration of exogenous economic variables. Full article
(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)
17 pages, 1555 KiB  
Article
A Method Inspired by One-Dimensional Discrete-Time Quantum Walks for Influential Node Identification
by Wen Liang, Yifan Wang, Qiwei Liu and Wenbo Zhang
Entropy 2025, 27(6), 634; https://doi.org/10.3390/e27060634 (registering DOI) - 14 Jun 2025
Abstract
Identifying influential nodes in complex networks is essential for a wide range of applications, from social network analysis to enhancing infrastructure resilience. While quantum walk-based methods offer potential advantages, existing approaches face challenges in dimensionality, computational efficiency, and accuracy. To address these limitations, [...] Read more.
Identifying influential nodes in complex networks is essential for a wide range of applications, from social network analysis to enhancing infrastructure resilience. While quantum walk-based methods offer potential advantages, existing approaches face challenges in dimensionality, computational efficiency, and accuracy. To address these limitations, this study proposes a novel method inspired by the one-dimensional discrete-time quantum walk (IOQW). This design enables the development of a simplified shift operator that leverages both self-loops and the network’s structural connectivity. Furthermore, degree centrality and path-based features are integrated into the coin operator, enhancing the accuracy and scalability of the IOQW framework. Comparative evaluations against state-of-the-art quantum and classical methods demonstrate that IOQW excels in capturing both local and global topological properties while maintaining a low computational complexity of O(N⟨k⟩), where ⟨k⟩ denotes the average degree. These advancements establish IOQW as a powerful and practical tool for influential node identification in complex networks, bridging quantum-inspired techniques with real-world network science applications. Full article
(This article belongs to the Special Issue Quantum Information and Quantum Computation)
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16 pages, 9151 KiB  
Article
Insulator Defect Detection in Complex Environments Based on Improved YOLOv8
by Yuxin Qin, Ying Zeng and Xin Wang
Entropy 2025, 27(6), 633; https://doi.org/10.3390/e27060633 (registering DOI) - 13 Jun 2025
Abstract
Insulator defect detection is important in ensuring power systems’ safety and stable operation. To solve the problems of its low accuracy, high delay, and large model size in complex environments, following the principle of progressive extraction from high-entropy details to low-entropy semantics, an [...] Read more.
Insulator defect detection is important in ensuring power systems’ safety and stable operation. To solve the problems of its low accuracy, high delay, and large model size in complex environments, following the principle of progressive extraction from high-entropy details to low-entropy semantics, an improved YOLOv8 target detection network for insulator defects based on bidirectional weighted feature fusion was proposed. A C2f_DSC feature extraction module was designed to identify more insulator tube features, an EMA (encoder–modulator–attention) mechanism and a BiFPN (bidirectional weighted feature pyramid network) fusion layer in the backbone network were introduced to extract different features in complex environments, and EIOU (efficient intersection over union) as the model’s loss function was used to accelerate model convergence. The CPLID (China Power Line Insulator Dataset) was tested to verify the effectiveness of the proposed algorithm. The results show its model size is only 6.40 M, and the mean accuracy on the CPLID dataset reaches 98.6%, 0.8% higher than that of the YOLOv8n. Compared with other lightweight models, such as YOLOv8s, YOLOv6, YOLOv5s, and YOLOv3Tiny, not only is the model size reduced, but also the accuracy is effectively improved with the proposed algorithm, demonstrating excellent practicality and feasibility for edge devices. Full article
(This article belongs to the Section Signal and Data Analysis)
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24 pages, 417 KiB  
Article
A Novel Alpha-Power X Family: A Flexible Framework for Distribution Generation with Focus on the Half-Logistic Model
by A. A. Bhat, Aadil Ahmad Mir, S. P. Ahmad, Badr S. Alnssyan, Abdelaziz Alsubie and Yashpal Singh Raghav
Entropy 2025, 27(6), 632; https://doi.org/10.3390/e27060632 (registering DOI) - 13 Jun 2025
Abstract
This study introduces a new and flexible class of probability distributions known as the novel alpha-power X (NAP-X) family. A key development within this framework is the novel alpha-power half-logistic (NAP-HL) distribution, which extends the classical half-logistic model through an alpha-power transformation, allowing [...] Read more.
This study introduces a new and flexible class of probability distributions known as the novel alpha-power X (NAP-X) family. A key development within this framework is the novel alpha-power half-logistic (NAP-HL) distribution, which extends the classical half-logistic model through an alpha-power transformation, allowing for greater adaptability to various data shapes. The paper explores several theoretical aspects of the proposed model, including its moments, quantile function and hazard rate. To assess the effectiveness of parameter estimation, a detailed simulation study is conducted using seven estimation techniques: Maximum likelihood estimation (MLE), Cramér–von Mises estimation (CVME), maximum product of spacings estimation (MPSE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson–Darling estimation (ADE) and a right-tailed version of Anderson–Darling estimation (RTADE). The results offer comparative insights into the performance of each method across different sample sizes. The practical value of the NAP-HL distribution is demonstrated using two real datasets from the metrology and engineering domains. In both cases, the proposed model provides a better fit than the traditional half-logistic and related distributions, as shown by lower values of standard model selection criteria. Graphical tools such as fitted density curves, Q–Q and P–P plots, survival functions and box plots further support the suitability of the model for real-world data analysis. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
13 pages, 556 KiB  
Article
Defending Against the Homodyne Detector-Blinding Attack on Continuous-Variable Quantum Key Distribution Using an Adjustable Optical Attenuator
by Yijun Wang, Yanyan Li, Wenqi Jiang and Ying Guo
Entropy 2025, 27(6), 631; https://doi.org/10.3390/e27060631 - 13 Jun 2025
Abstract
A homodyne detector, which is also a common element in current telecommunication, is a core component of continuous-variable quantum key distribution (CV-QKD) since it is considered the simplest setup for the distinguishing of coherent states with minimum error. However, the theoretical security of [...] Read more.
A homodyne detector, which is also a common element in current telecommunication, is a core component of continuous-variable quantum key distribution (CV-QKD) since it is considered the simplest setup for the distinguishing of coherent states with minimum error. However, the theoretical security of CV-QKD is based on the assumption that the responses of the homodyne detector are always linear with respect to the input, which is impossible in practice. In the real world, a homodyne detector has a finite linear domain, so the linearity assumption is broken when the input is too large. Regarding this security vulnerability, the eavesdropper Eve can perform the so-called homodyne detector-blinding attack by saturating the homodyne detector and then stealing key information without being detected by the legitimate users. In this paper, we propose a countermeasure for the homodyne detector-blinding attack by using an adjustable optical attenuator with a feedback structure. Specifically, we estimate the suitable attenuation value in the data processing of CV-QKD and feed it back to the adjustable optical attenuator before the detector in real time. Numerical simulation shows that the proposed countermeasure can effectively defend against homodyne detector-blinding attacks and ensure the security of the Gaussian-modulated coherent state protocol with finite-size effect. Full article
(This article belongs to the Special Issue Recent Advances in Continuous-Variable Quantum Key Distribution)
10 pages, 2841 KiB  
Article
Disentanglement—Induced Superconductivity
by Eyal Buks
Entropy 2025, 27(6), 630; https://doi.org/10.3390/e27060630 - 13 Jun 2025
Abstract
The current study is motivated by a difficulty in reconciling between particle number conservation and superconductivity. An alternative modeling, which is based on the hypothesis that disentanglement spontaneously ocuurs in quantum systems, is explored. The Fermi–Hubbard mode is employed to demonstrate a disentanglement-induced [...] Read more.
The current study is motivated by a difficulty in reconciling between particle number conservation and superconductivity. An alternative modeling, which is based on the hypothesis that disentanglement spontaneously ocuurs in quantum systems, is explored. The Fermi–Hubbard mode is employed to demonstrate a disentanglement-induced quantum phase transition into a state with a finite superconducting order parameter. Moreover, the effect of disentanglement on Josephson junction’s current phase relation is explored Full article
(This article belongs to the Special Issue Quantum Entanglement—Second Edition)
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17 pages, 372 KiB  
Article
Layered HARQ Design for LDPC-Based Multi-Level Coded Modulation
by Yuejun Wei, Yue Chen, Chunqi Chen, Bin Xia and Liandong Wang
Entropy 2025, 27(6), 629; https://doi.org/10.3390/e27060629 - 13 Jun 2025
Abstract
Multi-level coded modulation (MLCM) enhances data transmission by allocating error correction more effectively to bits with higher error probabilities, thus optimizing redundancy and improving performance. Despite MLCM’s advantages over traditional bit-interleaved coded modulation (BICM) systems in certain scenarios, its integration with hybrid automatic [...] Read more.
Multi-level coded modulation (MLCM) enhances data transmission by allocating error correction more effectively to bits with higher error probabilities, thus optimizing redundancy and improving performance. Despite MLCM’s advantages over traditional bit-interleaved coded modulation (BICM) systems in certain scenarios, its integration with hybrid automatic repeat request (HARQ) systems remains underexplored. HARQ, which combines the benefits of forward error correction (FEC) and automatic repeat request (ARQ), significantly increases resilience to interference and fading, enhancing overall system reliability. This paper bridges the gap by integrating HARQ techniques into the MLCM framework, which was specifically adapted to the layered nature of MLCM. We present tailored hybrid retransmission strategies for each layer of MLCM, demonstrating substantial gains in retransmission efficiency and overall transmission performance. Full article
(This article belongs to the Special Issue LDPC Codes for Communication Systems)
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12 pages, 840 KiB  
Article
Extreme Value Statistics of Community Detection in Complex Networks with Reduced Network Extremal Ensemble Learning (RenEEL)
by Tania Ghosh, Royce K. P. Zia and Kevin E. Bassler
Entropy 2025, 27(6), 628; https://doi.org/10.3390/e27060628 - 13 Jun 2025
Abstract
Arguably, the most fundamental problem in Network Science is finding structure within a complex network. Often, this is achieved by partitioning the network’s nodes into communities in a way that maximizes an objective function. However, finding the maximizing partition is generally a computationally [...] Read more.
Arguably, the most fundamental problem in Network Science is finding structure within a complex network. Often, this is achieved by partitioning the network’s nodes into communities in a way that maximizes an objective function. However, finding the maximizing partition is generally a computationally difficult NP-complete problem. Recently, a machine learning algorithmic scheme was introduced that uses information within a set of partitions to find a new partition that better maximizes an objective function. The scheme, known as RenEEL, uses Extremal Ensemble Learning. Starting with an ensemble of K partitions, it updates the ensemble by considering replacing its worst member with the best of L partitions found by analyzing a reduced network formed by collapsing nodes, which all the ensemble partitions agree should be grouped together, into super-nodes. The updating continues until consensus is achieved within the ensemble about what the best partition is. The original K ensemble partitions and each of the L partitions used for an update are found using a simple “base” partitioning algorithm. We perform an empirical study of how the effectiveness of RenEEL depends on the values of K and L and relate the results to the extreme value statistics of record-breaking. We find that increasing K is generally more effective than increasing L for finding the best partition. Full article
(This article belongs to the Section Complexity)
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13 pages, 820 KiB  
Article
An Efficient Algorithmic Way to Construct Boltzmann Machine Representations for Arbitrary Stabilizer Code
by Yuan-Hang Zhang, Zhian Jia, Yu-Chun Wu and Guang-Can Guo
Entropy 2025, 27(6), 627; https://doi.org/10.3390/e27060627 - 13 Jun 2025
Abstract
Restricted Boltzmann machines (RBMs) have demonstrated considerable success as variational quantum states; however, their representational power remains incompletely understood. In this work, we present an analytical proof that RBMs can exactly and efficiently represent stabilizer code states—a class of highly entangled quantum states [...] Read more.
Restricted Boltzmann machines (RBMs) have demonstrated considerable success as variational quantum states; however, their representational power remains incompletely understood. In this work, we present an analytical proof that RBMs can exactly and efficiently represent stabilizer code states—a class of highly entangled quantum states that are central to quantum error correction. Given a set of stabilizer generators, we develop an efficient algorithm to determine both the RBM architecture and the exact values of its parameters. Our findings provide new insights into the expressive power of RBMs, highlighting their capability to encode highly entangled states, and may serve as a useful tool for the classical simulation of quantum error-correcting codes. Full article
(This article belongs to the Special Issue Quantum Information and Quantum Computation)
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26 pages, 914 KiB  
Article
Threshold Successive Cancellation Flip Decoding Algorithm for Polar Codes: Design and Performance
by Zhicheng Liu, Liuquan Yao, Shuai Yuan, Guiying Yan, Zhiming Ma and Yuting Liu
Entropy 2025, 27(6), 626; https://doi.org/10.3390/e27060626 - 12 Jun 2025
Abstract
In this paper, we propose the threshold successive cancellation flip (Th-SCF) decoding algorithm for polar codes, which enhances the performance of the SC decoder while maintaining low complexity. Theoretical analysis reveals that Th-SCF asymptotically delays the first error position (FEP, the first part [...] Read more.
In this paper, we propose the threshold successive cancellation flip (Th-SCF) decoding algorithm for polar codes, which enhances the performance of the SC decoder while maintaining low complexity. Theoretical analysis reveals that Th-SCF asymptotically delays the first error position (FEP, the first part where the SC decoder fails) with probability 1, ensuring high decoding performance. Simulation results show that the Th-SCF algorithm achieves performance comparable to the dynamic SC flip (D-SCF) algorithm, but with a reduction in complexity by eliminating the need for sorting operations. A key contribution of this work is the rigorous theoretical framework supporting the Th-SCF algorithm, distinguishing it from existing SC flip (SCF) decoding methods. This theoretical foundation not only explains the performance improvements but also provides insights into the underlying mechanisms of flipping. The proposed Th-SCF algorithm demonstrates strong performance across a wide range of code lengths and rates, and its performance remains stable within a certain threshold range, indicating its practical applicability in real-world communication systems. These results offer valuable perspectives for the design of efficient flip decoding strategies in 5G and future networks. Full article
(This article belongs to the Special Issue Network Information Theory and Its Applications)
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22 pages, 665 KiB  
Article
Operational Constraints in Quantum Otto Engines: Energy-Gap Modulation and Majorization
by Sachin Sonkar and Ramandeep S. Johal
Entropy 2025, 27(6), 625; https://doi.org/10.3390/e27060625 - 12 Jun 2025
Abstract
The performance of a quantum Otto engine is analyzed with regard to the constraints on the modulation of energy gaps relative to the changes in probability distributions at the two given heat reservoirs. We performed a detailed analysis with a generic three-level system [...] Read more.
The performance of a quantum Otto engine is analyzed with regard to the constraints on the modulation of energy gaps relative to the changes in probability distributions at the two given heat reservoirs. We performed a detailed analysis with a generic three-level system (3LS), which serves as a non-trivial working medium with two energy gaps. A three-level Otto engine becomes feasible if at least one energy gap shrinks during the first quantum adiabatic stage. The operating regimes are derived for each allowed energy gap modulation, and majorization is observed to play a crucial role in determining the engine operation. This results in an enhanced Otto efficiency when the probability distributions fulfill the majorization condition. Finally, we show that our formalism applies to a swap engine based on a working medium composed of two 3LSs. Full article
(This article belongs to the Special Issue Advances in Quantum Thermodynamics)
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20 pages, 1513 KiB  
Article
Simulation Study on How Input Data Affects Time-Series Classification Model Results
by Maria Sadowska and Krzysztof Gajowniczek
Entropy 2025, 27(6), 624; https://doi.org/10.3390/e27060624 - 12 Jun 2025
Abstract
This paper discusses the results of a study investigating how input data characteristics affect the performance of time-series classification models. In this experiment, we used 82 synthetically generated time-series datasets, created based on predefined functions with added noise. These datasets varied in structure, [...] Read more.
This paper discusses the results of a study investigating how input data characteristics affect the performance of time-series classification models. In this experiment, we used 82 synthetically generated time-series datasets, created based on predefined functions with added noise. These datasets varied in structure, including differences in the number of classes and noise levels, while maintaining a consistent length and total number of observations. This design allowed us to systematically assess the influence of dataset characteristics on classification outcomes. Seven classification models were evaluated and their performance was compared using accuracy metrics, training time and memory requirements. According to the evaluation, the CNN Classifier achieved the best results, demonstrating the highest robustness to an increasing number of classes and noise. In contrast, the least effective model was the Catch22 Classifier. Overall, the performed research leads to the conclusion that as the number of classes and the level of noise in the data increase, all classification models become less effective, achieving lower accuracy metrics. Full article
(This article belongs to the Section Signal and Data Analysis)
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15 pages, 675 KiB  
Article
Edge States, Bulk Spectra, and Topological Phases of Szegedy’s Quantum Search on a One-Dimensional Cycle with Self-Loops
by Mengke Xu, Xi Li, Xunan Wang, Wanglei Mi and Xiao Chen
Entropy 2025, 27(6), 623; https://doi.org/10.3390/e27060623 - 12 Jun 2025
Abstract
Topological transitions are relevant for boundary conditions. Therefore, we investigate the bulk spectra, edge states, and topological phases of Szegedy’s quantum search on a one-dimensional (1D) cycle with self-loops, where the search operator can be formulated as an open boundary condition. By establishing [...] Read more.
Topological transitions are relevant for boundary conditions. Therefore, we investigate the bulk spectra, edge states, and topological phases of Szegedy’s quantum search on a one-dimensional (1D) cycle with self-loops, where the search operator can be formulated as an open boundary condition. By establishing an equivalence with coined quantum walks (QWs), we analytically derive and numerically illustrate the quasienergies dispersion relations of bulk spectra and edge states for Szegedy’s quantum search. Interestingly, novel gapless three-band structures are observed, featuring a flat band and three-fold degenerate points. We identify the topological phases ±2 as the Chern number. This invariant is computed by leveraging chiral symmetry in zero diagonal Hermitian Hamiltonians that satisfy our quasienergies constraints. Furthermore, we demonstrate that the edge states enhance searches on the marked vertices, while the nontrivial bulk spectra facilitate ballistic spread for Szegedy’s quantum search. Crucially, we find that gapless topological phases arise from three-fold degenerate points and are protected by chiral symmetry, distinguishing ill-defined topological transition boundaries. Full article
(This article belongs to the Special Issue Entanglement Entropy and Quantum Phase Transition)
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24 pages, 1562 KiB  
Article
A Novel Framework for Enhancing Decision-Making in Autonomous Cyber Defense Through Graph Embedding
by Zhen Wang, Yongjie Wang, Xinli Xiong, Qiankun Ren and Jun Huang
Entropy 2025, 27(6), 622; https://doi.org/10.3390/e27060622 - 11 Jun 2025
Viewed by 35
Abstract
Faced with challenges posed by sophisticated cyber attacks and dynamic characteristics of cyberspace, the autonomous cyber defense (ACD) technology has shown its effectiveness. However, traditional decision-making methods for ACD are unable to effectively characterize the network topology and internode dependencies, which makes it [...] Read more.
Faced with challenges posed by sophisticated cyber attacks and dynamic characteristics of cyberspace, the autonomous cyber defense (ACD) technology has shown its effectiveness. However, traditional decision-making methods for ACD are unable to effectively characterize the network topology and internode dependencies, which makes it difficult for defenders to identify key nodes and critical attack paths. Therefore, this paper proposes an enhanced decision-making method combining graph embedding with reinforcement learning algorithms. By constructing a game model for cyber confrontations, this paper models important elements of the network topology for decision-making, which guide the defender to dynamically optimize its strategy based on topology awareness. We improve the reinforcement learning with the Node2vec algorithm to characterize information for the defender from the network. And, node attributes and network structural features are embedded into low-dimensional vectors instead of using traditional one-hot encoding, which can address the perceptual bottleneck in high-dimensional sparse environments. Meanwhile, the algorithm training environment Cyberwheel is extended by adding new fine-grained defense mechanisms to enhance the utility and portability of ACD. In experiments, our decision-making method based on graph embedding is compared and analyzed with traditional perception methods. The results show and verify the superior performance of our approach in the strategy selection of defensive decision-making. Also, diverse parameters of the graph representation model Node2vec are analyzed and compared to find the impact on the enhancement of the embedding effectiveness for the decision-making of ACD. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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32 pages, 441 KiB  
Article
The Method of Types for the AWGN Channel
by Sergey Tridenski and Anelia Somekh-Baruch
Entropy 2025, 27(6), 621; https://doi.org/10.3390/e27060621 - 11 Jun 2025
Viewed by 32
Abstract
For the discrete-time AWGN channel with a power constraint, we give an alternative derivation for the sphere-packing upper bound on the optimal block error exponent and an alternative derivation for the analogous lower bound on the optimal correct-decoding exponent. The derivations use the [...] Read more.
For the discrete-time AWGN channel with a power constraint, we give an alternative derivation for the sphere-packing upper bound on the optimal block error exponent and an alternative derivation for the analogous lower bound on the optimal correct-decoding exponent. The derivations use the method of types with finite alphabets of sizes depending on the block length n and with the number of types sub-exponential in n. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
29 pages, 3108 KiB  
Article
Soft Classification in a Composite Source Model
by Yuefeng Cao, Jiakun Liu and Wenyi Zhang
Entropy 2025, 27(6), 620; https://doi.org/10.3390/e27060620 - 11 Jun 2025
Viewed by 33
Abstract
A composite source model consists of an intrinsic state and an extrinsic observation. The fundamental performance limit of reproducing the intrinsic state is characterized by the indirect rate–distortion function. In a remote classification application, a source encoder encodes the extrinsic observation (e.g., image) [...] Read more.
A composite source model consists of an intrinsic state and an extrinsic observation. The fundamental performance limit of reproducing the intrinsic state is characterized by the indirect rate–distortion function. In a remote classification application, a source encoder encodes the extrinsic observation (e.g., image) into bits, and a source decoder plays the role of a classifier that reproduces the intrinsic state (e.g., label of image). In this work, we characterize the general structure of the optimal transition probability distribution, achieving the indirect rate–distortion function. This optimal solution can be interpreted as a “soft classifier”, which generalizes the conventionally adopted “classify-then-compress” scheme. We then apply the soft classification to aid the lossy compression of the extrinsic observation of a composite source. This leads to a coding scheme that exploits the soft classifier to guide reproduction, outperforming existing coding schemes without classification or with hard classification. Full article
(This article belongs to the Special Issue Semantic Information Theory)
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20 pages, 3217 KiB  
Article
Kinetic Monte Carlo Modeling of the Spontaneous Deposition of Platinum on Au(111) Surfaces
by María Cecilia Gimenez, Oscar A. Oviedo and Ezequiel P. M. Leiva
Entropy 2025, 27(6), 619; https://doi.org/10.3390/e27060619 - 11 Jun 2025
Viewed by 67
Abstract
The spontaneous deposition of platinum (Pt) atoms on Au(111) surfaces is systematically investigated through kinetic Monte Carlo simulations within the Embedded Atom Model framework. The kinetic model aims to capture both stoichiometric, atomic-scale interactions and the [...] Read more.
The spontaneous deposition of platinum (Pt) atoms on Au(111) surfaces is systematically investigated through kinetic Monte Carlo simulations within the Embedded Atom Model framework. The kinetic model aims to capture both stoichiometric, atomic-scale interactions and the more relevant processes that describe the kinetics of a physical problem. Various deposition rates are examined, encompassing a thorough exploration of Pt adsorption up to a coverage degree of θ=0.25. The resulting 2D islands exhibit a ramified structure, mirroring the experimental methodologies. For the first time, this study extensively analyzes the dependence of both the mean island size and island density on spontaneous deposition, thereby offering valuable insights into the intricate dynamics of the system. Full article
(This article belongs to the Special Issue Statistical Mechanics of Lattice Gases)
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22 pages, 7220 KiB  
Article
Identifying Polycentric Urban Structure Using the Minimum Cycle Basis of Road Network as Building Blocks
by Yuanbiao Li, Tingyu Wang, Yu Zhao and Bo Yang
Entropy 2025, 27(6), 618; https://doi.org/10.3390/e27060618 - 11 Jun 2025
Viewed by 135
Abstract
A graph’s minimum cycle basis is defined as the smallest collection of cycles that exhibit linear independence in the cycle space, serving as fundamental building blocks for constructing any cyclic structure within the graph. These bases are useful in various contexts, including the [...] Read more.
A graph’s minimum cycle basis is defined as the smallest collection of cycles that exhibit linear independence in the cycle space, serving as fundamental building blocks for constructing any cyclic structure within the graph. These bases are useful in various contexts, including the intricate analysis of electrical networks, structural engineering endeavors, chemical processes, and surface reconstruction techniques, etc. This study investigates the urban road networks of six Chinese cities to analyze their topological features, node centrality, and robustness (resilience to traffic disruptions) using motif analysis and minimum cycle bases methodologies. Some interesting conclusions are obtained: the frequency of motifs containing cycles exceeds that of random networks with equivalent degree sequences; the frequency distribution of minimum cycle lengths and surface areas obeys the power-law distribution. The cycle contribution rate is introduced to investigate the centrality of nodes within road networks, and has a significant impact on the total number of cycles in the robustness analysis. Finally, we construct two types of cycle-based dual networks for urban road networks by representing cycles as nodes and establishing edges between two cycles sharing a common node and edge, respectively. The results show that cycle-based dual networks exhibit small-world and scale-free properties. The research facilitates a comprehensive understanding of the cycle structure characteristics in urban road networks, thereby providing a theoretical foundation for both subsequent modeling endeavors of transportation networks and optimization strategies for existing road infrastructure. Full article
(This article belongs to the Section Complexity)
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39 pages, 7439 KiB  
Article
Identification and Evolution of Core Technologies in the Chip Field Based on Patent Networks
by Ying Wang, Renda Chen and Jindong Chen
Entropy 2025, 27(6), 617; https://doi.org/10.3390/e27060617 - 10 Jun 2025
Viewed by 217
Abstract
Currently, the global technological competition pattern is accelerating its restructuring, and chip technology, as a core technology for national strategic security and industrial competition, faces a serious bottleneck that seriously restricts the construction of China’s industrial chain security and innovation ecology. A “recognition-evolution” [...] Read more.
Currently, the global technological competition pattern is accelerating its restructuring, and chip technology, as a core technology for national strategic security and industrial competition, faces a serious bottleneck that seriously restricts the construction of China’s industrial chain security and innovation ecology. A “recognition-evolution” collaborative analysis system was proposed in this study using patent data as a carrier. Firstly, a PKCN-BERT-LDA fusion module was constructed to identify the core technologies of chip design, manufacturing, and packaging testing. Secondly, the traditional main path analysis method was improved by innovatively introducing information entropy theory to construct a dynamic evolution model, and the technological evolution path in the chip field during 2010–2024 was systematically tracked based on the Derwent patent database. According to this study, the field of chip design exhibited a bidirectional innovation feature of “system optimization regional deep cultivation”, while the manufacturing process highlights the non-linear accumulation law of process complexity. Packaging and testing technology tended to develop in synergy with integration and intelligence. Full article
(This article belongs to the Special Issue Information Spreading Dynamics in Complex Networks)
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7 pages, 173 KiB  
Editorial
Advances in New Physical Layer Technologies for Next-Generation Wireless Communications
by Lei Liu
Entropy 2025, 27(6), 616; https://doi.org/10.3390/e27060616 - 10 Jun 2025
Viewed by 155
Abstract
The world of wireless communication is undergoing an exhilarating transformation [...] Full article
(This article belongs to the Special Issue Advanced New Physical Layer Technologies for Next-Generation Wireless Communications)
37 pages, 799 KiB  
Article
Efficient Entanglement Swapping in Quantum Networks for Multi-User Scenarios
by Binjie He, Seng W. Loke, Luke Lu and Dong Zhang
Entropy 2025, 27(6), 615; https://doi.org/10.3390/e27060615 - 9 Jun 2025
Viewed by 71
Abstract
Entanglement swapping is a crucial step in quantum communication, generating long-distance entanglements between quantum users for quantum network applications, such as distributed quantum computing. This study focuses on the efficiency of entanglement swapping strategies in quantum networks, particularly in multi-user concurrent quantum communication. [...] Read more.
Entanglement swapping is a crucial step in quantum communication, generating long-distance entanglements between quantum users for quantum network applications, such as distributed quantum computing. This study focuses on the efficiency of entanglement swapping strategies in quantum networks, particularly in multi-user concurrent quantum communication. Since multi-user concurrent quantum communication consists of multiple point-to-point quantum communications, we first analyze the challenges faced by existing entanglement swapping strategies in this scenario and then propose Parallel Segment Entanglement Swapping (PSES) to address them. PSES utilizes a tree-like model to divide the path into segments and execute entanglement swapping in parallel across them, thereby enhancing the generation rate of long-distance entanglement. Furthermore, we analyze the impact of resource contention on entanglement swapping in multi-user concurrent quantum communication and propose Multi-user PSES (M-PSES) to alleviate this negative impact. M-PSES leverages the entanglement swapping trigger signal and resource locking mechanisms to mitigate resource contention. The simulation results show that PSES performs superiorly to existing entanglement swapping strategies in point-to-point quantum communication, and M-PSES can achieve better performance than PSES in multi-user concurrent quantum communication. Full article
(This article belongs to the Special Issue Quantum Communication, Quantum Radar, and Quantum Cipher, 2nd Edition)
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26 pages, 4773 KiB  
Article
LSE-CVCNet: A Generalized Stereoscopic Matching Network Based on Local Structural Entropy and Multi-Scale Fusion
by Wenbang Yang, Yong Zhao, Ye Gu, Lu Huang, Jianhua Li and Jianchuan Zhao
Entropy 2025, 27(6), 614; https://doi.org/10.3390/e27060614 - 9 Jun 2025
Viewed by 54
Abstract
This study presents LSE-CVCNet, a novel stereo matching network designed to resolve challenges in dynamic scenes, including dynamic feature misalignment caused by texture variability and contextual ambiguity from occlusions. By integrating three key innovations—local structural entropy (LSE) to quantify structural uncertainty in disparity [...] Read more.
This study presents LSE-CVCNet, a novel stereo matching network designed to resolve challenges in dynamic scenes, including dynamic feature misalignment caused by texture variability and contextual ambiguity from occlusions. By integrating three key innovations—local structural entropy (LSE) to quantify structural uncertainty in disparity maps and guide adaptive attention, a cross-image attention mechanism (CIAM-T) to asymmetrically extract features from left/right images for improved feature alignment, and multi-resolution cost volume fusion (MRCV-F) to preserve fine-grained details through multi-scale fusion—LSE-CVCNet enhances disparity estimation accuracy and cross-domain generalization. The experimental results demonstrate robustness under varying lighting, occlusions, and complex geometries, outperforming state-of-the-art methods across multiple data sets. Ablation studies validate each module’s contribution, while cross-domain tests confirm generalization in unseen scenarios. This work establishes a new paradigm for adaptive stereo matching in dynamic environments. Full article
(This article belongs to the Section Multidisciplinary Applications)
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17 pages, 472 KiB  
Article
Long-Range Dependence in Word Time Series: The Cosine Correlation of Embeddings
by Paweł Wieczyński and Łukasz Dębowski
Entropy 2025, 27(6), 613; https://doi.org/10.3390/e27060613 - 9 Jun 2025
Viewed by 92
Abstract
We analyze long-range dependence (LRD) for word time series, understood as a slower than exponential decay of the two-point Shannon mutual information. We achieve this by examining the decay of the cosine correlation, a proxy object defined in terms of the cosine similarity [...] Read more.
We analyze long-range dependence (LRD) for word time series, understood as a slower than exponential decay of the two-point Shannon mutual information. We achieve this by examining the decay of the cosine correlation, a proxy object defined in terms of the cosine similarity between word2vec embeddings of two words, computed by an analogy to the Pearson correlation. By the Pinsker inequality, the squared cosine correlation between two random vectors lower bounds the mutual information between them. Using the Standardized Project Gutenberg Corpus, we find that the cosine correlation between word2vec embeddings exhibits a readily visible stretched exponential decay for lags roughly up to 1000 words, thus corroborating the presence of LRD. By contrast, for the Human vs. LLM Text Corpus entailing texts generated by large language models, there is no systematic signal of LRD. Our findings may support the need for novel memory-rich architectures in large language models that exceed not only hidden Markov models but also Transformers. Full article
(This article belongs to the Special Issue Complexity Characteristics of Natural Language)
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25 pages, 578 KiB  
Article
Entropy Generation Optimization in Multidomain Systems: A Generalized Gouy-Stodola Theorem and Optimal Control
by Hanz Richter, Meysam Fathizadeh and Tyler Kaptain
Entropy 2025, 27(6), 612; https://doi.org/10.3390/e27060612 - 9 Jun 2025
Viewed by 47
Abstract
The paper considers an extended interpretation of the second law of thermodynamics and its implications to power conversion optimization in multidomain systems. First, a generalized, domain-independent version of the classical Gouy-Stodola theorem is derived for interconnected systems which satisfy the Clausius postulate of [...] Read more.
The paper considers an extended interpretation of the second law of thermodynamics and its implications to power conversion optimization in multidomain systems. First, a generalized, domain-independent version of the classical Gouy-Stodola theorem is derived for interconnected systems which satisfy the Clausius postulate of the second law. Mechanical, electrical and more general Hamiltonian systems do not satisfy this postulate, however the related property of energy cyclodirectionality may be satisfied. A generalized version of the Gouy-Stodola theorem is then obtained in inequality form for systems satisfying this property. The result defines average forms of entropy generation and lost work for multi-domain systems. The paper then formulates an optimal control problem for a representative electromechanical system, obtaining complete, closed-form solutions for the load power transfer and energy harvesting cases. The results indicate that entropy generation minimization is akin to the maximum power transfer theorem. For the power harvesting case, closed-loop stability is guaranteed and practical controllers may be designed. The approach is compared against direct minimization of losses, both theoretically and with Monte Carlo simulations. Full article
(This article belongs to the Section Thermodynamics)
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25 pages, 3049 KiB  
Article
Sic Transit Gloria Mundi: A Mathematical Theory of Popularity Waves Based on a SIIRR Model of Epidemic Spread
by Nikolay K. Vitanov and Zlatinka I. Dimitrova
Entropy 2025, 27(6), 611; https://doi.org/10.3390/e27060611 - 9 Jun 2025
Viewed by 204
Abstract
We discuss the spread of epidemics caused by two viruses which cannot infect the same individual at the same time. The mathematical modeling of this epidemic leads to a kind of SIIRR model with two groups of infected individuals and two groups of [...] Read more.
We discuss the spread of epidemics caused by two viruses which cannot infect the same individual at the same time. The mathematical modeling of this epidemic leads to a kind of SIIRR model with two groups of infected individuals and two groups of recovered individuals. An additional assumption is that after recovering from one of the viruses, the individual cannot be infected by the other virus. The mathematical model consists of five equations which can be reduced to a system of three differential equations for the susceptible and for the recovered individuals. This system has analytical solutions for the case when one of the viruses infects many more individuals than the other virus. Cases which are more complicated than this one can be studied numerically. The theory is applied to the study of waves of popularity of an individual/groups of individuals or of an idea/group of ideas in the case of the presence of two opposite opinions about the popularity of the corresponding individual/group of individuals or idea/group of ideas. We consider two cases for the initial values of the infected individuals: (a) the initial value of the individuals infected with one of the viruses is much larger than the initial values of the individuals infected by the second virus, and (b) the two initial values of the infected individuals are the same. The following effects connected to the evolution of the numbers of infected individuals are observed: 1. arising of bell-shaped profiles of the numbers of infected individuals; 2. suppression of popularity; 3. faster increase–faster decrease effect for the peaks of the bell-shaped profiles; 4. peak shift in the time; 5. effect of forgetting; 6. window of dominance; 7. short-term win–long-term loss effect; 8. effect of the single peak. The proposed SIIRR model is used to build a mathematical theory of popularity waves where a person or idea can have positive and negative popularity at the same time and these popularities evolve with time. Full article
(This article belongs to the Special Issue Aspects of Social Dynamics: Models and Concepts)
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15 pages, 419 KiB  
Article
Ordinal Random Processes
by Christoph Bandt
Entropy 2025, 27(6), 610; https://doi.org/10.3390/e27060610 - 7 Jun 2025
Viewed by 157
Abstract
Ordinal patterns have proven to be a valuable tool in many fields. Here, we address the need for theoretical models. A paradigmatic example shows that a model for frequencies of ordinal patterns can be determined without any numerical values. We specify the important [...] Read more.
Ordinal patterns have proven to be a valuable tool in many fields. Here, we address the need for theoretical models. A paradigmatic example shows that a model for frequencies of ordinal patterns can be determined without any numerical values. We specify the important concept of stationary order and the fundamental problems to be solved in order to establish a genuine statistical methodology for ordinal time series. Full article
(This article belongs to the Special Issue Ordinal Patterns-Based Tools and Their Applications)
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14 pages, 15596 KiB  
Article
Quasi-Discrete Time Crystals in the Quasiperiodically Driven Lipkin–Meshkov–Glick Model
by Sk Anisur, Wensheng Vincent Liu and Sayan Choudhury
Entropy 2025, 27(6), 609; https://doi.org/10.3390/e27060609 - 7 Jun 2025
Viewed by 157
Abstract
A discrete time crystal (DTC) is a remarkable non-equilibrium phase of matter characterized by the persistent sub-harmonic oscillations of physical observables in periodically driven many-body systems. Motivated by the question of whether such a temporal periodic order can persist when the drive becomes [...] Read more.
A discrete time crystal (DTC) is a remarkable non-equilibrium phase of matter characterized by the persistent sub-harmonic oscillations of physical observables in periodically driven many-body systems. Motivated by the question of whether such a temporal periodic order can persist when the drive becomes aperiodic, we investigate the dynamics of a Lipkin–Meshkov–Glick model under quasi-periodic Thue–Morse (TM) driving. Intriguingly, this infinite-range-interacting spin system can host “quasi-discrete time crystal” (quasi-DTC) phases characterized by periodic oscillations of the magnetization. We demonstrate that our model can host the quasi-DTC analog of both period-doubling DTCs as well as higher-order DTCs. These quasi-DTCs are robust to various perturbations, and they originate from the interplay of “all-to-all” interactions and the recursive structure of the TM sequence. Our results suggest that quasi-periodic driving protocols can provide a promising route for realizing novel non-equilibrium phases of matter in long-range interacting systems. Full article
(This article belongs to the Special Issue Non-Equilibrium Dynamics in Ultra-Cold Quantum Gases)
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26 pages, 519 KiB  
Article
Generalized Derangetropy Functionals for Modeling Cyclical Information Flow
by Masoud Ataei and Xiaogang Wang
Entropy 2025, 27(6), 608; https://doi.org/10.3390/e27060608 - 7 Jun 2025
Viewed by 170
Abstract
This paper introduces a functional framework for modeling cyclical and feedback-driven information flow using a generalized family of derangetropy operators. In contrast to scalar entropy measures such as Shannon entropy, these operators act directly on probability densities, providing a topographical representation of information [...] Read more.
This paper introduces a functional framework for modeling cyclical and feedback-driven information flow using a generalized family of derangetropy operators. In contrast to scalar entropy measures such as Shannon entropy, these operators act directly on probability densities, providing a topographical representation of information across the support of the distribution. The proposed framework captures periodic and self-referential aspects of information evolution through functional transformations governed by nonlinear differential equations. When applied recursively, these operators induce a spectral diffusion process governed by the heat equation, with convergence toward a Gaussian characteristic function. This convergence result establishes an analytical foundation for describing the long-term dynamics of information under cyclic modulation. The framework thus offers new tools for analyzing the temporal evolution of information in systems characterized by periodic structure, stochastic feedback, and delayed interaction, with potential applications in artificial neural networks, communication theory, and non-equilibrium statistical mechanics. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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