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Entropy, Volume 28, Issue 7

2026 July - 117 articles

Cover Story: Artificial transaction generation remains an important source of potential market manipulation on cryptocurrency exchanges, as it may distort reported liquidity and reduce market transparency. This study proposes a diagnostic framework for detecting unusual trading patterns based on complexity and statistical-structure measures derived from high-frequency trade-level data. Applied to BTC, ETH, and XRP on Binance, Bitget, KuCoin, and Kraken, the analysis reveals a pronounced anomaly on Bitget for BTC and ETH after mid-May 2025: transaction counts rose sharply without a proportional increase in traded volume or return fluctuations. Our findings show that complexity-based indicators can be useful for detecting exchange-specific trading anomalies that remain hidden in price-based measures. View this paper
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Articles (117)

  • Article
  • Open Access
553 Views
26 Pages

22 July 2026

k-entanglement, including entanglement relative to full separability and genuinely multipartite entanglement, is a fundamental quantum resource in multipartite quantum systems. Its identification and quantification play essential roles in quantum inf...

(This article belongs to the Special Issue New Advances in Quantum Communication and Networks, 2nd Edition)
  • Article
  • Open Access
505 Views
24 Pages

Image Encryption via DDPM Skipping-Step Diffusion Based on a Six-Dimensional Hyperchaotic System with Feedback Control

  • Songran Wang,
  • Hanqing Zhao,
  • Wei He,
  • Tao Wang and ,
  • Zhiben Zhuang,
  • Tianfu Zhang and
  • Jiacheng Xu
  • + 2 authors+ 0 author

22 July 2026

In this paper, we propose a novel image encryption algorithm that integrates a six-dimensional hyperchaotic system with the forward diffusion process of denoising diffusion probabilistic models (DDPMs). The proposed framework synergistically combines...

  • Feature Paper
  • Article
  • Open Access
817 Views
19 Pages

22 July 2026

Thermophysical properties of thermal plasmas are essential input data for computational models. The required data are usually taken from the literature without examination of their reliability. Cross-code verifications of properties are rare in the t...

(This article belongs to the Section Thermodynamics)
  • Article
  • Open Access
587 Views
22 Pages

22 July 2026

Quantum neural architecture search (QNAS) has emerged as a promising approach for automatically designing parameterized quantum circuits (PQCs) for near-term quantum machine learning tasks. However, quantum evolutionary algorithm (QEA)-based QNAS met...

(This article belongs to the Section Quantum Information)
  • Article
  • Open Access
438 Views
29 Pages

21 July 2026

Moment condition models are popular in statistics and econometrics, as they provide a powerful and flexible framework for estimation. However, estimation procedures based on these models can be sensitive to misspecification or the presence of outlier...

(This article belongs to the Special Issue Statistical Inference: Theory and Methods)
  • Article
  • Open Access
590 Views
16 Pages

20 July 2026

Classical evolutionary game theory rests on a hidden assumption: that an actor holds a definite strategy, pure or randomized, before it ever interacts. Yet human and organizational choices routinely violate this premise, displaying interference, orde...

(This article belongs to the Section Multidisciplinary Applications)
  • Article
  • Open Access
510 Views
22 Pages

20 July 2026

We present a systematic derivation of asymptotic expansions of nonequilibrium thermodynamics for chemical reaction networks (CRNs) based on singular perturbation theory. For a general reversible CRN with fast–slow kinetics, we obtain the first...

(This article belongs to the Section Thermodynamics)
  • Article
  • Open Access
432 Views
23 Pages

20 July 2026

Understanding how regional innovation networks maintain functionality under disruption is critical for regional economic sustainability. This study investigates the structural evolution and topological resilience of inter-city patent cooperation netw...

(This article belongs to the Special Issue Advances in Complex Networks and Their Applications, from COMPLEX NETWORKS 2025)
  • Article
  • Open Access
541 Views
16 Pages

20 July 2026

Product codes (PCs) are widely used in high-speed communication systems due to their attractive trade-off between error-correction performance and complexity. To further meet the rapidly growing demand for higher data rates, soft-aided hard-decision...

(This article belongs to the Section Information Theory, Probability and Statistics)
  • Article
  • Open Access
539 Views
31 Pages

20 July 2026

Cross-border multimodal transportation systems are essential for regional connectivity, yet their structural concentration, modal imbalance, community organization, and accessibility differentiation remain insufficiently understood from an entropy pe...

(This article belongs to the Special Issue Insight into Entropy)
  • Article
  • Open Access
733 Views
22 Pages

19 July 2026

Carbon market prices are jointly shaped by policy interventions, energy market fluctuations, and macroeconomic dynamics, and thus exhibit pronounced nonlinearity, non-stationarity, localized abrupt changes, and time-varying uncertainty. From an infor...

(This article belongs to the Special Issue Complexity Features and Blockchain Foundations of the Digital Instruments Market)
  • Feature Paper
  • Article
  • Open Access
1 Citations
548 Views
20 Pages

Exact Combinatorial Density of States for the Critical 1D Ising Model

  • Bastian Castorene,
  • Francisco J. Peña,
  • Martin HvE Groves and
  • Patricio Vargas

19 July 2026

This work presents an exact microcanonical combinatorial analysis of the one-dimensional antiferromagnetic Ising model. At the primary ground-state level crossing B/J=2, degeneracies follow the Fibonacci and Lucas sequences for open chains and period...

(This article belongs to the Special Issue Ising Model—100 Years Old and Still Attractive)
  • Article
  • Open Access
462 Views
19 Pages

19 July 2026

Rapid and accurate multi-class fault diagnosis is essential for high-end equipment because different fault categories require different maintenance responses. This study aims to develop a lightweight and discriminative diagnostic framework that can i...

(This article belongs to the Special Issue Failure Diagnosis of Complex Systems)
  • Article
  • Open Access
446 Views
50 Pages

Statistic Maximal Leakage

  • Shuaiqi Wang,
  • Zinan Lin and
  • Giulia Fanti

18 July 2026

We introduce a privacy measure called statistic maximal leakage that quantifies how much a privacy mechanism leaks about a specific secret random variable, relative to the adversary’s prior information about that secret, in the worst case over...

(This article belongs to the Special Issue Information Theory and Differential Privacy)
  • Article
  • Open Access
565 Views
31 Pages

17 July 2026

Complex multimodal optimization problems are widespread in machine learning, engineering design, and data science, where multiple local optima often trap conventional algorithms. Balancing global exploration and local exploitation remains a fundament...

(This article belongs to the Special Issue Entropy-Guided Evolutionary Intelligence: Information Dynamics for Adaptive and Explainable Machine Learning)
  • Article
  • Open Access
658 Views
23 Pages

17 July 2026

Quantitative phylogenetics in historical linguistics has relied almost entirely on lexical cognate data. This study asks a different question: how much genealogical signal can be recovered from structural features extracted from annotated corpora, an...

(This article belongs to the Section Multidisciplinary Applications)
  • Article
  • Open Access
440 Views
15 Pages

17 July 2026

Lei proposed an algorithm Algorithm A3 in 2023 to generate an exact discrete uniform distribution from an unknown biased Bernoulli source. The present paper does not claim a new extraction algorithm. Its contributions are analytical: first, we provid...

(This article belongs to the Section Information Theory, Probability and Statistics)
  • Article
  • Open Access
466 Views
23 Pages

17 July 2026

Future wireless networks require channel coding schemes that can provide high reliability, low latency, and strong adaptability under finite-blocklength and structurally heterogeneous transmission scenarios. Globally coupled low-density parity-check...

(This article belongs to the Special Issue Key Technologies Towards Future Wireless Networks)
  • Article
  • Open Access
1 Citations
428 Views
19 Pages

17 July 2026

In light of growing concerns about sustainable development and green innovation, the green market has progressively taken center stage in the financial markets. From the nonlinear information transmission angle, we look into the interconnectedness be...

(This article belongs to the Section Multidisciplinary Applications)
  • Article
  • Open Access
479 Views
38 Pages

17 July 2026

In 2000, Carver Mead introduced a time-symmetrical theory of energy exchange between two atoms, building on the Transactional Interpretation of Quantum Mechanics by John Cramer in 1986. In 2020, Cramer and Mead developed the theory further, proposing...

(This article belongs to the Special Issue Time in Quantum Mechanics)
  • Article
  • Open Access
581 Views
49 Pages

Time Series Correlations and Kolmogorov Complexity: A Hausdorff Dimension Perspective

  • Boumediene Hamzi,
  • Marianne Clausel,
  • Kamal Dingle,
  • Marcus Hutter and
  • Mohammed Terry Jack

16 July 2026

Spurious correlations between time series are a persistent problem: simple, low-complexity patterns are abundant, so unrelated series can easily exhibit high Pearson correlation. We argue that Kolmogorov complexity—a series’ resistance to...

(This article belongs to the Special Issue Kolmogorov Complexity and Applications—Dedicated to Professor Paul Vitanyi on the Occasion of His 80th Birthday)
  • Review
  • Open Access
1 Citations
1,052 Views
48 Pages

16 July 2026

Entropy regularization is a recurring mechanism in reinforcement learning (RL), but its meaning changes across algorithmic settings. In classical online RL, entropy encourages exploration and smooths policy improvement; in inverse RL and imitation le...

(This article belongs to the Section Entropy Reviews)
  • Article
  • Open Access
1 Citations
462 Views
24 Pages

16 July 2026

To effectively extract fault characteristics from complex vibration signals and improve the diagnostic performance of deep learning networks, this paper introduces a wind turbine blade fault diagnosis method that combines Multi-scale Enhanced Hierarc...

(This article belongs to the Special Issue Multivariate Entropy-Informed Fault Diagnosis and Structural Health Monitoring)
  • Article
  • Open Access
418 Views
32 Pages

From Global to Local: Semantic-Aware Instance-Wise Feature Selection

  • Zihan Wang,
  • Yue Zhang,
  • Hengpeng Xu,
  • Zhenglu Yang and
  • Jun Wang

16 July 2026

Feature selection is a promising dimension reduction technology that focuses on a reduced subspace by selecting excellent features. Most existing approaches tend to emphasize the discriminative ability of features based on either a global or a local...

  • Article
  • Open Access
923 Views
26 Pages

15 July 2026

This manuscript gives a solution to the black hole information paradox by bringing to the debate a fundamental aspect of information science: the process of measurement by a receiver. Bekenstein and Hawking established the foundations of black hole t...

(This article belongs to the Special Issue The Landauer Principle in Physics, Biophysics, Engineering and Computer Science: From Foundations of Thermodynamics to Computer Engineering)
  • Article
  • Open Access
904 Views
24 Pages

Modelling Cumulative Seismic Damage at the Urban Scale

  • Rosa Maria Sava,
  • Annalisa Greco,
  • Alessandro Pluchino and
  • Andrea Rapisarda

15 July 2026

The analysis of earthquake-induced damage scenarios at the urban scale is a fundamental tool for seismic risk assessment and mitigation and the management of urbanized areas exposed to seismic hazards. This paper presents a methodology for simulating...

  • Article
  • Open Access
535 Views
16 Pages

15 July 2026

Conflict management is crucial in information fusion. One of the efficient algorithms to address conflicting data fusion is discounting method. However, how to determine the discounting coefficient in conflict management remains an open issue. A heur...

(This article belongs to the Special Issue Entropy Method for Decision Making with Uncertainty, 2nd Edition)
  • Feature Paper
  • Article
  • Open Access
484 Views
25 Pages

15 July 2026

Quantum memories are a critical component of entanglement-based quantum networks, enabling the storage and synchronisation of quantum states across dynamic links. However, current quantum memories have significantly lower capacity than the rate at wh...

(This article belongs to the Special Issue Space Quantum Communication)
  • Feature Paper
  • Article
  • Open Access
1,195 Views
41 Pages

Detecting Unusual Trading Patterns on Cryptocurrency Exchanges by Means of Complexity Measures

  • Jakub Zwydak,
  • Marcin Wątorek,
  • Jarosław Kwapień and
  • Stanisław Drożdż

15 July 2026

Artificial transaction generation remains an important source of potential market manipulation on cryptocurrency exchanges, as it may distort reported liquidity and reduce market transparency. This study proposes a diagnostic framework for detecting...

(This article belongs to the Special Issue Complexity Features and Blockchain Foundations of the Digital Instruments Market)
  • Article
  • Open Access
734 Views
23 Pages

14 July 2026

Very-high-resolution (VHR) multispectral satellite imagery contains rich semantic information, yet its real-time transmission is constrained by limited satellite-to-ground bandwidth and dynamic channel impairments. Conventional communication schemes...

(This article belongs to the Special Issue AI for Wireless Communication Systems: From Semantic Communications to 6G)
  • Article
  • Open Access
561 Views
27 Pages

Quantum Cosmology in Krylov Space: Complexity and Entropy

  • Meysam Motaharfar,
  • Maxwell R. Siebersma and
  • Parampreet Singh

14 July 2026

We study the quantum dynamics in Krylov space of a spatially flat, homogeneous, and isotropic universe sourced with a massless scalar field within Wheeler–DeWitt (WDW) quantum cosmology and loop quantum cosmology (LQC) frameworks. The availabil...

(This article belongs to the Section Multidisciplinary Applications)
  • Article
  • Open Access
341 Views
11 Pages

Topological Complexity of the Length-Constrained Systems of Finite Symbols

  • Qingsong Wang,
  • Cailing Yao,
  • Jiaxing He and
  • Bingzhe Hou

14 July 2026

In this paper, we consider a class of constrained systems named n-tuple upper bound (m1,⋯,mn)-constrained systems (n-TUB systems briefly) for 2≤n<∞, which are subshifts of finite type. We determinate the topological entropies (Shann...

(This article belongs to the Section Complexity)
  • Article
  • Open Access
754 Views
30 Pages

14 July 2026

Image encryption schemes based on chaotic maps offer strong statistical properties but are vulnerable to quantum attacks, and their integration with post-quantum cryptography has not been sufficiently explored. This paper presents a post-quantum secu...

(This article belongs to the Section Multidisciplinary Applications)
  • Article
  • Open Access
481 Views
14 Pages

14 July 2026

We analyze the effect of microscopic heterogeneity on the Lorenz curve of macroscopic observables. The Lorenz curve of a response function, being a cumulative and bounded quantity; it is often a more stable function than the corresponding probability...

(This article belongs to the Special Issue Ising Model—100 Years Old and Still Attractive)
  • Feature Paper
  • Article
  • Open Access
537 Views
33 Pages

Polar Codes for Decomposed Multi-Input Multi-Output Gaussian Broadcast Channels

  • Muhammed Yusuf Şener,
  • Gerhard Kramer,
  • Shlomo Shamai (Shitz),
  • Ronald Böhnke and
  • Wen Xu

14 July 2026

Dirty paper coding (DPC) is applied to multi-input multi-output (MIMO) broadcast channels with additive Gaussian noise and one message per receiver. The method decomposes each receiver MIMO channel into parallel scalar channels and applies modulo ope...

(This article belongs to the Special Issue Foundations and Frontiers of Information Theory—Dedicated to Professor H. Vincent Poor on the Occasion of His 75th Birthday)
  • Article
  • Open Access
454 Views
24 Pages

14 July 2026

In the early fault stage of rolling bearings, the fault-induced impact signals in vibration data are often extremely weak and easily obscured by strong noise, making effective extraction and analysis challenging. To address this issue, this paper pro...

  • Article
  • Open Access
409 Views
30 Pages

13 July 2026

Categorisation is often treated as a form of compression: a high-dimensional stimulus space is reduced to a smaller set of behaviourally or cognitively useful classes. However, compression alone does not determine whether a category map is useful. Th...

(This article belongs to the Section Information Theory, Probability and Statistics)
  • Article
  • Open Access
2 Citations
495 Views
35 Pages

13 July 2026

With the widespread adoption of digital images in network transmission and storage, the demand for image privacy protection keeps rising. We propose a robust scheme combining a four-dimensional variable-order fractional hyperchaotic system (4D-VOFHS)...

(This article belongs to the Special Issue Image Encryption and Privacy Protection Based on Chaotic Systems—Third Edition)
  • Article
  • Open Access
1 Citations
410 Views
29 Pages

13 July 2026

This paper investigates statistical inference for the Shannon entropy of the Transmuted Weibull Distribution under progressively Type-II censored samples. The Transmuted Weibull Distribution is obtained by applying the quadratic rank transmutation ma...

  • Article
  • Open Access
623 Views
27 Pages

HH-MAPPO: A Hierarchical Reinforcement Learning Framework for Dynamic-Scale Target–Attacker–Defender Games

  • Junhui Huang,
  • Yan Guo,
  • Xiliang Chen,
  • Jianyu Wei and ,
  • Jiawei Yi,
  • Xinliang Chen and
  • Lifeng Chen
  • + 2 authors+ 0 author

13 July 2026

The Target–Attacker–Defender (TAD) pursuit–evasion game is a core challenge in multi-agent cooperative control, yet real-world settings involving dynamic team scaling and strict energy constraints remain largely unaddressed. When sc...

(This article belongs to the Section Multidisciplinary Applications)
  • Review
  • Open Access
843 Views
21 Pages

13 July 2026

The traditional paradigm of natural science treats the laws of nature as eternal and immutable. This review examines a powerful alternative tradition that views these laws as historically evolving and constructed entities, tracing this shift from anc...

(This article belongs to the Special Issue Symmetry and Its Applications in Complex Systems)
  • Article
  • Open Access
608 Views
40 Pages

12 July 2026

This paper investigates the stability of high-dimensional financial portfolios using concentration inequalities, information-theoretic measures, optimal transport metrics, and financial network analysis. Asset returns are generated under both multiva...

(This article belongs to the Section Information Theory, Probability and Statistics)
  • Article
  • Open Access
1 Citations
332 Views
20 Pages

12 July 2026

The onset of quantum behavior in gases is traditionally established through a criterion that is external to classical statistical mechanics. One introduces the thermal de Broglie wavelength and compares it with the mean intermolecular separation, con...

  • Article
  • Open Access
1 Citations
412 Views
20 Pages

12 July 2026

This paper investigates how quantum entanglement and heterogeneous expectations jointly affect the stability, complexity, and controllability of a Cournot triopoly with isoelastic demand. Based on the Li–Du–Massar quantization scheme, we...

(This article belongs to the Section Quantum Information)
  • Article
  • Open Access
552 Views
46 Pages

12 July 2026

Complex nonlinear dynamical systems, often associated with high-entropy time series, have been widely employed to describe and predict intricate dynamic phenomena in real-world systems. Motivated by the need to better understand such complex dynamics...

(This article belongs to the Special Issue Nonlinear Dynamics of Complex Systems)
  • Article
  • Open Access
541 Views
25 Pages

12 July 2026

Aiming at the problem that sparse channel estimation in underwater acoustic communication is susceptible to complex multipath propagation, non-Gaussian impulsive noise, and channel time variations, this paper proposes a bidirectional proportionate re...

(This article belongs to the Section Signal and Data Analysis)
  • Article
  • Open Access
392 Views
22 Pages

11 July 2026

In the context of global climate change and China’s “Dual Carbon” target, the misallocation of carbon emission reduction responsibilities and low regulatory efficiency urgently require analysis and resolution. Based on China’s...

(This article belongs to the Section Complexity)
  • Feature Paper
  • Article
  • Open Access
466 Views
23 Pages

Entropy, Inhibition and Memory in Balanced Spiking Reservoirs

  • Luigi Rosati,
  • Nicola Toschi and
  • Andrea Duggento

10 July 2026

Recurrent neural networks are studied along two largely parallel tracks: as machine-learning models evaluated by task performance and as computational-neuroscience models of cortical circuits evaluated by dynamical realism. Reservoir computing offers...

(This article belongs to the Special Issue Statistical and Physics-Based Interpretation of AI and Machine Learning Methods for Biomedical Data)
  • Article
  • Open Access
1 Citations
471 Views
24 Pages

10 July 2026

Long-tailed data are very common in industrial scenarios because equipment failures occur with a low probability, resulting in far fewer faulty samples than normal ones. However, when facing long-tailed data distributions, existing deep learning meth...

(This article belongs to the Special Issue Multivariate Entropy-Informed Fault Diagnosis and Structural Health Monitoring)

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Entropy - ISSN 1099-4300