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Entropy, Volume 28, Issue 5

2026 May - 99 articles

Cover Story: Quantum key distribution (QKD) promises unconditionally secure communication, yet practical devices remain vulnerable to side-channel attacks on both source and detection sides. While measurement-device-independent QKD removes detection vulnerabilities, source-side attacks persist. Here, we show that entanglement swapping fundamentally solves this problem, making QKD immune to external probing side channels. We conducted a field demonstration of this ES-QKD scheme using two independent entangled photon sources and the Ekert-91 protocol, achieving a Bell violation S = 2.659 ± 0.092 and a secret key rate of 0.0163 bit/s over a channel equivalent to 100 km of standard optical fiber. View this paper
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Articles (99)

  • Article
  • Open Access
616 Views
31 Pages

Information-Driven Rule Reduction in Belief Rule Bases for Complex System Modeling

  • Xingzhi Liu,
  • Haolan Huang,
  • Yingmei Li,
  • Zida Xia and
  • Shutong Zhao

21 May 2026

In the analysis of complex engineering systems, managing uncertainty and optimizing information processing structures are critical for reliable state prediction. The Belief Rule Base (BRB) provides a powerful machine learning approach for integrating...

  • Article
  • Open Access
895 Views
27 Pages

Causal Structure Learning Assumptions Shape Counterfactual Safety: Expert-Guided Constraints vs. Data-Driven DAGs with Probabilistic Logic Twin Networks

  • Héctor Avilés,
  • Ingridh Gracia,
  • Rafael Kiesel,
  • Verónica Rodríguez and ,
  • Rubén Machucho,
  • Alberto Reyes,
  • Marco Negrete,
  • Gabriel Ramírez,
  • Nicolás Luévano and
  • Felix Weitkämper
  • + 7 authors+ 2 authors

21 May 2026

We investigate how causal DAG learning algorithms and structural assumptions influence counterfactual decision safety. Four structure learning regimes are compared: expert-guided edge-constrained HC+BIC, unconstrained HC+BIC, MMPC+HC+BIC, and the PC-...

(This article belongs to the Special Issue Causal Graphical Models and Their Applications, 2nd Edition)
  • Article
  • Open Access
2 Citations
561 Views
33 Pages

21 May 2026

Digital images are easily transmitted in Internet, but there is also a great risk of information leakage. To meet the requirements of secure image transmission and real-time communication, an image encryption algorithm based on a novel chaotic map an...

(This article belongs to the Section Complexity)
  • Article
  • Open Access
1 Citations
505 Views
17 Pages

21 May 2026

This paper proposes a modeling framework for nonlinear degradation under constant-stress accelerated degradation testing (CSADT) to predict failure lifetime. The proposed employs a generalized Wiener process to characterize degradation, wherein the d...

  • Article
  • Open Access
422 Views
21 Pages

21 May 2026

Revealing correlations for styles in texts has been an interesting topic, providing an example of trans-disciplinarity between physics and linguistics. Typical cases can be seen for sound correlations in verses as well as for word correlations in pro...

(This article belongs to the Special Issue Entropy-Based Time Series Analysis: Theory and Applications)
  • Article
  • Open Access
615 Views
16 Pages

20 May 2026

Entropy generation analysis provides a thermodynamic framework for quantifying irreversibility in thermal systems. However, most existing second-law studies rely on simplified boundary conditions and do not consider fully coupled conjugate heat trans...

  • Article
  • Open Access
424 Views
21 Pages

19 May 2026

A remarkable feature of non-Hermitian topological systems with skin effects is that their spectra and eigenstates are strongly dependent on the choice of boundary conditions. Here, we investigate a system where the impurity couples to a nonreciprocal...

(This article belongs to the Section Statistical Physics)
  • Article
  • Open Access
476 Views
28 Pages

19 May 2026

This paper studies a dynamic price adjustment system in platform markets, where sellers continuously revise prices, and examines its implications for market stability. We develop a platform-led discrete-time Stackelberg game model to describe the evo...

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

19 May 2026

Understanding how information spreads in complex networks is essential for analyzing social influence, opinion formation, and the emergence of collective behavior. In many real-world systems, interactions are not instantaneous but involve delays due...

(This article belongs to the Section Complexity)
  • Article
  • Open Access
425 Views
27 Pages

19 May 2026

This paper introduces a geometric framework for analyzing finite-energy signals observed with additive noise by representing them as points on statistical manifolds equipped with the Fisher–Rao metric. Each signal is associated with a parameter...

(This article belongs to the Special Issue Methods from Differential Topology and Differential Geometry in Information Geometry)
  • Article
  • Open Access
1 Citations
400 Views
46 Pages

Research on Error Compensation Methods of Dynamic Gravity Measurement Based on Swarm Cooperation Evolution Strategy and Optimized LSTM

  • Xinyu Li,
  • Zhaofa Zhou,
  • Zhili Zhang,
  • Zhe Liang and ,
  • Zhenjun Chang and
  • Yiyi Li
  • + 1 author+ 0 author

19 May 2026

Dynamic gravity measurement, crucial for engineering application, suffers accuracy degradation due to errors induced by carrier maneuvers. To address the limitations of conventional swarm optimization algorithms in precision, stability, and generaliz...

(This article belongs to the Topic AI and Computational Methods for Modelling, Simulations and Optimizing of Advanced Systems: Innovations in Complexity, 2nd Edition)
  • Article
  • Open Access
1 Citations
508 Views
24 Pages

19 May 2026

Designing informative descriptors for time-varying complex networks is important for characterizing structural reconfiguration in evolving graph data. This paper introduces a thermodynamics-inspired framework for dynamic graph analysis, centered on S...

(This article belongs to the Special Issue Artificial Intelligence and Machine Learning for Biomedical Applications: Entropy and Information-Theoretic Perspectives)
  • Review
  • Open Access
608 Views
21 Pages

18 May 2026

This paper provides an overview of recent developments in quickest change detection (QCD) for high-dimensional multi-sensor systems, with an emphasis on settings involving structural constraints and limited sensing resources. Classical QCD methodolog...

(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
634 Views
17 Pages

18 May 2026

Accurate Remaining Useful Life (RUL) prediction is pivotal for the intelligent operation and maintenance of high-precision equipment. However, existing deep learning-based prognostic methods predominantly focus on point estimations and often overlook...

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

18 May 2026

In this paper we investigate the relationship between Shannon information entropy and symmetry in closed Euclidean polygons within the framework of the second law of information dynamics. Using Lagrange multiplier formalism, we derive the condition f...

(This article belongs to the Special Issue Modern Perspectives on the Second Law of Thermodynamics and Infodynamics)
  • Feature Paper
  • Article
  • Open Access
930 Views
22 Pages

Autoencoding-Assisted Quantum Cloning Machine

  • Qian Jun Beh,
  • Moritz Straeter,
  • Zeen Sun,
  • Leong Chuan Kwek and
  • Yuancheng Zhan

18 May 2026

Quantum cloning machines are essential in quantum information processing, finding applications in areas such as quantum communication and cryptographic protocols. However, the fidelity of universal quantum cloning machines diminishes as the dimension...

(This article belongs to the Section Quantum Information)
  • Article
  • Open Access
1 Citations
1,432 Views
19 Pages

A Comparative Analysis of Explainable AI (XAI) Techniques for Transparent and Reliable Image Classification

  • Sovon Chakraborty,
  • Shakib Mahmud Dipto,
  • Kevin R. Pilkiewicz,
  • Michael L. Mayo and
  • Pratip Rana

18 May 2026

Evaluating the trustworthiness of black-box machine learning models remains a significant methodological challenge. Their lack of transparency and interpretability limits applicability, because stakeholders often seek transparency before trusting the...

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

17 May 2026

Maritime emergency response requires broadband and reliable communications in sea areas where shore coverage is limited or emergency connectivity is temporarily unavailable, making rapid on-demand aerial networking essential. Unmanned aerial vehicles...

(This article belongs to the Special Issue Space-Air-Ground-Sea Integrated Communication Networks, Second Edition)
  • Article
  • Open Access
1,094 Views
36 Pages

17 May 2026

In recent years, cyberspace governance has become a critical component of national security strategies worldwide. Although social network platforms provide users with convenient channels for expression and information acquisition, unregulated, harmfu...

(This article belongs to the Special Issue Complexity of Social Networks)
  • Article
  • Open Access
5 Citations
494 Views
30 Pages

15 May 2026

The attribution of systemic financial stress to specific market sectors requires metrics that are faithful to the model’s computations, statistically consistent, and connected to a physically meaningful measure of directed information flow. Thi...

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

15 May 2026

We propose a new nonparametric estimator of the conditional mode in a regression framework where the covariates are functional in nature. The estimator is constructed through a quantile regression approach, which provides a robust alternative to clas...

  • Article
  • Open Access
1 Citations
1,051 Views
49 Pages

15 May 2026

This work proposes that fundamental physics remains unchanged, but its local classical representability is limited by the finite entropic capacity of causal horizons. Geometric entanglement entropy is treated as a thermodynamic potential, and horizon...

(This article belongs to the Section Thermodynamics)
  • Article
  • Open Access
708 Views
25 Pages

On Intention and Fluctuations in the Coordination Dynamics of Animate Movement

  • Amaury Dechaux,
  • Aliza T. Sloan and
  • J. A. Scott Kelso

15 May 2026

Many of life’s biggest dilemmas can be summed up as a tension between holding on and letting go. The very language evokes a notion of intentionality which, for the most part, has evaded scientific understanding. How might we even get a window i...

  • Feature Paper
  • Article
  • Open Access
466 Views
12 Pages

15 May 2026

A quantum model describing ion channels from an information-theoretic perspective is considered. The information χ-capacity of an ion channel, treated as an information channel whose properties are modified by continuous quantum measurements, is...

(This article belongs to the Special Issue Mathematical Modeling for Ion Channels)
  • Feature Paper
  • Article
  • Open Access
923 Views
16 Pages

14 May 2026

Classical Algorithmic Information Theory (AIT) provides a rigorous foundation for information-based similarity measurement, but classical formulations and their compression-based approximations largely operate at the syntactic level, making them sens...

(This article belongs to the Special Issue Kolmogorov Complexity and Applications—Dedicated to Professor Paul Vitanyi on the Occasion of His 80th Birthday)
  • Article
  • Open Access
550 Views
10 Pages

14 May 2026

Bayesian inference is predominantly formulated in a continuous framework, in which posterior beliefs are represented by smooth probability densities. However, an alternative discrete representation—already implicit in Bayes’s original con...

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

14 May 2026

The overall rate of a heterogeneous catalytic process may be limited by the rate of a chemical transformation on the catalyst surface, reactant transport to either external or internal catalyst surface, or by the interplay between these factors. In t...

(This article belongs to the Special Issue Kinetic Analysis and Engineering of (Bio)chemical Reactions—in Honor of the 85th Birthday of Professor Gregory Yablonsky)
  • Feature Paper
  • Article
  • Open Access
1,041 Views
31 Pages

13 May 2026

Real-world autonomous agents learn under nonstationarity, safety constraints, and finite energetic budgets. We develop a framework for perennial learning—agents that continuously refine their models while provably controlling the cost of forget...

(This article belongs to the Special Issue Kolmogorov Complexity and Applications—Dedicated to Professor Paul Vitanyi on the Occasion of His 80th Birthday)
  • Article
  • Open Access
847 Views
22 Pages

13 May 2026

Quantum machine learning integrates quantum computing with classical machine learning techniques to enhance computational power and efficiency. A major challenge in quantum machine learning is developing robust quantum classifiers capable of accurate...

(This article belongs to the Special Issue Quantum Algorithms and Quantum Machine Learning)
  • Article
  • Open Access
410 Views
24 Pages

12 May 2026

Accurately determining the parameters of an unmodeled spacecraft is crucial. Filtering methods that are resilient to uncertainty, employing dual quaternion frameworks to ascertain orientation and position, introduce a design for an extended Kalman fi...

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

Wavelet-Decoupled Spatiotemporal Network for Stock Return Prediction

  • Lei Liao,
  • Chao Wang,
  • Jun Wang,
  • Yinchao Liao and
  • Yanjie Lai

12 May 2026

Stock price prediction is a challenging problem in quantitative investment, as financial markets generate complex, noisy, and dynamic time series containing heterogeneous signals. Short-term fluctuations usually exhibit greater uncertainty and strong...

(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)
  • Article
  • Open Access
494 Views
25 Pages

11 May 2026

We consider a Markov chain that can be termed a discrete version of Blackwell’s example from 1958. It is constructed with the aid of a sequence of independent Markov chains with two states. It turns out its stationary distribution π and tran...

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

11 May 2026

The standard Landauer bound W≥kBTln2 sets the fundamental thermodynamic cost for information erasure under ideal conditions: weak system–bath coupling, quasistatic operation, and equilibrium reservoirs. However, realistic quantum error corre...

(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
416 Views
23 Pages

11 May 2026

People’s willingness to include others and their level of suspicion of those perceived to not belong are constrained by political affiliation and adherence to ideologies such as neoliberalism, Islamophobia, and ethnocentrism. In an era of heigh...

(This article belongs to the Section Multidisciplinary Applications)
  • Article
  • Open Access
1,066 Views
36 Pages

11 May 2026

We propose a microphysical completion for the scalar sector of dilatonic gravity by identifying the dilaton with the coarse-grained stiffness mode of a constrained complex tension field defined on a discrete relational network. Under a controlled ord...

(This article belongs to the Special Issue Modified Gravity: From Black Hole Entropy to Modern Cosmology)
  • Article
  • Open Access
433 Views
63 Pages

11 May 2026

This paper studies transfer learning for ridge-regularized robust linear regression in the moderate–dimensional regime, where the number of predictors is of the same order as the sample size and the regression coefficients are not assumed to be...

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

11 May 2026

Deploying neural networks on encrypted data requires efficient evaluation of nonlinear activations, especially the ReLU function, without decryption. While the CKKS homomorphic encryption scheme supports packed arithmetic over approximate numbers eff...

(This article belongs to the Special Issue Advancing Privacy-Preserving Federated Learning: Innovative Frameworks and Protocols)
  • Article
  • Open Access
508 Views
20 Pages

10 May 2026

In realistic social networks, individuals are influenced not only by current interactions, but also by recent historical opinions, prior experience, and external guidance. However, historical dependence and its decaying effect remain insufficiently s...

  • Article
  • Open Access
525 Views
14 Pages

10 May 2026

Quantum secret sharing (QSS) has been previously demonstrated with conceivability in optical-fiber channels. However, extending this framework to the microwave frequency band presents challenges in achieving secure quantum communications over turbule...

(This article belongs to the Topic Quantum Systems and Their Applications)
  • Article
  • Open Access
2,253 Views
27 Pages

9 May 2026

Brent crude oil prices are strategically important due to their sensitivity to geopolitical developments, financial market stress, and global monetary conditions. This study examines whether strategic risk indicators improve the forecasting performan...

(This article belongs to the Section Multidisciplinary Applications)
  • Feature Paper
  • Article
  • Open Access
594 Views
9 Pages

9 May 2026

Feedback delays and the coexistence of multiple timescales are central features of complex dynamical systems, ranging from neural networks and ecosystems to electronic and optical devices. Interactions between fast and slow dynamics can give rise to...

(This article belongs to the Special Issue Entropy-Based Time Series Analysis: Theory and Applications)
  • Article
  • Open Access
582 Views
40 Pages

9 May 2026

Mapping directed spillover pathways in urban housing prices is essential for monitoring the contagion of housing prices across cities. However, existing studies typically rely on either spatial gravity models or time-series models in isolation to ana...

(This article belongs to the Special Issue Analysis of the Structural Characteristics of Complex Networks Based on Entropy Measurement)
  • Article
  • Open Access
517 Views
27 Pages

8 May 2026

We study binary hypothesis testing for i.i.d. observations under a multiplicative context weight. For the optimal weighted total loss, defined as the sum of weighted type-I and type-II losses, we prove the logarithmic asymptotic Ln∗=exp{&minus...

(This article belongs to the Section Information Theory, Probability and Statistics)
  • Article
  • Open Access
6 Citations
578 Views
21 Pages

3D-TCM-Driven Bit-Level Image Encryption via S-Box Feedback Algorithm

  • Jie Zhang,
  • Wenjie Zhou,
  • Mingxu Wang and
  • Yiting Lin

8 May 2026

Most existing low-dimensional chaotic maps suffer from a limited dynamical complexity and dynamic degradation, which restrict their effectiveness in image encryption. To address this issue, a novel three-dimensional chaotic map (3D-TCM) was construct...

(This article belongs to the Special Issue Cutting-Edge Research in Nonlinear Dynamics, Memristive Devices, and Secure Image Processing)
  • Feature Paper
  • Article
  • Open Access
1,051 Views
39 Pages

It Is What It Isn’t: Introducing a Constraint-Based Approach to Structure Learning

  • Christoffer Lundbak Olesen,
  • Nace Mikuš,
  • Mads Hansen,
  • Nicolas Legrand and ,
  • Peter Thestrup Waade and
  • Christoph Mathys
  • + 1 author+ 0 author

7 May 2026

Biological cognition depends on learning-structured representations in ambiguous environments. Computational models of structure learning typically frame this as an inference problem, but often overlook the temporally extended dynamics that shape lea...

(This article belongs to the Special Issue Information Processing in Complex Biological Systems)
  • Article
  • Open Access
789 Views
15 Pages

7 May 2026

Accurate matching between molecular structures and NMR spectra is an important task in automated structure elucidation. However, existing methods still face difficulties in jointly modeling multi-scale molecular topology and effectively exploiting th...

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

7 May 2026

Health-state assessment is a critical component of prognostics and health management (PHM) for complex equipment. Previous studies on assessing the health state of complex equipment have overlooked the statistical dependence arising from causal coupl...

(This article belongs to the Special Issue Causal Representation Learning with Its Applications)
  • Article
  • Open Access
529 Views
12 Pages

7 May 2026

This paper presents an optimal L2-induced control problem for systems with multiple sector-bounded nonlinearities. Sufficient boundedness conditions for the L2-induced norm are derived in terms of a specific system of linear matrix inequalities (LMIs...

(This article belongs to the Special Issue Information Theory in Control Systems, 3rd Edition)
  • Article
  • Open Access
3 Citations
706 Views
29 Pages

7 May 2026

With the rapid advancement of information technology, the secure transmission and storage of digital images have garnered increasing attention. To safeguard image information from theft and enhance security during network transmission, a novel image...

(This article belongs to the Section Complexity)
  • Article
  • Open Access
509 Views
18 Pages

7 May 2026

We introduce a quantum multiplexer (GHZ MUX) architecture that enables deterministic routing of an unknown qubit from a single sender to one of 2n receivers using only local tripartite Greenberger–Horne–Zeilinger (GHZ) states arranged in...

(This article belongs to the Section Quantum Information)

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Entropy - ISSN 1099-4300