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Entropy

Entropy is an international and interdisciplinary peer-reviewed open access journal of entropy and information studies, published monthly online by MDPI. The International Society for the Study of Information (IS4SI) and Spanish Society of Biomedical Engineering (SEIB) are affiliated with Entropy and their members receive a discount on the article processing charge.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High Visibility: indexed within Scopus, SCIE (Web of Science), Inspec, PubMed, PMC, Astrophysics Data System, and other databases.
Journal Rank: JCR - Q2 (Physics, Multidisciplinary) / CiteScore - Q1 (Mathematical Physics)
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 22.3 days after submission; acceptance to publication is undertaken in 2.7 days (median values for papers published in this journal in the second half of 2024).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Testimonials: See what our editors and authors say about Entropy.
Companion journals for Entropy include: Foundations, Thermo and Complexities.

Impact Factor: 2.1 (2023); 5-Year Impact Factor: 2.2 (2023)

Imprint Information Journal Flyer Open Access ISSN: 1099-4300

Latest Articles

69 pages, 1603 KiB

Open AccessArticle

Intrinsic and Measured Information in Separable Quantum Processes

by David Gier and James P. Crutchfield

Entropy 2025, 27(6), 599; https://doi.org/10.3390/e27060599 - 3 Jun 2025

Stationary quantum information sources emit sequences of correlated qudits—that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a classical stochastic process. We introduce quantum-information-theoretic properties for separable qudit sequences that [...] Read more.

Stationary quantum information sources emit sequences of correlated qudits—that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a classical stochastic process. We introduce quantum-information-theoretic properties for separable qudit sequences that serve as bounds on the classical information properties of subsequent measured processes. For sources driven by hidden Markov dynamics, we describe how an observer can temporarily or permanently synchronize to the source’s internal state using specific positive operator-valued measures or adaptive measurement protocols. We introduce a method for approximating an information source with an independent and identically distributed, Markov, or larger memory model through tomographic reconstruction. We identify broad classes of separable processes based on their quantum information properties and the complexity of measurements required to synchronize to and accurately reconstruct them. Full article

(This article belongs to the Special Issue Quantum Probability and Randomness V)

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14 pages, 470 KiB

Open AccessReview

Permutation Entropy and Its Niche in Hydrology: A Review

by Dragutin T. Mihailović

Entropy 2025, 27(6), 598; https://doi.org/10.3390/e27060598 - 3 Jun 2025

One effective method for analyzing complexity involves applying information measures to time series derived from observational data. Permutation entropy (PE) is one such measure designed to quantify the degree of disorder or complexity within a time series by examining the order relations among [...] Read more.

One effective method for analyzing complexity involves applying information measures to time series derived from observational data. Permutation entropy (PE) is one such measure designed to quantify the degree of disorder or complexity within a time series by examining the order relations among its values. PE is distinguished by its simplicity, robustness, and exceptionally low computational cost, making it a benchmark tool for complexity analysis. This text reviews the advantages and limitations of PE while exploring its diverse applications in hydrology from 2002 to 2025. Specifically, it categorizes the uses of PE across various subfields, including runoff prediction, streamflow analysis, water level forecasting, assessment of hydrological changes, and evaluating the impact of infrastructure on hydrological systems. By leveraging PE’s ability to capture the intricate dynamics of hydrological processes, researchers can enhance predictive models and improve our understanding of water-related phenomena. Full article

(This article belongs to the Special Issue Ordinal Patterns-Based Tools and Their Applications)

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20 pages, 71722 KiB

Open AccessArticle

Dynamic-Step-Size Regulation in Pulse-Coupled Neural Networks

by Jiayi Geng, Fanqing Ji, Shouliang Li, Yulin Shen and Zhen Yang

Entropy 2025, 27(6), 597; https://doi.org/10.3390/e27060597 - 3 Jun 2025

Pulse-coupled neural networks (PCNNs) are capable of segmenting digital images in a multistage unsupervised fashion; however, optimal output selection remains challenging. To address the above problem, this paper emphasizes the role of the step size, which influences the decreasing speed of the membrane [...] Read more.

Pulse-coupled neural networks (PCNNs) are capable of segmenting digital images in a multistage unsupervised fashion; however, optimal output selection remains challenging. To address the above problem, this paper emphasizes the role of the step size, which influences the decreasing speed of the membrane potential and the dynamic threshold profoundly. A dynamic-step-size mechanism is proposed, utilizing trigonometric functions to adaptively control segmentation granularity, along with the supervised optimization of a single parameter

ϕ

via intersection over union (IoU) maximization, reducing tuning complexity. Thus, the number of groups of image segmentation becomes controllable and the model itself becomes more adaptive than ever for various scenarios. Experimental results further demonstrate the enhanced robustness under noise (92.1% Dice at

σ = 0.2

), outperforming SPCNN and PCNN with IoU = 0.8863, Dice = 0.901, and 0.8684 s/image. Full article

(This article belongs to the Section Signal and Data Analysis)

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13 pages, 332 KiB

Open AccessArticle

Phase Coordinate Uncomputation in Quantum Recursive Fourier Sampling

by Christoffer Hindlycke, Niklas Johansson and Jan-Åke Larsson

Entropy 2025, 27(6), 596; https://doi.org/10.3390/e27060596 - 2 Jun 2025

Recursive Fourier Sampling (RFS) was one of the earliest problems to demonstrate a quantum advantage, and is known to lie outside the Merlin–Arthur complexity class. This work contains a new description of quantum algorithms in phase space terminology, demonstrating its use in RFS, [...] Read more.

Recursive Fourier Sampling (RFS) was one of the earliest problems to demonstrate a quantum advantage, and is known to lie outside the Merlin–Arthur complexity class. This work contains a new description of quantum algorithms in phase space terminology, demonstrating its use in RFS, and how and why this gives a better understanding of the quantum advantage in RFS. Most importantly, describing the computational process of quantum computation in phase space terminology gives a much better understanding of why uncomputation is necessary when solving RFS: the advantage is present only when phase coordinate garbage is uncomputed. This is the underlying reason for the limitations of the quantum advantage. Full article

(This article belongs to the Topic Quantum Information and Quantum Computing, 2nd Volume)

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15 pages, 3161 KiB

Open AccessArticle

Fast Quantum Gates with Electric Field Pulses and Optical Tweezers in Trapped Ions

by Clara Robalo Pereira, Liam J. Bond, Matteo Mazzanti, Rene Gerritsma and Arghavan Safavi-Naini

Entropy 2025, 27(6), 595; https://doi.org/10.3390/e27060595 - 31 May 2025

We propose a two-qubit phase gate based on trapped ions that uses fast electric field pulses and spin-dependent local traps generated by optical tweezers. The phases are engineered by spin-dependent coherent evolution, interspersed with momentum kicks. We derive a set of commensurability conditions [...] Read more.

We propose a two-qubit phase gate based on trapped ions that uses fast electric field pulses and spin-dependent local traps generated by optical tweezers. The phases are engineered by spin-dependent coherent evolution, interspersed with momentum kicks. We derive a set of commensurability conditions and expressions for the spin-dependent accumulated phase that, when satisfied, realize the target two-qubit phase gate within tens of microseconds. We study the scalability of our proposal in larger-ion crystals and demonstrate the existence of solutions with up to four ions. Gates in larger crystals should also be possible but will require more commensurability conditions to be fulfilled. Full article

(This article belongs to the Special Issue Quantum Computing with Trapped Ions)

15 pages, 316 KiB

Open AccessArticle

On the Change of Measure for Brownian Processes

by Francis J. Pinski

Entropy 2025, 27(6), 594; https://doi.org/10.3390/e27060594 - 31 May 2025

Sometimes, limits can be singular, implying that they assume different values depending on the order of arithmetic operations. In other words, the limit map lacks commutativity. While all such limits are mathematically valid, only one can be the physical limit. For instance, the [...] Read more.

Sometimes, limits can be singular, implying that they assume different values depending on the order of arithmetic operations. In other words, the limit map lacks commutativity. While all such limits are mathematically valid, only one can be the physical limit. For instance, the change of measure for Brownian processes illustrates this phenomenon. A substantial body of elegant mathematics centered around continuous-time Brownian processes has been embraced by the physics community to investigate the nonequilibrium and equilibrium thermodynamics of systems composed of atoms and molecules. In this paper, we derive the continuous-time limit of discrete-time Brownian dynamics, specifically focusing on the change of measure. We demonstrate that this result yields the physical limit that differs from the commonly used expression. Consequently, the concepts of “the most probable path”, “minimum thermodynamic action”, and “the small-noise limit” are unphysical mathematical artifacts. Full article

(This article belongs to the Section Non-equilibrium Phenomena)

24 pages, 1005 KiB

Open AccessArticle

Kolmogorov GAM Networks Are All You Need!

by Sarah Polson and Vadim Sokolov

Entropy 2025, 27(6), 593; https://doi.org/10.3390/e27060593 - 31 May 2025

Kolmogorov GAM (K-GAM) networks have been shown to be an efficient architecture for both training and inference. They are additive models with embeddings that are independent of the target function of interest. They provide an alternative to Transformer architectures. They are the machine [...] Read more.

Kolmogorov GAM (K-GAM) networks have been shown to be an efficient architecture for both training and inference. They are additive models with embeddings that are independent of the target function of interest. They provide an alternative to Transformer architectures. They are the machine learning version of Kolmogorov’s superposition theorem (KST), which provides an efficient representation of multivariate functions. Such representations are useful in machine learning for encoding dictionaries (a.k.a. “look-up” tables). KST theory also provides a representation based on translates of the Köppen function. The goal of our paper is to interpret this representation in a machine learning context for applications in artificial intelligence (AI). Our architecture is equivalent to a topological embedding, which is independent of the function, together with an additive layer that uses a generalized additive model (GAM). This provides a class of learning procedures with far fewer parameters than current deep learning algorithms. Implementation can be parallelizable, which makes our algorithms computationally attractive. To illustrate our methodology, we use the iris data from statistical learning. We also show that our additive model with non-linear embedding provides an alternative to Transformer architectures, which, from a statistical viewpoint, are kernel smoothers. Additive KAN models, therefore, provide a natural alternative to Transformers. Finally, we conclude with directions for future research. Full article

(This article belongs to the Section Signal and Data Analysis)

4 pages, 146 KiB

Open AccessEditorial

The Black Hole Information Problem

by Xavier Calmet, Roberto Casadio and Stephen D. H. Hsu

Entropy 2025, 27(6), 592; https://doi.org/10.3390/e27060592 - 31 May 2025

This Special Issue of Entropy is focused on the black hole information paradox [...] Full article

(This article belongs to the Special Issue The Black Hole Information Problem)

22 pages, 2045 KiB

Open AccessArticle

A Judging Scheme for Large-Scale Innovative Class Competitions Based on Z-Score Pro Computational Model and BP Neural Network Model

by Zhuoting Yu, Hongzhong Deng and Shuaiwen Tang

Entropy 2025, 27(6), 591; https://doi.org/10.3390/e27060591 - 31 May 2025

Recently, interest in optimizing judging schemes for large-scale innovation competitions has grown as the complexities in evaluation processes continue to escalate. Although numerous methods have been developed to improve scoring fairness and precision, challenges such as evaluator subjectivity, workload imbalance, and the inherent [...] Read more.

Recently, interest in optimizing judging schemes for large-scale innovation competitions has grown as the complexities in evaluation processes continue to escalate. Although numerous methods have been developed to improve scoring fairness and precision, challenges such as evaluator subjectivity, workload imbalance, and the inherent uncertainty of scoring systems remain inadequately addressed. This study introduces a novel framework that integrates a genetic algorithm-based work cross-distribution model, advanced Z-score adjustment methods, and a BP neural network-enhanced score correction approach to tackle these issues. First, we propose a work crossover distribution model based on the concept of information entropy. The model employs a genetic algorithm to maximize the overlap between experts while ensuring a balanced distribution of evaluation tasks, thus reducing the entropy generated by imbalances in the process. By optimizing the distribution of submissions across experts, our model significantly mitigates inconsistencies arising from diverse scoring tendencies. Second, we developed modified Z-score and Z-score Pro scoring adjustment models aimed at eliminating the scoring discrepancies between judges, thereby enhancing the overall reliability of the normalization process and evaluation results. Additionally, evaluation metrics were proposed based on information theory. Finally, we incorporate a BP neural network-based score adjustment technique to further refine the assessment accuracy by capturing latent biases and uncertainties inherent in large-scale evaluations. Experimental results conducted on datasets from national-scale innovation competitions demonstrate that the proposed methods not only improve the fairness and robustness of the evaluation process but also contribute to a more scientific and objective assessment framework. This research advances the state of the art by providing a comprehensive and scalable solution for addressing the unique challenges of large-scale innovative competition judging. Full article

(This article belongs to the Section Multidisciplinary Applications)

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25 pages, 974 KiB

Open AccessArticle

Information-Theoretic Reliability Analysis of Linear Consecutive r-out-of-n:F Systems and Uniformity Testing

by Ghadah Alomani, Faten Alrewely and Mohamed Kayid

Entropy 2025, 27(6), 590; https://doi.org/10.3390/e27060590 - 31 May 2025

This paper explores the reliability of linear consecutive r-out-of-n:F systems from an information-theoretic perspective, with a particular focus on testing for uniformity. At the heart of the study is extropy, a complementary measure to entropy that we use to gain deeper insights into [...] Read more.

This paper explores the reliability of linear consecutive r-out-of-n:F systems from an information-theoretic perspective, with a particular focus on testing for uniformity. At the heart of the study is extropy, a complementary measure to entropy that we use to gain deeper insights into the uncertainty associated with system lifetimes. We begin by deriving general expressions for extropy in these systems and examine how it behaves under different component lifetime distributions, particularly highlighting the role of heterogeneity. Theoretical bounds are developed, along with new characterization results, shedding light on the unique properties of the uniform distribution within this framework. To bridge theory and application, we propose a nonparametric estimator for extropy and build a new test statistic to assess uniformity. The effectiveness of this test is evaluated through comprehensive simulation studies, where we compare its power against several well-known alternatives across a range of scenarios. Overall, our findings offer both theoretical contributions to the understanding of information measures in reliability analysis and practical tools for statistical testing in applied settings. Full article

(This article belongs to the Special Issue Information-Theoretic Methods in Data Analytics, 2nd Edition)

45 pages, 7516 KiB

Open AccessArticle

Information-Theoretical Analysis of a Transformer-Based Generative AI Model

by Manas Deb and Tokunbo Ogunfunmi

Entropy 2025, 27(6), 589; https://doi.org/10.3390/e27060589 - 31 May 2025

Large Language models have shown a remarkable ability to “converse” with humans in a natural language across myriad topics. Despite the proliferation of these models, a deep understanding of how they work under the hood remains elusive. The core of these Generative AI [...] Read more.

Large Language models have shown a remarkable ability to “converse” with humans in a natural language across myriad topics. Despite the proliferation of these models, a deep understanding of how they work under the hood remains elusive. The core of these Generative AI models is composed of layers of neural networks that employ the Transformer architecture. This architecture learns from large amounts of training data and creates new content in response to user input. In this study, we analyze the internals of the Transformer using Information Theory. To quantify the amount of information passing through a layer, we view it as an information transmission channel and compute the capacity of the channel. The highlight of our study is that, using Information-Theoretical tools, we develop techniques to visualize on an Information plane how the Transformer encodes the relationship between words in sentences while these words are projected into a high-dimensional vector space. We use Information Geometry to analyze the high-dimensional vectors in the Transformer layer and infer relationships between words based on the length of the geodesic connecting these vector distributions on a Riemannian manifold. Our tools reveal more information about these relationships than attention scores. In this study, we also show how Information-Theoretic analysis can help in troubleshooting learning problems in the Transformer layers. Full article

(This article belongs to the Special Issue Entropy and Information Theory in Machine Learning: Theoretical Insights and Applications)

8 pages, 379 KiB

Open AccessArticle

Scaling Laws in Language Families

by Maelyson Rolim Fonseca dos Santos and Marcelo Andrade de Filgueiras Gomes

Entropy 2025, 27(6), 588; https://doi.org/10.3390/e27060588 - 31 May 2025

This article investigates scaling laws within language families using data from over six thousand languages and analyzes emergent patterns observed in Zipf-like classification graphs. Both macroscopic (based on the number of languages by family) and microscopic (based on the number of speakers by [...] Read more.

This article investigates scaling laws within language families using data from over six thousand languages and analyzes emergent patterns observed in Zipf-like classification graphs. Both macroscopic (based on the number of languages by family) and microscopic (based on the number of speakers by language within a family) aspects of these classifications are examined. Particularly noteworthy is the discovery of a distinct division among the fourteen largest contemporary language families, excluding Afro-Asiatic and Nilo-Saharan languages. These families are found to be distributed across three language family quadruplets, each characterized by significantly different exponents in the Zipf graphs. This finding sheds light on the underlying structure and organization of major language families, revealing intriguing insights into the nature of linguistic diversity and distribution. Full article

(This article belongs to the Special Issue Complexity Characteristics of Natural Language)

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22 pages, 5716 KiB

Open AccessArticle

Order–Disorder-Type Transitions Through a Multifractal Procedure in Cu-Zn-Al Alloys—Experimental and Theoretical Design

by Constantin Plăcintă, Valentin Nedeff, Mirela Panainte-Lehăduş, Elena Puiu Costescu, Tudor-Cristian Petrescu, Sergiu Stanciu, Maricel Agop, Diana-Carmen Mirilă and Florin Nedeff

Entropy 2025, 27(6), 587; https://doi.org/10.3390/e27060587 - 30 May 2025

Experimental and theoretical design on thermal and structural properties of Cu-Zn-Al alloys are established. As such, from an experimental point of view, differential thermal analysis has been performed with the help of a DSC Netzsch STA 449 F1 Jupiter calorimeter with high levels [...] Read more.

Experimental and theoretical design on thermal and structural properties of Cu-Zn-Al alloys are established. As such, from an experimental point of view, differential thermal analysis has been performed with the help of a DSC Netzsch STA 449 F1 Jupiter calorimeter with high levels of sensitivity, and the structural analysis has been accomplished through X-ray diffraction and SEM analysis. An unusual specific property for a metallic material has been discovered, which is known as “rubber-type behavior”, a characteristic determined by micro-structural changes. From the theoretical point of view, the thermal transfer in Cu-Zn-Al is presented by assimilating this alloy, both structurally and functionally, with a multifractal, situation in which the order–disorder transitions assimilated with thermal “dynamics” of Cu-Zn-Al, are mimed through transitions from non-multifractal to multifractal curves. In such a context, the thermal expansion velocity contains both the propagation speed of the phase transformation (be it a direct one: austenitic–martensitic transformation, or an indirect one: martensitic–austenitic transformation) and the thermal diffusion speed. Then, through self-modulations of the thermal field, the Cu-Zn-Al alloy will self-structure in channel-type or cellular-type thermal patterns, which can be linked to obtained experimental data. Consequently, since the thermal conductivity becomes a function of the observation scale, and heat transfer is modified to reflect the multifractal, non-differentiable paths in the material, it leads to anomalous diffusion and complex thermal behaviors. Full article

(This article belongs to the Section Complexity)

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16 pages, 356 KiB

Open AccessArticle

Entropy Maximization, Time Emergence, and Phase Transition

by Jonathan Smith

Entropy 2025, 27(6), 586; https://doi.org/10.3390/e27060586 - 30 May 2025

We survey developments in the use of entropy maximization for applying the Gibbs Canonical Ensemble to finite situations. Biological insights are invoked along with physical considerations. In the game-theoretic approach to entropy maximization, the interpretation of the two player roles as predator and [...] Read more.

We survey developments in the use of entropy maximization for applying the Gibbs Canonical Ensemble to finite situations. Biological insights are invoked along with physical considerations. In the game-theoretic approach to entropy maximization, the interpretation of the two player roles as predator and prey provides a well-justified and symmetric analysis. The main focus is placed on the Lagrange multiplier approach. Using natural physical units with Planck’s constant set to unity, it is recognized that energy has the dimensions of inverse time. Thus, the conjugate Lagrange multiplier, traditionally related to absolute temperature, is now taken with time units and oriented to follow the Arrow of Time. In quantum optics, where energy levels are bounded above and below, artificial singularities involving negative temperatures are eliminated. In a biological model where species compete in an environment with a fixed carrying capacity, use of the Canonical Ensemble solves an instance of Eigen’s phenomenological rate equations. The Lagrange multiplier emerges as a statistical measure of the ecological age. Adding a weak inequality on an order parameter for the entropy maximization, the phase transition from initial unconstrained growth to constrained growth at the carrying capacity is described, without recourse to a thermodynamic limit for the finite system. Full article

(This article belongs to the Section Thermodynamics)

21 pages, 465 KiB

Open AccessArticle

Portfolio Model Considering Normal Uncertain Preference Relations of Investors

by Yu Zhou, Chun Yan and Xiangrong Wang

Entropy 2025, 27(6), 585; https://doi.org/10.3390/e27060585 - 30 May 2025

The paper examines the application of uncertainty theory to portfolio decision making, specifically focusing on constructing portfolio models based on uncertain preference relations. Firstly, we establish the theoretical foundation by introducing the theory of uncertainty, which includes uncertain measure and normal uncertain distribution. [...] Read more.

The paper examines the application of uncertainty theory to portfolio decision making, specifically focusing on constructing portfolio models based on uncertain preference relations. Firstly, we establish the theoretical foundation by introducing the theory of uncertainty, which includes uncertain measure and normal uncertain distribution. Then, building upon Markowitz portfolio theory, we propose an uncertain preference relation prioritization model with chance constraints and an additive consistency portfolio model to facilitate rational decision making in a complex and uncertain financial environment. Furthermore, empirical analysis validates our model’s feasibility, demonstrating its advantages in maximizing returns and minimizing risks. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

12 pages, 2019 KiB

Open AccessArticle

A Zero-Touch Dynamic Configuration Management Framework for Time-Sensitive Networking (TSN)

by Junhui Jiang, Shanyu Jin, Xinghan Li, Kaisong Zhang and Baodan Sun

Entropy 2025, 27(6), 584; https://doi.org/10.3390/e27060584 - 30 May 2025

As Industry 5.0 progresses, the demand for zero-touch configuration in industrial automation and smart manufacturing is increasing. This paper proposes a dynamic configuration management framework for Time-Sensitive Networking (TSN), aiming to address the challenges of flexibility and adaptability in dynamic network environments. A [...] Read more.

As Industry 5.0 progresses, the demand for zero-touch configuration in industrial automation and smart manufacturing is increasing. This paper proposes a dynamic configuration management framework for Time-Sensitive Networking (TSN), aiming to address the challenges of flexibility and adaptability in dynamic network environments. A zero-touch configuration model is presented for TSN by incorporating a Delay-Aware Shortest Path Search (DASPS) algorithm to improve scheduling success rates. Simulation results demonstrate the ability of the framework to reconfigure networks within 2.67 milliseconds. The DASPS algorithm achieves a scheduling success rate of 70.22% for 1000 TSN flows, in contrast to only 22.23% achieved by the Shortest Path Search (SPS) algorithm. The proposed model effectively adapts to dynamic network changes, guaranteeing real-time data transmission. To further evaluate system adaptability, path entropy is introduced as a metric to quantitatively assess the balance of scheduling outcomes under topological changes. In the event of link failures, path entropy experiences a sharp decline but rapidly recovers after reconfiguration, demonstrating the system’s strong self-healing capability. Full article

(This article belongs to the Special Issue Task-Oriented Communications in Industrial IoT: Age of Information and Beyond)

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18 pages, 752 KiB

Open AccessArticle

Towards Identifying Objectivity in Short Informal Text

by Chaowei Zhang, Cheng Zhao, Zewei Zhang and Yuchao Huang

Entropy 2025, 27(6), 583; https://doi.org/10.3390/e27060583 - 30 May 2025

Short informal texts are increasingly prevalent in modern communication, often containing fragmented grammar, personal opinions, and limited context. Traditional NLP tasks for the texts ordinarily focus on the subjective aspect learning, such as sentiment analysis and polarity classification. The study of learning objectivity [...] Read more.

Short informal texts are increasingly prevalent in modern communication, often containing fragmented grammar, personal opinions, and limited context. Traditional NLP tasks for the texts ordinarily focus on the subjective aspect learning, such as sentiment analysis and polarity classification. The study of learning objectivity from the texts is similarly significant, which can benefit many real-world applications including information filtering, content verification, etc. Unfortunately, this study is not being explored. This paper proposes a novel task that aims at identifying objectivity in short informal texts. Inspired by the characteristics of objective statements that normally need complete syntax structures for knowledge expression and delivery, we try to leverage the viewpoint of subjects (U), the tense of predicates (V), and the viewpoint of objects (O) as critical factors for objectivity learning. Upon that, we further propose a two-stage objectivity identification approach: (1) a UVO quantification module is implemented via a proposed OpenIE and large language model (LLM)-based triple feature quantification procedure; (2) an objectivity identification module employs pre-trained base models like BERT or RoBERTa that are constrained with the quantified UVO. The experimental result demonstrates our approach can outperform the base models up to

5.91 %

in objective-F1 and up to

6.97 %

in accuracy. Full article

(This article belongs to the Special Issue Complexity Characteristics of Natural Language)

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21 pages, 1689 KiB

Open AccessArticle

Outlier Detection and Explanation Method Based on FOLOF Algorithm

by Lei Bai, Jiasheng Wang and Yu Zhou

Entropy 2025, 27(6), 582; https://doi.org/10.3390/e27060582 - 30 May 2025

Outlier mining constitutes an essential aspect of modern data analytics, focusing on the identification and interpretation of anomalous observations. Conventional density-based local outlier detection methodologies frequently exhibit limitations due to their inherent lack of data preprocessing capabilities, consequently demonstrating degraded performance when applied [...] Read more.

Outlier mining constitutes an essential aspect of modern data analytics, focusing on the identification and interpretation of anomalous observations. Conventional density-based local outlier detection methodologies frequently exhibit limitations due to their inherent lack of data preprocessing capabilities, consequently demonstrating degraded performance when applied to novel or heterogeneous datasets. Moreover, the computation of the outlier factor for each sample in these algorithms results in considerably higher computational cost, especially in the case of large datasets. This paper introduces a local outlier detection method named FOLOF (FCM Objective Function-based LOF) through an examination of existing algorithms. The approach starts by applying the elbow rule to determine the optimal number of clusters in the dataset. Subsequently, the FCM objective function is employed to prune the dataset to extract a candidate set of outliers. Finally, a weighted local outlier factor detection algorithm computes the degree of anomaly for each sample in the candidate set. For the analysis, the Golden Section method was used to classify the outliers. The underlying causes of these outliers can be revealed by exploring the anomalous properties of each outlier data point through the outlier factors of each dimension property. This approach has been validated on artificial datasets, the UCI dataset, and an NBA player dataset to demonstrate its effectiveness. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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13 pages, 2067 KiB

Open AccessFeature PaperArticle

Quantum Mpemba Effect from Non-Normal Dynamics

by Stefano Longhi

Entropy 2025, 27(6), 581; https://doi.org/10.3390/e27060581 - 29 May 2025

The quantum Mpemba effect refers to the counterintuitive phenomenon in which a system initially farther from equilibrium relaxes faster than one prepared closer to it. Several mechanisms have been identified in open quantum systems to explain this behavior, including the strong Mpemba effect, [...] Read more.

The quantum Mpemba effect refers to the counterintuitive phenomenon in which a system initially farther from equilibrium relaxes faster than one prepared closer to it. Several mechanisms have been identified in open quantum systems to explain this behavior, including the strong Mpemba effect, non-Markovian memory, and initial system–reservoir entanglement. Here, we unveil a distinct mechanism rooted in the non-normal nature of the Liouvillian superoperator in Markovian dynamics. When the Liouvillian’s eigenmodes are non-orthogonal, transient interference between decaying modes can induce anomalous early-time behavior—such as delayed thermalization or transient freezing—even though asymptotic decay rates remain unchanged. This differs fundamentally from strong Mpemba effects, which hinge on suppressed overlap with slow-decaying modes. We demonstrate this mechanism using a waveguide quantum electrodynamics model, where quantum emitters interact with the photonic modes of a one-dimensional waveguide. The directional and radiative nature of these couplings naturally introduces non-normality into the system’s dynamics. As a result, certain initial states—despite being closer to equilibrium—can exhibit slower relaxation at short times. This work reveals a previously unexplored and universal source of Mpemba-like behavior in memoryless quantum systems, expanding the theoretical framework for anomalous relaxation and opening new avenues for control in engineered quantum platforms. Full article

(This article belongs to the Section Non-equilibrium Phenomena)

22 pages, 648 KiB

Open AccessArticle

Transport and Response Coefficients in Second-Order Dissipative Relativistic Hydrodynamics with Quantum Corrections: Probing the Quark–Gluon Plasma

by Iberê Kuntz and Roldao da Rocha

Entropy 2025, 27(6), 580; https://doi.org/10.3390/e27060580 - 29 May 2025

A functional measure encompasses quantum corrections and is explored in the fluid/gravity correspondence. Corrections to the response and transport coefficients in the second-order dissipative relativistic hydrodynamics are proposed, including those to the pressure, relaxation time, and shear relaxation time. Their dependence on the [...] Read more.

A functional measure encompasses quantum corrections and is explored in the fluid/gravity correspondence. Corrections to the response and transport coefficients in the second-order dissipative relativistic hydrodynamics are proposed, including those to the pressure, relaxation time, and shear relaxation time. Their dependence on the quark–gluon plasma (QGP) temperature sets a temperature dependence on the running parameter encoding the one-loop quantum gravity correction, driven by a functional measure. The experimental range of the bulk-viscosity-to-entropy-density ratio of the QGP, obtained by five different analyses (JETSCAPE Bayesian model, Duke, Jyväskylä–Helsinki–Munich, MIT–Utrecht–Genève, and Shanghai) corroborates the existence of the functional measure. Our results suggest that high-temperature plasmas could be used to experimentally test quantum gravity. Full article

(This article belongs to the Special Issue Nonequilibrium Quantum Field Processes and Phenomena)

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Topic in Atmosphere, Earth, Encyclopedia, Entropy, Fractal Fract, MAKE, Meteorology

Revisiting Butterfly Effect, Multiscale Dynamics, and Predictability Using Ai-Enhanced Modeling Framework (AEMF) and Chaos Theory Topic Editors: Bo-Wen Shen, Roger A. Pielke Sr., Xubin Zeng
Deadline: 31 July 2025

Topic in Entropy, Algorithms, Computation, Fractal Fract

Computational Complex Networks Topic Editors: Alexandre G. Evsukoff, Yilun Shang
Deadline: 30 September 2025

Topic in AI, Energies, Entropy, Sustainability

Game Theory and Artificial Intelligence Methods in Sustainable and Renewable Energy Power Systems Topic Editors: Lefeng Cheng, Pei Zhang, Anbo Meng
Deadline: 31 October 2025

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10–14 June 2025 The 1st International Online Conference of the Journal Philosophies: Intelligent Inquiry into Intelligence—Contributing to the 2025 IS4SI Summit

3–6 June 2025 32nd Biennial Symposium on Communications 2025 (BSC 2025)

17–20 June 2025 Time in Quantum Theory 2025 (TiQT 2025)

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Special Issue in Entropy

Goal-Oriented Communication: Freshness, Semantics, and Beyond Guest Editors: Xingran Chen, Shirin Saeedi Bidokhti
Deadline: 4 June 2025

Special Issue in Entropy

Complexity and Evolution, 2nd Edition Guest Editors: Francis Heylighen, Tomas Veloz
Deadline: 13 June 2025

Special Issue in Entropy

Natural Language Processing and Data Mining Guest Editor: Manling Li
Deadline: 15 June 2025

Special Issue in Entropy

Information-Theoretic Criteria for Statistical Model Selection Guest Editors: Abhijit Mandal, Suneel Babu Chatla
Deadline: 15 June 2025

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Topical Collection in Entropy

Quantum Information Collection Editor: Rosario Lo Franco

Topical Collection in Entropy

Information Geometry Collection Editor: Geert Verdoolaege

Topical Collection in Entropy

Do Entropic Approaches Improve Understanding of Biology? Collection Editors: William B. Sherwin, Robert Niven

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Algorithmic Information Dynamics: A Computational Approach to Causality from Cells to Networks Collection Editors: Hector Zenil, Felipe Abrahão

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