Entropy最新文献

{"title":"Fractals, Wealth Distributions, and Non-Euclidean Geometry: Quadrant Lorenz Curves.","authors":"Iddo Eliazar","doi":"10.3390/e28101085","DOIUrl":"https://doi.org/10.3390/e28101085","url":null,"abstract":"<p><p>Lorenz curves are a socioeconomic method of coding the statistics of positive-valued random variables. Standing at the confluence of fractals, wealth distributions, and non-Euclidean geometry, this paper presents quadrant Lorenz curves (QLCs): Lorenz curves whose shapes are that of the symmetric quarters of the <i>p</i>-norm unit circle. On the one hand, QLCs have a single parameter, and a clear geometric meaning. On the other hand, a comprehensive exploration establishes that QLCs display an assortment of socioeconomic and statistical behaviors. (1) They span a continuum of socioeconomic states ranging from perfect equality to perfect inequality, with three phase transitions along the continuum. (2) They display local rich fractality, local poor fractality, and double-Pareto tails. (3) They have inherent socioeconomic and statistical symmetries. The exploration includes a detailed socioeconomic-inequality analysis that illuminates QLCs from multiple inequality-indices 'angles'. In a nutshell: QLCs manifest a novel class of 'fractal' statistical distributions, and the QLC features are unmatched by those of any other such class.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bridging Machine Learning and Algorithmic Information Theory, Part VII: Algorithmic Information Kernels and Kernel Discrepancies on Countable Spaces.","authors":"Boumediene Hamzi, Marcus Hutter, Houman Owhadi","doi":"10.3390/e28101084","DOIUrl":"https://doi.org/10.3390/e28101084","url":null,"abstract":"<p><p>Compression-based dissimilarities such as the normalized compression distance are widely used, but direct exponentiation need not produce a positive semidefinite kernel. We develop a systematic interface between prefix algorithmic information theory and three kernel discrepancy methods on finite or countable spaces: maximum mean discrepancy (MMD), the Hilbert-Schmidt independence criterion (HSIC), and a Markov-operator kernel Stein discrepancy (KSD). Explicit feature realizations guarantee positive semidefiniteness for distance-to-kernel embeddings and for an ideal Solomonoff feature-mixture kernel satisfying kSol,U(x,y)≍U2-KU(⟨x,y⟩). Zero-mass signed measures give the exact characteristicity criterion, and whether the ideal Solomonoff kernel meets that criterion turns out to depend on the universal machine: two universal prefix machines are exhibited, one whose kernel is not characteristic on a two-point set and one whose kernel separates all finite-total-variation signed measures on the countable string space. In the resulting RKHS geometry, the MMD compares compressibility profiles, the HSIC is product-kernel MMD from the joint law to the product of its marginals, and KSDTP,k(Q)=MMDk(QTP,Q) for a target-stationary Markov kernel TP. Expected algorithmic mutual information is connected to the HSIC only through explicit source-description, mutual-information, support, and kernel conditions. Ideal AIT objects, computable feature surrogates, and finite-sample errors are separated explicitly. Reproducible synthetic experiments examine the identities, landmark approximation, and selected testing alternatives at the computable and empirical layers. They provide no evidence about ideal AIT quantities or general superiority over baselines. An algebraic example also shows that a characteristic finite-support kernel can give a constant permutation statistic: identification alone does not guarantee test power.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Key Node Ranking Method in Complex Networks by Integrating Semi-Local and Global Influence.","authors":"Xiaohu Chen, Xiaoyang Liu, Jiaojiao Jiang, Chao Liu, Xin Wang","doi":"10.3390/e28101077","DOIUrl":"https://doi.org/10.3390/e28101077","url":null,"abstract":"<p><p>The existing key node identification methods in complex networks rely on local topological information or global structural features, which are difficult to fully integrate multi-order local structural information and global propagation characteristics, resulting in the limitation of the accuracy and discrimination ability of node influence evaluation. In this paper, a key node ranking method combining semi-local and global influence, named SGIR, is proposed. Firstly, in the semi-local influence calculation stage, the second-order neighborhood, the third-order neighborhood, and the triangular closed structure of the node are used to construct the structural correlation matrix, and the structural energy migration mechanism is combined to quantify the local structural influence of the node, so as to enhance the expression ability of the semi-local structural features of the node. Secondly, in the global influence calculation stage, based on K-shell decomposition, a distance attenuation mechanism is introduced to weighted aggregate the influence of core nodes within the limited propagation range, and an adaptive propagation radius is designed by combining the average shortest path length of the network to effectively describe the global propagation ability of nodes. The semi-local influence and the global influence are fused to obtain the comprehensive influence ranking of nodes. Finally, comparative experiments are carried out on nine real complex networks from different fields such as communication, PowerGrid, and biological and social networks. The experimental results show that the proposed SGIR method achieves the best Kendall's τb on most data sets, and produces a highly discriminative ranking, which verifies the rationality, effectiveness, and stability of the proposed method and provides an effective solution for the identification of critical nodes in complex networks that takes into account both semi-local structural information and global propagation ability.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite-Bandwidth Protection of a Three-Level Quantum Heat Engine Against Parasitic Heat Leaks.","authors":"Gilberto Aparecido Prataviera, Marcos César de Oliveira","doi":"10.3390/e28101081","DOIUrl":"https://doi.org/10.3390/e28101081","url":null,"abstract":"<p><p>Finite-bandwidth reservoir engineering can suppress unwanted transitions in a quantum thermal machine, but a physical filter also introduces a finite response time. We study this competition in a continuous three-level heat engine whose hot environment couples parasitically to the cold transition. The corresponding three-state rate network is solved exactly, showing that the parasitic transition produces a hot-to-cold thermodynamic short circuit and yielding a closed threshold for the loss of positive-power operation. We then retain a damped auxiliary mode explicitly as a physical spectral filter. Its Lorentzian response suppresses the detuned parasitic transition, whereas excessive narrowing limits the useful energy throughput. Independent local-GKSL and nonsecular Bloch-Redfield calculations both recover the no-leak Markovian engine in the weak-coupling limit and predict a finite maximum-power bandwidth, although its precise location is model dependent. A frequency-resolved Lorentzian-rate reduction, by contrast, has no interior optimum. The resulting design principle is that spectral selectivity can protect the useful thermodynamic cycle, but a real filter cannot be narrowed without a dynamical throughput cost.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental Demonstration of Correlation-Assisted Energy Extraction Gain.","authors":"Alexander Stahl, Michael Kewming, John Goold, Janine Hilder, Ulrich Georg Poschinger, Ferdinand Schmidt-Kaler","doi":"10.3390/e28101079","DOIUrl":"https://doi.org/10.3390/e28101079","url":null,"abstract":"<p><p>Within the framework of microscopic thermodynamics, correlations can play a crucial role in energy extraction. We experimentally investigated the link between information encoded in tunable correlations and its utility for feedback-assisted energy transfer. We realized an agent-demon protocol involving two trapped-ion qubits and show that an appropriate feedback policy increases the average energy stored in the demon qubit by capitalizing on correlations between the constituents. For the chosen family of nearly pure resource states, we quantify both the concurrence and the feedback-assisted energy gain and observe the predicted relation between them. We also show theoretically that the same fixed protocol yields the same gain after complete dephasing in the local energy basis. The experiment establishes a concurrence-gain relation within the investigated pure-state family.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Coherence-Dissipation Framework for Brain Dynamics and Consciousness.","authors":"Ahmed Farag Ali, Nader Inan, Ruben Laukkonen, Pavlo Mikheenko","doi":"10.3390/e28101074","DOIUrl":"https://doi.org/10.3390/e28101074","url":null,"abstract":"<p><p>We develop a theoretical proposal linking vacuum stability and brain dynamics through superconductivity-inspired coherence, symmetry reduction, and the thermodynamic stabilization of low-entropy regimes. We take an unbroken SU(3) structure as a candidate stable residue of the low-temperature vacuum. At the neural level, we formulate a coarse-grained analog in which a two-fluid model with dissipative and coherence-supporting components describes brain dynamics. Specifically, the coherence-supporting component is proposed as a possible basis for the efficient binding and integration required to sustain a stable, unified conscious state. The proposal offers a common geometric language for relating physics and neuroscience with falsifiable signatures in coherence and state-dependent transitions. The main technical contribution is a computational algebraic model of conscious-state dynamics, where neural data are mapped to reconstructed state trajectories. Effective generators are inferred from those trajectories, and the two-fluid split is tested as a Cartan-root decomposition of su(3), with a rank-two commuting sector for coherence-preserving balance and six root directions for state transitions. This structure can be tested on neural data and contrasted with alternative dynamical models.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Arrival-Time Distributions as a Probe of the Preferred Foliation in Relativistic Bohmian Mechanics.","authors":"Arnaud Amblard, Aurélien Drezet","doi":"10.3390/e28101075","DOIUrl":"https://doi.org/10.3390/e28101075","url":null,"abstract":"<p><p>Relativistic extensions of de Broglie-Bohm theory postulate a preferred foliation of spacetime, an additional structure essential for defining simultaneous configurations on Minkowski spacetime but conventionally believed to be empirically undetectable at quantum equilibrium. In this paper, we outline an experimental protocol for empirically detecting the preferred foliation, which is assumed to be flat for simplicity. Building on the arrival-time distributions for spin-1/2 particles predicted by Das and Dürr, we show that, in an Einstein-Podolsky-Rosen-Bohm-type experiment with spacelike-separated spin and arrival-time measurements, the observed arrival-time statistics will depend crucially on the temporal order of these measurements relative to the preferred foliation of spacetime. This dependence offers a potential experimental signature of the preferred foliation postulated by relativistic Bohmian models. Moreover, it implies the possibility of superluminal signaling.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sample-Conditional Mixtures of Entropy Estimators for Short Sequences Under a Uniform Marginal Null.","authors":"Guillermo Sosa-Gómez","doi":"10.3390/e28101073","DOIUrl":"https://doi.org/10.3390/e28101073","url":null,"abstract":"&lt;p&gt;&lt;p&gt;Entropy estimation from short samples recurs in symmetric cryptography, where the reference distribution is uniform by design and no single estimator in the considered classical comparison set minimizes mean squared error (MSE) across the full range of ratios n/k. We introduce the adaptive sample-conditional entropy diagnostic (ASED), in which a compact network trained offline maps a frequency-of-frequencies descriptor of the sample to convex mixture weights over six classical estimators, at a cost of O(n+k). We prove an oracle inequality bounding the excess risk of such a mixture by the L1 error of its weights and fixed-alphabet consistency for every simplex-valued weighting rule, independently of the distribution used to train the weights. Under the uniform-null protocol, ASED attains an integrated MSE of 1.7×10-3 for bytes, compared with 3.8×10-2 for James-Stein shrinkage, a reduction that depends materially on the aggregation scheme: 95.4% for summed or averaged MSE across sample sizes versus 24% for the mean of per-size ratios. Both figures are reported together throughout, and neither is presented as the headline; the entire advantage is confined to the undersampled regime n&lt;k, the two estimators being indistinguishable for n≥k. A locked train/validate/test evaluation with an independently written implementation reproduces the reduction at 95.1%. Because a constant output achieves zero error by construction here, we add further checks: in a post hoc analysis, ASED is non-inferior to SHR in detection power at a 0.02 margin, both pointwise and simultaneously, whereas a constant control has none, and the advantage persists on held-out configurations. The 0.02 margin was selected after inspecting the power estimates, and at n=8 and n=16, it is smaller than the variation induced by tie handling at the empirical critical value, so the non-inferiority conclusion is confirmatory only for n≥32. At n≤16, the two statistics have identical null distributions up to monotone relabeling, and no test of size 0.05 exists, so no power difference is identifiable in either direction, and the comparison is withdrawn there. For strongly non-uniform sources, the ordering reverses, and NSB dominates, delimiting ASED as a uniformity diagnostic rather than a general-purpose entropy estimator. The design choices behind ASED, the feature map, architecture, and loss weighting were made while observing results on this same evaluation protocol, so no independent model-selection split separates development from the assessment reported here. That pipeline is accordingly designated exploratory, and the locked evaluation is confirmatory. The contribution is stated as sample-conditional convex aggregation of classical estimators rather than as the particular network realizing it: a five-feature variant and a gradient-boosted surrogate perform comparably, with no paired interval separating the three. Claims are restricted to short i.i.d. samples and marginal Shannon-entr","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction: de Forges de Parny et al. Towards a Global Scale Quantum Information Network: A Study Applied to Satellite-Enabled Distributed Quantum Computing. <i>Entropy</i> 2025, <i>27</i>, 1166.","authors":"Laurent de Forges de Parny, Luca Paccard, Mathieu Bertrand, Luca Lazzarini, Valentin Leloup, Raphael Aymeric, Agathe Blaise, Stéphanie Molin, Pierre Besancenot, Cyrille Laborde, Mathias van den Bossche","doi":"10.3390/e28101072","DOIUrl":"https://doi.org/10.3390/e28101072","url":null,"abstract":"<p><p><b>Text Correction</b> [...].</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Joint Trust-Aware Topology Adaptation and Resource-Constrained Patching for Malware Containment in the Social Internet of Things.","authors":"Xuejin Zhu, Shenyang Li","doi":"10.3390/e28101078","DOIUrl":"https://doi.org/10.3390/e28101078","url":null,"abstract":"<p><p>Social Internet of Things (SIoT) relationships enable service discovery and create pathways for malware propagation. We develop a heterogeneous susceptible-exposed-infected-recovered model coupling resource-constrained patching with reversible, trust-aware relationship suppression. A controlled next-generation operator yields a reproduction threshold, local stability, spectral monotonicity, and a uniform eradication condition. A finite-horizon security-service objective and its necessary conditions motivate joint adaptive topology and patching (JATP), a feasible sampled-data feedback heuristic combining prevalence, structural influence, trust evidence, and service importance. Under reference capacities, JATP reduces peak infection and cumulative burden by 49.43% and 38.97% relative to risk-only patching while retaining 0.8184 of weighted relationship intensity. Under a common expenditure ceiling, its objective is 59.56% above the best feasible offline nonlinear-programming value found. Explicit-network tests support aggregation under moderate heterogeneity and identify larger prediction errors under strong degree variation and susceptible-entry churn. Trust-related gains depend on alignment with model-defined propagation risk; field calibration remains open. These results characterize the operating scope of a feedback policy that coordinates two defense channels under hard resource limits. The framework links epidemic thresholds, intervention allocation, and service preservation to support the design of resource-limited SIoT containment.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 10","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149264427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}