EntropyPub Date : 2026-04-21DOI: 10.3390/e28040479
Michel Broniatowski, Emilie Miranda
{"title":"A Sequential Design for Extreme Quantile Estimation Under Binary Sampling.","authors":"Michel Broniatowski, Emilie Miranda","doi":"10.3390/e28040479","DOIUrl":"10.3390/e28040479","url":null,"abstract":"<p><p>We propose a sequential design method aiming at the estimation of an extreme quantile based on a sample of binary data corresponding to peaks over a given threshold. This study is motivated by an industrial challenge in material reliability and consists of estimating a failure quantile from trials whose outcomes are reduced to indicators of whether the specimen has failed at the tested stress levels. The proposed approach relies on a splitting strategy that decomposes the target extreme probability into a product of higher-order conditional probabilities, enabling a progressive exploration of the tail of the distribution through sampling under truncated laws. We consider GEV and Weibull models for the underlying distribution, and the sequential estimation of their parameters is carried out using an enhanced maximum likelihood procedure specifically adapted to binary data, addressing the substantial uncertainty inherent to such limited information.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13114713/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147812363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2026-04-21DOI: 10.3390/e28040478
Kun Hao, Meng Bi, Yuliang Ma
{"title":"VeriFed: Temporally Consistent Continuous Cross-Chain Data Federation.","authors":"Kun Hao, Meng Bi, Yuliang Ma","doi":"10.3390/e28040478","DOIUrl":"10.3390/e28040478","url":null,"abstract":"<p><p>Cross-chain analytics increasingly demand <i>continuous</i> joins across ledgers with asynchronous state evolution. Existing solutions, however, typically assume static snapshots or neglect temporal alignment, yielding semantically inconsistent results when epochs drift. This paper introduces VeriFed, a system for temporally consistent continuous cross-chain joins. We formalize the problem of snapshot-aligned continuous joins, design a Unified Adapter Layer (UAL) to align finalized snapshots across heterogeneous protocols, and develop <i>incremental verification</i> that composes per-chain proofs into a global summary via the Epoch Attestation Mesh (EAM) and the Delta-Linked Proof Forest (DLPF). To sustain high-throughput execution, VeriFed further adopts an incremental multi-objective optimizer that balances latency and monetary cost. Experiments on Ethereum transaction data with a simulated wide-area network (WAN) demonstrate that VeriFed achieves sub-second per-epoch latency (approx. 38 ms) and reduces verification overhead by orders of magnitude compared to state-of-the-art baselines, while effectively detecting tampering with zero false positives. These results confirm consistent efficiency and verifiability under continuous updates.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13114699/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147812085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2026-04-20DOI: 10.3390/e28040477
Megan Simons, Elshad Allahyarov, Jonathan Washburn
{"title":"A Discrete Informational Framework for Classical Gravity: Ledger Foundations and Galaxy Rotation Curve Constraints.","authors":"Megan Simons, Elshad Allahyarov, Jonathan Washburn","doi":"10.3390/e28040477","DOIUrl":"10.3390/e28040477","url":null,"abstract":"<p><p>The weak-field, quasi-static regime of gravity is commonly described by the Newton-Poisson equation as an effective response law. We construct this response within a cost-first discrete variational framework. The Recognition Composition Law (RCL) uniquely selects a reciprocal closure cost within the restricted quadratic symmetric composition class; together with the discrete ledger axioms AX1-AX5 (including conservation) and standard DEC refinement, the Newton-Poisson baseline is then recovered in the instantaneous-closure limit. Conditional on Assumption AS1 (scale-free latency) and Assumption AS2 (causal frequency-wavenumber ansatz), allowing finite equilibration introduces fractional memory into the response, yielding a scale-free modification of the source-potential relation characterized by a power-law kernel wker(k)=1+C(k0/k)α in Fourier space. The kernel exponent α=12(1-φ-1)≈0.191, where φ=(1+5)/2, is derived from self-similarity of the discrete ledger closure; the amplitude C=φ-2≈0.382 is identified as a hypothesis from a three-channel factorization argument. We evaluate this quasi-static kernel-motivated response against SPARC galaxy rotation curves under a strict global-only protocol (fixed M/L=1, no per-galaxy tuning, conservative σtot), using a controlled multiplicative surrogate for the full nonlocal disk operator implied by the kernel. In this deliberately over-constrained setting, the surrogate interface achieves median(χ2/N)=3.06 over 147 galaxies (2933 points), outperforming a strict global-only NFW benchmark and remaining less efficient than MOND under identical constraints. The analysis is restricted to the non-relativistic, quasi-static sector and should be read as a falsifier-oriented galactic-regime consistency check of the scaling window, not as a relativistic completion or a claim of Solar System viability without additional UV regularization/screening.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13115379/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147812120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2026-04-20DOI: 10.3390/e28040468
Yao Qu, Changjing Wang, Qi Tian
{"title":"Modeling and Dynamic Analysis of Trust Decay in Social Media Based on Triadic Closure Structure.","authors":"Yao Qu, Changjing Wang, Qi Tian","doi":"10.3390/e28040468","DOIUrl":"10.3390/e28040468","url":null,"abstract":"<p><p>Trust decay in social media is a serious threat to user experience and platform ecology. To solve this problem, this paper focuses on triadic closure in the infrastructure of social networks and explores its mechanism in trust decay prevention. Based on the systematic comparison of the ER random graph, the BA scale-free network, a forest fire model, and complete graph approaches, two core metrics, the trust decay risk index and trust resilience index, are proposed in this paper. Combined with structural indices such as the clustering coefficient, the average path length, and the triangular closure number and its growth rate, the quantitative relationship between network structure evolution and trust decay risk is established. It is found that the forest fire model exhibits optimal trust resilience in structure due to its power-law growth characteristics of high clustering, short path length and triangular closure; the dynamic mechanism of trust decay under different network growth modes is significantly different. The validity of the theoretical framework is further supported by the verification of Sina Weibo attention relationship network data. The analysis framework of network growth evolution based on fusion triangle closure and the risk and resilience indicators defined in this paper provides a computable theoretical tool for understanding and predicting trust evolution in social media from the perspective of network structure.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13114998/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147812347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2026-04-20DOI: 10.3390/e28040474
Juan José Seoane, Abdelilah Benali, Xavier Oriols
{"title":"A Simple Understanding of Quantum Electrodynamics Using Bohmian Trajectories: Detecting Non-Ontic Photons.","authors":"Juan José Seoane, Abdelilah Benali, Xavier Oriols","doi":"10.3390/e28040474","DOIUrl":"10.3390/e28040474","url":null,"abstract":"<p><p>The use of Bohmian mechanics as a practical tool for modeling non-relativistic quantum phenomena of matter provides clear evidence of its success, not only as a way to interpret the foundations of quantum mechanics, but also as a computational framework. In the literature, it is frequently argued that such a realistic view-based on deterministic trajectories-cannot account for phenomena involving the \"creation\" and \"annihilation\" of photons. In this paper, by revisiting and rehabilitating earlier proposals, we show how quantum optics can be modeled using Bohmian trajectories for electrons in physical space, together with well-defined electromagnetic fields evolving in time. By paying special attention to an experimental scenario demonstrating partition noise for photons, and to how the Born rule emerges in this context, the paper pursues two main goals. First, it validates the use of this simple Bohmian framework for pedagogical and computational purposes in understanding and visualizing quantum electrodynamics phenomena. Second, given that measurements are ultimately indicated on matter pointers, it clarifies what it means to measure photon or electromagnetic-field properties, even when they are considered non-ontic elements.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13114591/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147812379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2026-04-20DOI: 10.3390/e28040467
S I Kruglov
{"title":"The Rényi Entropy and Entropic Cosmology.","authors":"S I Kruglov","doi":"10.3390/e28040467","DOIUrl":"10.3390/e28040467","url":null,"abstract":"<p><p>Entropic cosmology with the Rényi entropy of the apparent horizon SR=(1/α)ln(1+αSBH), where SBH is the Bekenstein-Hawking entropy, is studied. By virtue of the thermodynamics-gravity correspondence, a model of dark energy is investigated. The generalized Friedmann equations for the Friedmann-Lemaître-Robertson-Walker spatially flat universe with barotropic matter fluid are obtained. We compute the dark energy density ρD, pressure pD, and the deceleration parameter <i>q</i> of the universe. At some model parameters, the normalized density parameter of the matter Ωm0≈0.315 and the deceleration parameter q0≈-0.535 for the current epoch, which are in the agreement with the Planck data, are found. Making use of the thermodynamics-gravity correspondence, we describe the late-time acceleration of the universe. The entropic cosmology considered here is equivalent to cosmology based on the teleparallel gravity with the definite function F(T). The Hubble parameters are in approximate agreement (within 5 percents) with the observational Hubble data for redshifts 0.07≤z≤1.75 at the entropy parameter α≈0.305GH02.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13115408/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147812668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fragmentation of Nuclear Remnants in Electron-Nucleus Collisions at High Energy as a Nonextensive Process.","authors":"Ting-Ting Duan, Sahanaa Büriechin, Hai-Ling Lao, Fu-Hu Liu, Khusniddin K Olimov","doi":"10.3390/e28040470","DOIUrl":"10.3390/e28040470","url":null,"abstract":"<p><p>Utilizing a partitioning method based on equal (or unequal) probabilities-without incorporating the alpha-cluster (<i>α</i>-cluster) model-allows for the derivation of diverse topological configurations of nuclear fragments resulting from fragmentation. Subsequently, we predict the multiplicity distribution of nuclear fragments for specific excited nuclei, such as Be*9, C*12, and O*16, which can be formed as nuclear remnants in electron-nucleus (eA) collisions at high energy. Based on the α-cluster model, an α-cluster structure may result in deviations in the multiplicity distributions of nuclear fragments with charge Z=2, compared to those predicted by the partitioning methods. Furthermore, in the framework of Tsallis statistics, the nonextensive generalized temperature, entropy index, and <i>q</i>-entropy are obtained from the multiplicity distribution of nuclear fragments with a given charge number. Our work shows that fragmentation of nuclear remnants in electron-nucleus collisions at high energy is a nonextensive process.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13114318/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147812685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2026-04-20DOI: 10.3390/e28040473
Salomé A Sepúlveda-Fontaine, José M Amigó
{"title":"An Entropy-Based Framework for Hybrid Coalitions in Game Theory-Part I: Human Arbitration.","authors":"Salomé A Sepúlveda-Fontaine, José M Amigó","doi":"10.3390/e28040473","DOIUrl":"10.3390/e28040473","url":null,"abstract":"<p><p>Classical Game Theory underpins much of AI and multi-agent research, but hybrid Human-AI systems require a framework in which execution authority can alternate within a digital environment. We introduce Neo-Game Theory, an extension of Classical Game Theory for hybrid Human-AI coalitions operating under Virtual Nature, the algorithmic analogue of classical (physical) Nature. The framework combines a lexicographic coalition utility with a delegation rule based on the Jensen-Shannon divergence between Human and AI policies. Two thresholds define agreement, contextual, and disagreement regions. In the contextual region, execution follows a scenario-specific rule. Apart from the theory, in this paper we develop the first regime, Human arbitration, in which the AI learns by observation and frequency matching while the Human retains final execution authority. We establish the axiomatic basis of the framework and characterize a frequency-convergence equilibrium, providing the foundation for later extensions and computational validation.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13114561/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147812484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2026-04-20DOI: 10.3390/e28040472
Daniel Chicharro
{"title":"Causally Informative Entropic Inequalities within Families of Distributions with Shared Marginals.","authors":"Daniel Chicharro","doi":"10.3390/e28040472","DOIUrl":"10.3390/e28040472","url":null,"abstract":"<p><p>The joint probability distribution of observable variables from a system is constrained by the underlying causal structure. In the presence of hidden variables, untestable independencies that involve hidden variables lead to testable causally-imposed inequality constraints for observable variables, whose violation can reject the compatibility of a causal structure with data. One type of causally informative inequalities is entropic inequalities, which appear in the space of entropic terms associated with the distribution of observable variables. We derive a new type of minimum information (minInf) entropic inequalities that substantially increases causal inference power. These new entropic inequalities appear when considering the constraints that the causal structure imposes on entropic terms determined by information minimization within families of distributions that preserve sets of marginals shared with the original distribution. We introduce a new family of minInf data processing inequalities and a procedure to recursively combine different types of data processing inequalities to create tighter testable entropic inequalities. We extensively illustrate the applicability of this procedure in the instrumental causal scenario, integrating the new inequalities with standard instrumental entropic inequalities constructed with multivariate instrumental sets. We also provide additional examples with other types of entropic inequalities, such as the Information Causality and Groups-Decomposition inequalities.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13114625/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147812531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
EntropyPub Date : 2026-04-20DOI: 10.3390/e28040475
Fei Wang, Lin Song, Pengfei Wang, Ping Deng, Tianwei Lan
{"title":"MFAFENet: A Multi-Sensor Collaborative and Multi-Scale Feature Information Adaptive Fusion Network for Spindle Rotational Error Classification in CNC Machine Tools.","authors":"Fei Wang, Lin Song, Pengfei Wang, Ping Deng, Tianwei Lan","doi":"10.3390/e28040475","DOIUrl":"10.3390/e28040475","url":null,"abstract":"<p><p>Accurate classification of spindle rotational errors is critical for ensuring machining precision and operational reliability of CNC machine tools. However, existing methods face challenges in extracting discriminative feature information from vibration signals due to small inter-class differences and complex electromechanical interference. This paper proposes a novel deep learning model, MFAFENet, based on multi-sensor collaboration and multi-scale feature information adaptive fusion. Vibration signals from three mounting positions are transformed into time-frequency information representations via Short-time Fourier Transform. The proposed network adaptively fuses multi-scale feature information from parallel branches with different kernel sizes through a branch attention mechanism. An efficient channel attention module is then incorporated to recalibrate channel-wise feature responses. The cross-entropy loss function is employed to optimize the network parameters during training. Experiments on a spindle reliability test bench demonstrate that MFAFENet achieves 93.37% average test accuracy, outperforming other comparative methods. Ablation and comparative studies confirm the effectiveness of each module and the clear advantage of adaptive fusion over fixed-weight multi-scale methods. Multi-sensor fusion further improves accuracy by 7.23% over the best single-sensor setup. The proposed method establishes an effective end-to-end mapping between vibration signals and rotational errors, providing a promising solution for high-precision spindle condition monitoring.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13114703/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147812342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}