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Volume 27
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Entropy, Volume 27, Issue 6 (June 2025) – 108 articles

Cover Story (view full-size image): This cover illustrates the quantum Mpemba effect in open quantum systems, where two distinct initial states—entangled photon–atom configurations in a cavity QED setup—relax toward equilibrium along different paths. The colorful trajectory shows how interference between non-orthogonal decay modes can lead to surprising behavior, i.e., a state closer to equilibrium may relax more slowly than one farther away. This highlights how non-reciprocal couplings, radiative dissipation, and directional interactions shape anomalous early-time dynamics, expanding our view of quantum relaxation. View this paper
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23 pages, 375 KiB  
Article
Combining Statistical Evidence When Evidence Is Measured by Relative Belief
by Michael Evans
Entropy 2025, 27(6), 654; https://doi.org/10.3390/e27060654 - 18 Jun 2025
Viewed by 220
Abstract
The problem of combining statistical evidence concerning an unknown, contained in each of the k Bayesian inference bases, is discussed. This can be considered as being related to the problem of pooling k priors to determine a consensus prior, but the focus here [...] Read more.
The problem of combining statistical evidence concerning an unknown, contained in each of the k Bayesian inference bases, is discussed. This can be considered as being related to the problem of pooling k priors to determine a consensus prior, but the focus here is instead on combining a measure of statistical evidence to obtain a consensus measure of statistical evidence. The linear opinion pool is seen to have the most appropriate properties for this role. In particular, linear pooling preserves a consensus with respect to the evidence, and other rules do not. While linear pooling does not preserve prior independence, it is shown that it still behaves appropriately with respect to the expression of statistical evidence in such a context. For the more general problem of combining statistical evidence, where the priors as well as the sampling models may differ, Jeffrey conditionalization plays a key role. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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29 pages, 19381 KiB  
Article
Error-Constrained Entropy-Minimizing Strategies for Multi-UAV Deception Against Networked Radars
by Honghui Ban, Jifei Pan, Zheng Wang, Rui Cui, Yuting Ming and Qiuxi Jiang
Entropy 2025, 27(6), 653; https://doi.org/10.3390/e27060653 - 18 Jun 2025
Viewed by 322
Abstract
In complex electromagnetic environments, spatial coupling uncertainties—position errors and timing jitter—increase false target information entropy, reducing strategy effectiveness and posing challenges for robust UAV swarm track deception. This paper proposes an error-constrained entropy-minimizing compensation framework to model radar/UAV errors and their spatial coupling. [...] Read more.
In complex electromagnetic environments, spatial coupling uncertainties—position errors and timing jitter—increase false target information entropy, reducing strategy effectiveness and posing challenges for robust UAV swarm track deception. This paper proposes an error-constrained entropy-minimizing compensation framework to model radar/UAV errors and their spatial coupling. The framework establishes closed-form gate association conditions based on the principle of entropy minimization, ensuring mutual consistency of false target measurements across multiple radars. Two strategies are proposed to reduce false target information entropy: 1. Zonal track compensation forms dense “information entropy bands” around each preset false target by inserting auxiliary deception echoes, enhancing mutual information concentration in the measurement space; 2. Formation jamming compensation adaptively reshapes the UAV swarm into regular polygons, leveraging geometric symmetry to suppress spatial diffusion of position errors. Simulation results show that compared with traditional methods, the proposed approach reduces the spatial inconsistency entropy by 50%, improving false target consistency and radar deception reliability. Full article
(This article belongs to the Section Multidisciplinary Applications)
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11 pages, 334 KiB  
Article
Why Is the Universe Not Frozen by the Quantum Zeno Effect?
by Antoine Soulas
Entropy 2025, 27(6), 652; https://doi.org/10.3390/e27060652 - 18 Jun 2025
Viewed by 205
Abstract
We built a discrete model that simulates the ubiquitous competition between the free internal evolution of a two-level system and the decoherence induced by the interaction with its surrounding environment. It is aimed at being as universal as possible, so that no specific [...] Read more.
We built a discrete model that simulates the ubiquitous competition between the free internal evolution of a two-level system and the decoherence induced by the interaction with its surrounding environment. It is aimed at being as universal as possible, so that no specific Hamiltonian is assumed. This leads to an analytic criterion, depending on the level of short time decoherence, allowing one to determine whether the system will freeze due to the Zeno effect. We checked this criterion on several classes of functions which correspond to different physical situations. In the most generic case, the free evolution wins over decoherence, thereby explaining why the universe is indeed not frozen. We finally make a quantitative comparison with the continuous model of Presilla, Onofrio and Tambini, based on a Lindblad’s master equation, a find good agreement at least in the low coupling regime. Full article
(This article belongs to the Section Astrophysics, Cosmology, and Black Holes)
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14 pages, 907 KiB  
Article
Extended Blahut–Arimoto Algorithm for Semantic Rate-Distortion Function
by Yuxin Han, Yang Liu, Yaping Sun, Kai Niu, Nan Ma, Shuguang Cui and Ping Zhang
Entropy 2025, 27(6), 651; https://doi.org/10.3390/e27060651 - 18 Jun 2025
Viewed by 215
Abstract
Semantic communication has recently gained significant attention in theoretical analysis due to its potential to improve communication efficiency by focusing on meaning rather than exact signal reconstruction. In this paper, we extend the Blahut–Arimoto (BA) algorithm, a fundamental method in classical information theory [...] Read more.
Semantic communication has recently gained significant attention in theoretical analysis due to its potential to improve communication efficiency by focusing on meaning rather than exact signal reconstruction. In this paper, we extend the Blahut–Arimoto (BA) algorithm, a fundamental method in classical information theory (CIT) for computing the rate-distortion (RD) function, to semantic communication by proposing the extended Blahut–Arimoto (EBA) algorithm, which iteratively updates transition and reconstruction distributions to calculate the semantic RD function based on synonymous mapping in semantic information theory (SIT). To address scenarios where synonymous mappings are unknown, we develop an optimization framework that combines the EBA algorithm with simulated annealing. Initialized with a syntactic mapping, the framework progressively merges syntactic symbols and identifies the mapping with a maximum synonymous number that satisfies objective constraints. Furthermore, by considering the semantic knowledge base (SKB) as a specific instance of synonymous mapping, the EBA algorithm provides a theoretical approach for analyzing and predicting the SKB size. Numerical results validate the effectiveness of the EBA algorithm. For Gaussian sources, the semantic RD function decreases with an increasing synonymous number and becomes significantly lower than its classical counterpart. Additionally, analysis on the CUB dataset demonstrates that larger SKB sizes lead to higher semantic communication compression efficiency. Full article
(This article belongs to the Special Issue Semantic Information Theory)
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20 pages, 528 KiB  
Article
Analysis of Outage Probability and Average Bit Error Rate of Parallel-UAV-Based Free-Space Optical Communications
by Sheng-Hong Lin, Jin-Yuan Wang and Xinyi Hua
Entropy 2025, 27(6), 650; https://doi.org/10.3390/e27060650 - 18 Jun 2025
Viewed by 186
Abstract
Recently, free-space optical (FSO) communication systems utilizing unmanned aerial vehicle (UAV) relays have garnered significant attention. Integrating UAV relays into FSO communication and employing cooperative diversity techniques not only fulfill the need for long-distance transmission but also enable flexible adjustments of relay positions [...] Read more.
Recently, free-space optical (FSO) communication systems utilizing unmanned aerial vehicle (UAV) relays have garnered significant attention. Integrating UAV relays into FSO communication and employing cooperative diversity techniques not only fulfill the need for long-distance transmission but also enable flexible adjustments of relay positions based on the actual environment. This paper investigates the performance of a parallel-UAV-relay-based FSO communication system. In the considered system, the channel fadings include atmospheric loss, atmospheric turbulence, pointing errors, and angle-of-arrival fluctuation. Using the established channel model, we derive a tractable expression for the probability density function of the total channel gain. Then, we derive closed-form expressions of the system outage probability (OP) and average bit error rate (ABER). Moreover, we also derive the asymptotic OP and ABER for a high-optical-intensity regime. Our numerical results validate the accuracy of the derived theoretical expressions. Additionally, the effects of the number of relay nodes, the field of view, the direction deviation, the signal-to-noise ratio threshold, the atmospheric turbulence intensity, the transmit power, and the transmission distance on the system’s performance are also discussed. Full article
(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives, 2nd Edition)
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26 pages, 328 KiB  
Article
Finite-Time Thermodynamics: Problems, Approaches, and Results
by Anatoly M. Tsirlin, Alexander I. Balunov and Ivan A. Sukin
Entropy 2025, 27(6), 649; https://doi.org/10.3390/e27060649 - 17 Jun 2025
Viewed by 216
Abstract
In this manuscript, the typical problems of “finite-time thermodynamics”, their general methodology, and the general features of their solutions are considered. We also consider the role of minimal dissipation processes, the properties of the irreversibility index, and the consequences of its existence. A [...] Read more.
In this manuscript, the typical problems of “finite-time thermodynamics”, their general methodology, and the general features of their solutions are considered. We also consider the role of minimal dissipation processes, the properties of the irreversibility index, and the consequences of its existence. A generalization of the Carathéodory theorem for averaged optimization problems corresponding to cyclic processes and the properties of optimal solutions following from it are given. The existence of the irreversibility index for economic macrosystems and their analogies to and differences from thermodynamic systems are proven. Full article
(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)
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18 pages, 8099 KiB  
Article
Lipschitz-Nonlinear Heterogeneous Multi-Agent Adaptive Distributed Time-Varying Formation-Tracking Control with Jointly Connected Topology
by Ling Zhu, Yuyi Huang, Yandong Li, Hui Cai, Wei Zhao, Xu Liu and Yuan Guo
Entropy 2025, 27(6), 648; https://doi.org/10.3390/e27060648 - 17 Jun 2025
Viewed by 264
Abstract
This paper studies the problem of time-varying formation-tracking control for a class of nonlinear multi-agent systems. A distributed adaptive controller that avoids the global non-zero minimum eigenvalue is designed for heterogeneous systems in which leaders and followers contain different nonlinear terms, and which [...] Read more.
This paper studies the problem of time-varying formation-tracking control for a class of nonlinear multi-agent systems. A distributed adaptive controller that avoids the global non-zero minimum eigenvalue is designed for heterogeneous systems in which leaders and followers contain different nonlinear terms, and which relies only on the relative errors between adjacent agents. By adopting the Riccati inequality method, the adaptive adjustment factor in the controller is designed to solve the problem of automatically adjusting relative errors based solely on local information. Unlike existing research on time-varying formations with fixed and switching topologies, the method of jointly connected topological graphs is adopted to enable nonlinear followers to track the trajectories of leaders with different nonlinear terms and simultaneously achieve the control objective of the desired time-varying formation. The stability of the system under the jointly connected graph is proved by the Lyapunov stability proof method. Finally, numerical simulation experiments confirm the effectiveness of the proposed control method. Full article
(This article belongs to the Section Complexity)
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10 pages, 2312 KiB  
Article
Synchronizations in Complex Systems Dynamics Through a Multifractal Procedure
by Vlad Ghizdovat, Diana Carmen Mirila, Florin Nedeff, Dragos Ioan Rusu, Oana Rusu, Maricel Agop and Decebal Vasincu
Entropy 2025, 27(6), 647; https://doi.org/10.3390/e27060647 - 17 Jun 2025
Viewed by 235
Abstract
The dynamics of complex systems often exhibit multifractal properties, where interactions across different scales influence their evolution. In this study, we apply the Multifractal Theory of Motion within the framework of scale relativity theory to explore synchronization phenomena in complex systems. We demonstrate [...] Read more.
The dynamics of complex systems often exhibit multifractal properties, where interactions across different scales influence their evolution. In this study, we apply the Multifractal Theory of Motion within the framework of scale relativity theory to explore synchronization phenomena in complex systems. We demonstrate that the motion of such systems can be described by multifractal Schrödinger-type equations, offering a new perspective on the interplay between deterministic and stochastic behaviors. Our analysis reveals that synchronization in complex systems emerges from the balance of multifractal acceleration, convection, and dissipation, leading to structured yet highly adaptive behavior across scales. The results highlight the potential of multifractal analysis in predicting and controlling synchronized dynamics in real-world applications. Several applications are also discussed. Full article
(This article belongs to the Special Issue Nonlinear Dynamics of Complex Systems)
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20 pages, 1163 KiB  
Article
Exploring Numerical Correlations: Models and Thermodynamic Kappa
by Nicholas V. Sarlis, David J. McComas and George Livadiotis
Entropy 2025, 27(6), 646; https://doi.org/10.3390/e27060646 - 17 Jun 2025
Viewed by 283
Abstract
McComas et al. (2025) introduced a numerical experiment, where ordinary uncorrelated collisions between collision pairs are followed by other, controlled (correlated) collisions, shedding light on the emergence of kappa distributions through particle correlations in space plasmas. We extend this experiment by introducing correlations [...] Read more.
McComas et al. (2025) introduced a numerical experiment, where ordinary uncorrelated collisions between collision pairs are followed by other, controlled (correlated) collisions, shedding light on the emergence of kappa distributions through particle correlations in space plasmas. We extend this experiment by introducing correlations indicating that (i) when long-range correlations are interwoven with collision pairs, the resulting thermodynamic kappa are described as that corresponding to an ‘interatomic’ potential interaction among particles; (ii) searching for a closer description of heliospheric plasmas, we found that pairwise short-range correlations are sufficient to lead to appropriate values of thermodynamic kappa, especially when forming correlated clusters; (iii) multi-particle correlations do not lead to physical stationary states; finally, (iv) an optimal model arises when combining all previous findings. In an excellent match with space plasmas observations, the thermodynamic kappa that describes the stationary state at which the system is stabilized behaves as follows: (a) When correlations are turned off, kappa is turning toward infinity, indicating the state of classical thermal equilibrium (Maxwell-Boltzmann distribution), (b) When collisions are turned off, kappa is turning toward the anti-equilibrium state, the furthest state from the classical thermal equilibrium (−5 power-law phase-space distribution), and (c) the finite kappa values are generally determined by the competing factor of collisions and correlations. Full article
(This article belongs to the Collection Foundations of Statistical Mechanics)
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13 pages, 3561 KiB  
Article
Attention-Based Batch Normalization for Binary Neural Networks
by Shan Gu, Guoyin Zhang, Chengwei Jia and Yanxia Wu
Entropy 2025, 27(6), 645; https://doi.org/10.3390/e27060645 - 17 Jun 2025
Viewed by 281
Abstract
Batch normalization (BN) is crucial for achieving state-of-the-art binary neural networks (BNNs). Unlike full-precision neural networks, BNNs restrict activations to discrete values {−1,1}, which requires a renewed understanding and research of the role and significance of the [...] Read more.
Batch normalization (BN) is crucial for achieving state-of-the-art binary neural networks (BNNs). Unlike full-precision neural networks, BNNs restrict activations to discrete values {−1,1}, which requires a renewed understanding and research of the role and significance of the BN layers in BNNs. Many studies notice this phenomenon and try to explain it. Inspired by these studies, we introduce the self-attention mechanism into BN and propose a novel Attention-Based Batch Normalization (ABN) for Binary Neural Networks. Also, we present an ablation study of parameter trade-offs in ABN, as well as an experimental analysis of the effect of ABN on BNNs. Experimental analyses show that our ABN method helps to capture image features, provide additional activation-like functions, and increase the imbalance of the activation distribution, and these features help to improve the performance of BNNs. Furthermore, we conduct image classification experiments over the CIFAR10, CIFAR100, and TinyImageNet datasets using BinaryNet and ResNet-18 network structures. The experimental results demonstrate that our ABN consistently outperforms the baseline BN across various benchmark datasets and models in terms of image classification accuracy. In addition, ABN exhibits less variance on the CIFAR datasets, which suggests that ABN can improve the stability and reliability of models. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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26 pages, 3758 KiB  
Review
Information Theory Meets Quantum Chemistry: A Review and Perspective
by Yilin Zhao, Dongbo Zhao, Chunying Rong, Shubin Liu and Paul W. Ayers
Entropy 2025, 27(6), 644; https://doi.org/10.3390/e27060644 - 16 Jun 2025
Viewed by 578
Abstract
In this survey, we begin with a concise introduction to information theory within Shannon’s framework, focusing on the key concept of Shannon entropy and its related quantities: relative entropy, joint entropy, conditional entropy, and mutual information. We then demonstrate how to apply these [...] Read more.
In this survey, we begin with a concise introduction to information theory within Shannon’s framework, focusing on the key concept of Shannon entropy and its related quantities: relative entropy, joint entropy, conditional entropy, and mutual information. We then demonstrate how to apply these information-theoretic tools in quantum chemistry, adopting either classical or quantum formalisms based on the choice of information carrier involved. Full article
(This article belongs to the Special Issue The Information-Theoretic Approach in Density Functional Theory and Beyond)
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30 pages, 982 KiB  
Article
Brown and Levy Steady-State Motions
by Iddo Eliazar
Entropy 2025, 27(6), 643; https://doi.org/10.3390/e27060643 - 16 Jun 2025
Viewed by 212
Abstract
This paper introduces and explores a novel class of Brown and Levy steady-state motions. These motions generalize, respectively, the Ornstein-Uhlenbeck process (OUP) and the Levy-driven OUP. As the OUP and the Levy-driven OUP: the motions are Markov; their dynamics are Langevin; and their [...] Read more.
This paper introduces and explores a novel class of Brown and Levy steady-state motions. These motions generalize, respectively, the Ornstein-Uhlenbeck process (OUP) and the Levy-driven OUP. As the OUP and the Levy-driven OUP: the motions are Markov; their dynamics are Langevin; and their steady-state distributions are, respectively, Gauss and Levy. As the Levy-driven OUP: the motions can display the Noah effect (heavy-tailed amplitudal fluctuations); and their memory structure is tunable. And, as Gaussian-stationary processes: the motions can display the Joseph effect (long-ranged temporal dependencies); and their correlation structure is tunable. The motions have two parameters: a critical exponent which determines the Noah effect and the memory structure; and a clock function which determines the Joseph effect and the correlation structure. The novel class is a compelling stochastic model due to the following combination of facts: on the one hand the motions are tractable and amenable to analysis and use; on the other hand the model is versatile and the motions display a host of both regular and anomalous features. Full article
(This article belongs to the Collection Advances in Applied Statistical Mechanics)
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9 pages, 276 KiB  
Article
Stochastic Model for a 4 QAM Transmission Subject to the Epidemic Interference Effect
by Marcelo S. Alencar
Entropy 2025, 27(6), 642; https://doi.org/10.3390/e27060642 - 16 Jun 2025
Viewed by 157
Abstract
This article presents a stochastic model for the effect of interference caused by a sudden increase in the number of users that access a 4 QAM digital communication system. As demonstrated, the rapid increase in the number of users that access the system [...] Read more.
This article presents a stochastic model for the effect of interference caused by a sudden increase in the number of users that access a 4 QAM digital communication system. As demonstrated, the rapid increase in the number of users that access the system causes a non-stationary traffic in the network. A stochastic differential approach is used to model the epidemic interference effect. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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35 pages, 1553 KiB  
Article
Efficient Learning-Based Robotic Navigation Using Feature-Based RGB-D Pose Estimation and Topological Maps
by Eder A. Rodríguez-Martínez, Jesús Elías Miranda-Vega, Farouk Achakir, Oleg Sergiyenko, Julio C. Rodríguez-Quiñonez, Daniel Hernández Balbuena and Wendy Flores-Fuentes
Entropy 2025, 27(6), 641; https://doi.org/10.3390/e27060641 - 15 Jun 2025
Viewed by 392
Abstract
Robust indoor robot navigation typically demands either costly sensors or extensive training data. We propose a cost-effective RGB-D navigation pipeline that couples feature-based relative pose estimation with a lightweight multi-layer-perceptron (MLP) policy. RGB-D keyframes extracted from human-driven traversals form nodes of a topological [...] Read more.
Robust indoor robot navigation typically demands either costly sensors or extensive training data. We propose a cost-effective RGB-D navigation pipeline that couples feature-based relative pose estimation with a lightweight multi-layer-perceptron (MLP) policy. RGB-D keyframes extracted from human-driven traversals form nodes of a topological map; edges are added when visual similarity and geometric–kinematic constraints are jointly satisfied. During autonomy, LightGlue features and SVD give six-DoF relative pose to the active keyframe, and the MLP predicts one of four discrete actions. Low visual similarity or detected obstacles trigger graph editing and Dijkstra replanning in real time. Across eight tasks in four Habitat-Sim environments, the agent covered 190.44 m, replanning when required, and consistently stopped within 0.1 m of the goal while running on commodity hardware. An information-theoretic analysis over the Multi-Illumination dataset shows that LightGlue maximizes per-second information gain under lighting changes, motivating its selection. The modular design attains reliable navigation without metric SLAM or large-scale learning, and seamlessly accommodates future perception or policy upgrades. Full article
(This article belongs to the Special Issue Application of Information Theory to Computer Vision and Image Processing, 3rd Edition)
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20 pages, 1481 KiB  
Article
Analysis and Research on Spectrogram-Based Emotional Speech Signal Augmentation Algorithm
by Huawei Tao, Sixian Li, Xuemei Wang, Binkun Liu and Shuailong Zheng
Entropy 2025, 27(6), 640; https://doi.org/10.3390/e27060640 - 15 Jun 2025
Viewed by 243
Abstract
Data augmentation techniques are widely applied in speech emotion recognition to increase the diversity of data and enhance the performance of models. However, existing research has not deeply explored the impact of these data augmentation techniques on emotional data. Inappropriate augmentation algorithms may [...] Read more.
Data augmentation techniques are widely applied in speech emotion recognition to increase the diversity of data and enhance the performance of models. However, existing research has not deeply explored the impact of these data augmentation techniques on emotional data. Inappropriate augmentation algorithms may distort emotional labels, thereby reducing the performance of models. To address this issue, in this paper we systematically evaluate the influence of common data augmentation algorithms on emotion recognition from three dimensions: (1) we design subjective auditory experiments to intuitively demonstrate the impact of augmentation algorithms on the emotional expression of speech; (2) we jointly extract multi-dimensional features from spectrograms based on the Librosa library and analyze the impact of data augmentation algorithms on the spectral features of speech signals through heatmap visualization; and (3) we objectively evaluate the recognition performance of the model by means of indicators such as cross-entropy loss and introduce statistical significance analysis to verify the effectiveness of the augmentation algorithms. The experimental results show that “time stretching” may distort speech features, affect the attribution of emotional labels, and significantly reduce the model’s accuracy. In contrast, “reverberation” (RIR) and “resampling” within a limited range have the least impact on emotional data, enhancing the diversity of samples. Moreover, their combination can increase accuracy by up to 7.1%, providing a basis for optimizing data augmentation strategies. Full article
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12 pages, 360 KiB  
Article
Reputation in the Iterated Prisoner’s Dilemma: A Simple, Analytically Solvable Agents’ Model
by Michał Cieśla
Entropy 2025, 27(6), 639; https://doi.org/10.3390/e27060639 - 15 Jun 2025
Viewed by 332
Abstract
This study introduces a simple model, which can be used to examine the influence of reputation on expected income achieved within the Iterated Prisoner’s Dilemma (IPD) game framework. The research explores how different reputation distributions among society members impact overall outcomes by modeling [...] Read more.
This study introduces a simple model, which can be used to examine the influence of reputation on expected income achieved within the Iterated Prisoner’s Dilemma (IPD) game framework. The research explores how different reputation distributions among society members impact overall outcomes by modeling a society of agents, each characterized by a reputation score that dictates their likelihood of cooperation. Due to the simplicity of the model, we can analytically determine the expected incomes based on the distribution of agents’ reputations and model parameters. The results show that a higher reputation generally leads to greater expected income, thereby promoting cooperation over defection. However, in some cases, where there are more defecting individuals, the expected income reaches the maximum for agents with an average reputation, and then decreases for individuals who cooperate more. Various scenarios, including uniform, increasing, and decreasing reputation distributions, are analyzed to understand their effects on the promoted interaction strategy. Finally, we outline future extensions of the model and potential research directions, including the exploration of alternative reputation distributions, variable interaction parameters, and different payoff structures in the dilemma games. Full article
(This article belongs to the Collection Social Sciences)
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14 pages, 4151 KiB  
Article
Fisher Information and the Dynamics of Multicellular Ageing
by Zachary F. Hale, Gonzalo A. Cánez and Thomas C. T. Michaels
Entropy 2025, 27(6), 638; https://doi.org/10.3390/e27060638 - 15 Jun 2025
Viewed by 409
Abstract
Information theory has long been integrated into the study of biological ageing, for example, in examining the roles of genetic and epigenetic fidelity in cellular and organismal longevity. Here, we introduce a theoretical model that interprets ageing in multicellular systems through the lens [...] Read more.
Information theory has long been integrated into the study of biological ageing, for example, in examining the roles of genetic and epigenetic fidelity in cellular and organismal longevity. Here, we introduce a theoretical model that interprets ageing in multicellular systems through the lens of Fisher information. Previous theories have suggested that the ageing of multicellular organisms is an inevitable consequence of the inherent tension between individual cell reproduction and the homeostasis of the multicellular system. Utilising concepts from information theory and statistical mechanics, we show that Fisher information parametrises the dynamics of this tension through non-monotonic behaviour, which depends on an optimal balance of competition and cooperation between cells. Moreover, Fisher information suggests that the ability to infer true biological age from a sample evolves through complex dynamics over an organism’s lifespan. Full article
(This article belongs to the Collection Disorder and Biological Physics)
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24 pages, 5959 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 - 14 Jun 2025
Viewed by 373
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)
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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 - 14 Jun 2025
Viewed by 322
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, 12521 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 - 14 Jun 2025
Viewed by 342
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)
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17 pages, 1566 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 - 14 Jun 2025
Viewed by 199
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 - 13 Jun 2025
Viewed by 388
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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23 pages, 422 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 - 13 Jun 2025
Viewed by 269
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)
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13 pages, 563 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
Viewed by 223
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)
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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
Viewed by 214
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
Viewed by 343
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
Viewed by 274
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
Viewed by 302
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
Viewed by 334
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
Viewed by 291
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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