Entropy

16 pages, 504 KiB

Open AccessArticle

Near-Horizon Carnot Engines Beyond Schwarzschild: Exploring Black Brane Thermodynamics

by Lotte Mertens and Jasper van Wezel

Entropy 2025, 27(5), 491; https://doi.org/10.3390/e27050491 (registering DOI) - 1 May 2025

Sadi Carnot’s seminal work laid the foundation for exploring the effects of thermodynamics across diverse domains of physics, stretching from quantum to cosmological scales. Here, we build on the principles of the original Carnot heat engine, and apply it in the context of [...] Read more.

Sadi Carnot’s seminal work laid the foundation for exploring the effects of thermodynamics across diverse domains of physics, stretching from quantum to cosmological scales. Here, we build on the principles of the original Carnot heat engine, and apply it in the context of a particular toy model black brane. This theoretical construct of an effectively two-dimensional, stable, and stationary gravitational object in four-dimensional spacetime derives from a hypothetical flat planet collapsed under the influence of gravity. By constructing a thermodynamic cycle involving three such black branes, we explore the possibility of energy extraction or mining, driven by the temperature gradients and gravitational potential differences characteristic of curved spacetime. Analytic solutions obtainable within this toy model illuminate key aspects of black hole thermodynamics in general, particularly for spacetimes that are not asymptotically flat. Central to these findings is the relation between gravitationally induced temperature ratios and entropy changes, which collectively offer a novel perspective on obtainable energy transfer processes around gravitational structures. This analysis highlights potential implications for understanding energy dynamics in gravitational systems in general, including for black hole evaporation and experimentally implemented black hole analogues. The presented findings not only emphasise the universality of the thermodynamic principles first uncovered by Carnot, but also suggest future research directions in gravitational thermodynamics. Full article

(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)

28 pages, 2747 KiB

Open AccessArticle

Exploring Quantum Neural Networks for Demand Forecasting

by Gleydson Fernandes de Jesus, Maria Heloísa Fraga da Silva, Otto Menegasso Pires, Lucas Cruz da Silva, Clebson dos Santos Cruz and Valéria Loureiro da Silva

Entropy 2025, 27(5), 490; https://doi.org/10.3390/e27050490 (registering DOI) - 1 May 2025

Abstract

Forecasting demand for assets and services can be addressed in various markets, providing a competitive advantage when the predictive models used demonstrate high accuracy. However, the training of machine learning models incurs high computational costs, which may limit the training of prediction models [...] Read more.

Forecasting demand for assets and services can be addressed in various markets, providing a competitive advantage when the predictive models used demonstrate high accuracy. However, the training of machine learning models incurs high computational costs, which may limit the training of prediction models based on available computational capacity. In this context, this paper presents an approach for training demand prediction models using quantum neural networks. For this purpose, a quantum neural network was used to forecast demand for vehicle financing. A classical recurrent neural network was used to compare the results, and they show a similar predictive capacity between the classical and quantum models, with the advantage of using a lower number of training parameters and also converging in fewer steps. Utilizing quantum computing techniques offers a promising solution to overcome the limitations of traditional machine learning approaches in training predictive models for complex market dynamics. Full article

(This article belongs to the Special Issue Classical and Quantum Networks: Theory, Modeling and Optimization)

12 pages, 526 KiB

Open AccessArticle

Time Dilation of Quantum Clocks in a Relativistic Gravitational Potential

by Tommaso Favalli and Augusto Smerzi

Entropy 2025, 27(5), 489; https://doi.org/10.3390/e27050489 (registering DOI) - 1 May 2025

Abstract

We study the dynamical evolution of two quantum clocks interacting with a relativistic gravitational potential. We find a time dilation effect for the clocks in agreement with the gravitational time dilation as obtained from the Schwarzschild solution in General Relativity. We perform our [...] Read more.

We study the dynamical evolution of two quantum clocks interacting with a relativistic gravitational potential. We find a time dilation effect for the clocks in agreement with the gravitational time dilation as obtained from the Schwarzschild solution in General Relativity. We perform our investigation via the Page and Wootters quantum-time formalism, exploring the dynamics of clocks assuming them in both a product state and a more general (entangled) state. The gravitational redshift, as emerging from our framework, is also proposed and discussed. Full article

(This article belongs to the Special Issue Time, Change, Observables, and Quantum Gravity)

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30 pages, 21914 KiB

Open AccessArticle

Turbulent Flow in Street Canyons: A Complexity Approach

by Csanád Árpád Hubay, Bálint Papp and Tamás Kalmár-Nagy

Entropy 2025, 27(5), 488; https://doi.org/10.3390/e27050488 (registering DOI) - 30 Apr 2025

Abstract

Velocity measurements and simulations in an idealized urban environment were studied, focusing on turbulent flow over street canyons. Time series of fluctuating velocities were considered as marked point processes, and the distribution of mean residence times was characterized using a lognormal fit. The [...] Read more.

Velocity measurements and simulations in an idealized urban environment were studied, focusing on turbulent flow over street canyons. Time series of fluctuating velocities were considered as marked point processes, and the distribution of mean residence times was characterized using a lognormal fit. The quadrant method was applied to transform time series into symbolic sequences, enabling the investigation of their information content. By analyzing word frequency and normalized entropy levels, we compared measured and simulated sequences with periodic symbol sequences with and without noise. Our results indicate that noisy periodic sequences exhibit entropy distributions qualitatively similar to those of the measured and simulated data. Surrogate sequences generated using first-, and higher-order Markov statistics also displayed similarity. Higher-order Markov chains provide a more accurate representation of the information content of velocity fluctuation series. These findings contribute to the comparison of experimental and simulation techniques in the investigation of turbulence. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Applications—In Honor of Professor Osvaldo Anibal Rosso's 70th Birthday)

21 pages, 887 KiB

Open AccessArticle

Detecting Signatures of Criticality Using Divergence Rate

by Tenzin Chan, De Wen Soh and Christopher Hillar

Entropy 2025, 27(5), 487; https://doi.org/10.3390/e27050487 (registering DOI) - 30 Apr 2025

Abstract

Oftentimes in a complex system it is observed that as a control parameter is varied, there are certain intervals during which the system undergoes dramatic change. In biology especially, these signatures of criticality are thought to be connected with efficient computation and information [...] Read more.

Oftentimes in a complex system it is observed that as a control parameter is varied, there are certain intervals during which the system undergoes dramatic change. In biology especially, these signatures of criticality are thought to be connected with efficient computation and information processing. Guided by the classical theory of rate–distortion (RD) from information theory, we propose a measure for detecting and characterizing such phenomena from data. When applied to RD problems, the measure correctly identifies exact critical trade-off parameters emerging from the theory and allows for the discovery of new conjectures in the field. Other application domains include efficient sensory coding, machine learning generalization, and natural language. Our findings give support to the hypothesis that critical behavior is a signature of optimal processing. Full article

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

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28 pages, 2526 KiB

Open AccessArticle

Baselining Urban Ecosystems from Sentinel Species: Fitness, Flows, and Sinks

by Matteo Convertino, Yuhan Wu and Hui Dong

Entropy 2025, 27(5), 486; https://doi.org/10.3390/e27050486 - 30 Apr 2025

Abstract

How can the shape of biodiversity inform us about cities’ ecoclimatic fitness and guide their development? Can we use species as the harbingers of climatic extremes? Eco-climatically sensitive species carry information about hydroclimatic change in their distribution, fitness, and preferential gradients of habitat [...] Read more.

How can the shape of biodiversity inform us about cities’ ecoclimatic fitness and guide their development? Can we use species as the harbingers of climatic extremes? Eco-climatically sensitive species carry information about hydroclimatic change in their distribution, fitness, and preferential gradients of habitat suitability. Conversely, environmental features outside of the species’ fitness convey information on potential ecological anomalies in response to extremes to adapt or mitigate, such as through urban parks. Here, to quantify ecosystems’ fitness, we propose a novel computational model to extract multivariate functional ecological networks and their basins, which carry the distributed signature of the compounding hydroclimatic pressures on sentinel species. Specifically, we consider butterflies and their habitat suitability (HS) to infer maximum suitability gradients that are meaningful of potential species networks and flows, with the smallest hydroclimatic resistance across urban landscapes. These flows are compared to the distribution of urban parks to identify parks’ ecological attractiveness, actual and potential connectivity, and park potential to reduce hydroclimatic impacts. The ecosystem fitness index (EFI) is novelly introduced by combining HS and the divergence of the relative species abundance (RSA) from the optimal log-normal Preston plot. In Shenzhen, as a case study, eco-flow networks are found to be spatially very extended, scale-free, and clustering for low HS gradient and EFI areas, where large water bodies act as sources of ecological corridors draining into urban parks. Conversely, parks with higher HS, HS gradients, and EFIs have small-world connectivity non-overlapping with hydrological networks. Diverging patterns of abundance and richness are inferred as increasing and decreasing with HS. HS is largely determined by temperature and precipitation of the coldest quarter and seasonality, which are critical hydrologic variables. Interestingly, a U-shape pattern is found between abundance and diversity, similar to the one in natural ecosystems. Additionally, both abundance and richness are mildly associated with park area according to a power function, unrelated to longitude but linked to the degree of urbanization or park centrality, counterintuitively. The Preston plot’s richness–abundance and abundance-rank patterns were verified to reflect the stationarity or ecological meta-equilibrium with the environment, where both are a reflection of community connectivity. Ecological fitness is grounded on the ecohydrological structure and flows where maximum HS gradients are indicative of the largest eco-changes like climate-driven species flows. These flows, as distributed stress-response functions, inform about the collective eco-fitness of communities, like parks in cities. Flow-based networks can serve as blueprints for designing ecotones that regulate key ecosystem functions, such as temperature and evapotranspiration, while generating cascading ecological benefits across scales. The proposed model, novelly infers HS eco-networks and calculates the EFI, is adaptable to diverse sensitive species and environmental layers, offering a robust tool for precise ecosystem assessment and design. Full article

(This article belongs to the Topic Bioterraformation: Emergent Function from Systemic Eco-Engineering)

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22 pages, 1752 KiB

Open AccessArticle

Bias Reduction of Modified Maximum Likelihood Estimates for a Three-Parameter Weibull Distribution

by Adriana da Silva, Felipe Quintino, Frederico Almeida and Dióscoros Aguiar

Entropy 2025, 27(5), 485; https://doi.org/10.3390/e27050485 - 30 Apr 2025

Abstract

In this work, we investigate the parameter estimation problem based on the three-parameter Weibull models, for which non-finite estimates may be obtained for the log-likelihood function in some regions of the parametric space. Based on an information criterion with penalization of the modified [...] Read more.

In this work, we investigate the parameter estimation problem based on the three-parameter Weibull models, for which non-finite estimates may be obtained for the log-likelihood function in some regions of the parametric space. Based on an information criterion with penalization of the modified log-likelihood function, we propose a new class of estimators for this distribution model. In addition to providing finite estimates for the model parameters, this procedure reduces the bias of the modified estimator. The performance of the new estimator is evaluated through simulations and real-life data set modeling. An economic application on a real data set is discussed, as well as an engineering one. Full article

(This article belongs to the Special Issue Information-Theoretic Criteria for Statistical Model Selection)

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17 pages, 4401 KiB

Open AccessArticle

Unveiling Learning Strategies in the Mirror-Drawing Task: A Single-Case Study of Movement Stability and Complexity Using Entropy

by Hiroki Murakami and Norimasa Yamada

Entropy 2025, 27(5), 484; https://doi.org/10.3390/e27050484 - 30 Apr 2025

Abstract

The mirror-drawing task has been widely used in motor learning research to investigate procedural memory and movement control. However, studies have primarily focused on global performance measures such as movement time and the number of errors and lack insight into localized learning patterns. [...] Read more.

The mirror-drawing task has been widely used in motor learning research to investigate procedural memory and movement control. However, studies have primarily focused on global performance measures such as movement time and the number of errors and lack insight into localized learning patterns. This case study aimed to analyze motor learning characteristics by combining traditional measures with entropy analysis, a method for capturing movement stability and complexity. Using a star-shaped figure divided into 12 segments, a single participant performed 100 trials of the mirror-drawing task. The movement coordinates were recorded at 60 Hz using a stylus on a mirrored tablet screen. The results showed that movement time decreased over the trials and entropy values showed an initial increase, followed by a decrease, suggesting exploratory behavior and subsequent stabilization. In particular, the interference side segments requiring complex visual–motor transformations showed prolonged instability and delayed control stabilization compared with the noninterference side segments. The integration of entropy analysis allowed a clearer visualization of the trial-and-error phases and movement instability, providing novel insights into the motor learning process. These findings, though limited to a single case, contribute to the understanding of adaptive movement control strategies and suggest that local learning properties should be considered in skill acquisition research. Full article

(This article belongs to the Section Multidisciplinary Applications)

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20 pages, 1621 KiB

Open AccessReview

Entropy Production in Epithelial Monolayers Due to Collective Cell Migration

by Ivana Pajic-Lijakovic and Milan Milivojevic

Entropy 2025, 27(5), 483; https://doi.org/10.3390/e27050483 - 29 Apr 2025

Abstract

The intricate multi-scale phenomenon of entropy generation, resulting from the inhomogeneous and anisotropic rearrangement of cells during their collective migration, is examined across three distinct regimes: (i) convective, (ii) conductive (diffusion), and (iii) sub-diffusion. The collective movement of epithelial monolayers on substrate matrices [...] Read more.

The intricate multi-scale phenomenon of entropy generation, resulting from the inhomogeneous and anisotropic rearrangement of cells during their collective migration, is examined across three distinct regimes: (i) convective, (ii) conductive (diffusion), and (iii) sub-diffusion. The collective movement of epithelial monolayers on substrate matrices induces the accumulation of mechanical stress within the cells, which subsequently influences cell packing density, velocity, and alignment. Variations in these physical parameters affect cell-cell interactions, which play a crucial role in the storage and dissipation of energy within multicellular systems. The internal dynamics of entropy generation, as a consequence of energy dissipation, are characterized in each regime using viscoelastic constitutive models and the surface properties at the cell-matrix biointerface. The focus of this theoretical review is to clarify how cells can modulate their rate of energy dissipation by altering cell-cell and cell-matrix adhesion interactions, undergoing changes in shape, and re-establishing polarity due to the contact inhibition of locomotion. We approach these questions by discussing the physical aspects of these complex phenomena. Full article

(This article belongs to the Special Issue From Order to Disorder: Superfluidity, Stochastic Processes, and the Dynamics of Life—Dedicated to Professor Peter McClintock on the Occasion of His 85th Birthday)

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25 pages, 349 KiB

Open AccessArticle

Quantum κ-Entropy: A Quantum Computational Approach

by Demosthenes Ellinas and Giorgio Kaniadakis

Entropy 2025, 27(5), 482; https://doi.org/10.3390/e27050482 (registering DOI) - 29 Apr 2025

Abstract

A novel approach to the quantum version of

κ

-entropy that incorporates it into the conceptual, mathematical and operational framework of quantum computation is put forward. Various alternative expressions stemming from its definition emphasizing computational and algorithmic aspects are worked out: First, for [...] Read more.

A novel approach to the quantum version of

κ

-entropy that incorporates it into the conceptual, mathematical and operational framework of quantum computation is put forward. Various alternative expressions stemming from its definition emphasizing computational and algorithmic aspects are worked out: First, for the case of canonical Gibbs states, it is shown that

κ

-entropy is cast in the form of an expectation value for an observable that is determined. Also, an operational method named “the two-temperatures protocol” is introduced that provides a way to obtain the

κ

-entropy in terms of the partition functions of two auxiliary Gibbs states with temperatures

κ

-shifted above, the hot-system, and

κ

-shifted below, the cold-system, with respect to the original system temperature. That protocol provides physical procedures for evaluating entropy for any

κ

. Second, two novel additional ways of expressing the

κ

-entropy are further introduced. One determined by a non-negativity definite quantum channel, with Kraus-like operator sum representation and its extension to a unitary dilation via a qubit ancilla. Another given as a simulation of the

κ

-entropy via the quantum circuit of a generalized version of the Hadamard test. Third, a simple inter-relation of the von Neumann entropy and the quantum

κ

-entropy is worked out and a bound of their difference is evaluated and interpreted. Also the effect on the

κ

-entropy of quantum noise, implemented as a random unitary quantum channel acting in the system’s density matrix, is addressed and a bound on the entropy, depending on the spectral properties of the noisy channel and the system’s density matrix, is evaluated. The results obtained amount to a quantum computational tool-box for the

κ

-entropy that enhances its applicability in practical problems. Full article

(This article belongs to the Section Statistical Physics)

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28 pages, 15480 KiB

Open AccessArticle

Analysis and Synchronous Study of a Five-Dimensional Multistable Memristive Chaotic System with Bidirectional Offset Increments

by Lina Ding and Mengtian Xuan

Entropy 2025, 27(5), 481; https://doi.org/10.3390/e27050481 - 29 Apr 2025

Abstract

In order to further explore the complex dynamical behavior involved in super-multistability, a new five-dimensional memristive chaotic system was obtained by using a magnetically controlled memristor to construct a four-dimensional equation on the basis of a three-dimensional chaotic system, adding a five-dimensional equation [...] Read more.

In order to further explore the complex dynamical behavior involved in super-multistability, a new five-dimensional memristive chaotic system was obtained by using a magnetically controlled memristor to construct a four-dimensional equation on the basis of a three-dimensional chaotic system, adding a five-dimensional equation and selecting parameter

y

as the control term. Firstly, the multistability of the system was analyzed by using a Lyapunov exponential diagram, a bifurcation diagram and a phase portrait; the experimental results show that the system has parameter-related periodic chaotic alternating characteristics, symmetric attractors and transient chaotic characteristics, and it also has the characteristics of homogeneous multistability, heterogeneous multistability and super-multistability, which depend on the initial memristive values. Secondly, two offset constants

g

and

h

were added to the linear state variables, which were used as controllers of the attractors in the

z

and

w

directions, respectively, and the influences of the bidirectional offset increments on the system were analyzed. The complexity of the system was analyzed; the higher the complexity of the system, the larger the values of the complexity, and the darker the colors of the spectrogram. The five-dimensional memristive chaotic system was simulated using Multisim to verify the feasibility of the new system. Finally, an adaptive synchronization controller was designed using the method of adaptive synchronization; then, synchronization of the drive system and the response system was realized by changing the positive gain constant

k

, which achieved encryption and decryption of sinusoidal signals based on chaotic synchronization. Full article

(This article belongs to the Section Complexity)

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40 pages, 794 KiB

Open AccessArticle

An Automated Decision Support System for Portfolio Allocation Based on Mutual Information and Financial Criteria

by Massimiliano Kaucic, Renato Pelessoni and Filippo Piccotto

Entropy 2025, 27(5), 480; https://doi.org/10.3390/e27050480 - 29 Apr 2025

Abstract

This paper introduces a two-phase decision support system based on information theory and financial practices to assist investors in solving cardinality-constrained portfolio optimization problems. Firstly, the approach employs a stock-picking procedure based on an interactive multi-criteria decision-making method (the so-called TODIM method). More [...] Read more.

This paper introduces a two-phase decision support system based on information theory and financial practices to assist investors in solving cardinality-constrained portfolio optimization problems. Firstly, the approach employs a stock-picking procedure based on an interactive multi-criteria decision-making method (the so-called TODIM method). More precisely, the best-performing assets from the investable universe are identified using three financial criteria. The first criterion is based on mutual information, and it is employed to capture the microstructure of the stock market. The second one is the momentum, and the third is the upside-to-downside beta ratio. To calculate the preference weights used in the chosen multi-criteria decision-making procedure, two methods are compared, namely equal and entropy weighting. In the second stage, this work considers a portfolio optimization model where the objective function is a modified version of the Sharpe ratio, consistent with the choices of a rational agent even when faced with negative risk premiums. Additionally, the portfolio design incorporates a set of bound, budget, and cardinality constraints, together with a set of risk budgeting restrictions. To solve the resulting non-smooth programming problem with non-convex constraints, this paper proposes a variant of the distance-based parameter adaptation for success-history-based differential evolution with double crossover (DISH-XX) algorithm equipped with a hybrid constraint-handling approach. Numerical experiments on the US and European stock markets over the past ten years are conducted, and the results show that the flexibility of the proposed portfolio model allows the better control of losses, particularly during market downturns, thereby providing superior or at least comparable ex post performance with respect to several benchmark investment strategies. Full article

(This article belongs to the Special Issue Entropy, Econophysics, and Complexity)

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25 pages, 36928 KiB

Open AccessArticle

Exploring Entanglement Spectra and Phase Diagrams in Multi-Electron Quantum Dot Chains

by Guanjie He and Xin Wang

Entropy 2025, 27(5), 479; https://doi.org/10.3390/e27050479 - 29 Apr 2025

Abstract

We investigate the entanglement properties in semiconductor quantum dot systems modeled by the extended Hubbard model, focusing on the impacts of potential energy variations and electron interactions within a four-site quantum dot spin chain. Our study explores local and pairwise entanglement across configurations [...] Read more.

We investigate the entanglement properties in semiconductor quantum dot systems modeled by the extended Hubbard model, focusing on the impacts of potential energy variations and electron interactions within a four-site quantum dot spin chain. Our study explores local and pairwise entanglement across configurations with electron counts

N = 4

and

N = 6

, under different potential energy settings. By adjusting the potential energy in specific dots and examining the entanglement across various interaction regimes, we identify significant variations in the ground states of quantum dots. We extend this analysis to larger systems with

L = 6

and

L = 8

, comparing electron counts

N = L

and

N = L + 2

, revealing sharper entanglement transitions and reduced finite-size effects as the system size increases. Our results show that local potential shifts and the Coulomb interaction strength lead to notable redistributions of the electron configurations in the quantum dot spin chain, significantly affecting the entanglement properties. These changes are depicted in phase diagrams that highlight entanglements’ dependencies on the interaction strengths and potential energy adjustments, illustrating complex entanglement dynamics shifts triggered by interdot interactions. Full article

(This article belongs to the Section Quantum Information)

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17 pages, 722 KiB

Open AccessArticle

Thermal Fisher Information for a Rotating BTZ Black Hole

by Everett A. Patterson and Robert B. Mann

Entropy 2025, 27(5), 478; https://doi.org/10.3390/e27050478 - 28 Apr 2025

Abstract

Relativistic quantum metrology provides a framework within which we can quantify the quality of measurement and estimation procedures while accounting for both quantum and relativistic effects. The chief measure for describing such procedures is the Fisher information, which quantifies how sensitive a given [...] Read more.

Relativistic quantum metrology provides a framework within which we can quantify the quality of measurement and estimation procedures while accounting for both quantum and relativistic effects. The chief measure for describing such procedures is the Fisher information, which quantifies how sensitive a given estimation is to a variance in some underlying parameter. Recently, the Fisher information has been used to quantify the spacetime information accessible to two-level quantum particle detectors. We have previously shown that such a system is capable of discerning black hole mass for static black holes in 2 + 1 dimensions. Here, we extend these results to the astrophysically interesting case of rotating black holes and show that the Fisher information is also sensitive to the rotation of a black hole. Full article

(This article belongs to the Special Issue Applications of Fisher Information in Sciences II)

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22 pages, 678 KiB

Open AccessArticle

Classical Versus Bayesian Error-Controlled Sampling Under Lognormal Distributions with Type II Censoring

by Huasen Zhou and Wenhao Gui

Entropy 2025, 27(5), 477; https://doi.org/10.3390/e27050477 - 28 Apr 2025

Abstract

This paper presents a comparative study of classical and Bayesian risks in the design of optimal failure-censored sampling plans for lognormal lifetime models. The analysis focuses on how variations in prior distributions, specifically the beta distribution for defect rates, influence the producer’s and [...] Read more.

This paper presents a comparative study of classical and Bayesian risks in the design of optimal failure-censored sampling plans for lognormal lifetime models. The analysis focuses on how variations in prior distributions, specifically the beta distribution for defect rates, influence the producer’s and consumer’s risks, along with the optimal sample size. We explore the sensitivity of the sampling plan’s risks to changes in the prior mean and variance, offering insight into the impacts of uncertainty in prior knowledge on sampling efficiency. Classical and Bayesian approaches are evaluated, highlighting the trade-offs between minimizing sample size and controlling risks for both the producer and the consumer. The results demonstrate that Bayesian methods generally provide more robust designs under uncertain prior information, while classical methods exhibit greater sensitivity to parameter changes. A computational procedure for determining the optimal sampling plans is provided, and the outcomes are validated through simulations, showcasing the practical implications for quality control in reliability testing and industrial applications. Full article

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

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16 pages, 304 KiB

Open AccessArticle

LDPC Codes on Balanced Incomplete Block Designs: Construction, Girth, and Cycle Structure Analysis

by Hengzhou Xu, Xiaodong Zhang, Mengmeng Xu, Haipeng Yu and Hai Zhu

Entropy 2025, 27(5), 476; https://doi.org/10.3390/e27050476 - 27 Apr 2025

Abstract

In this paper, we investigate the cycle structure inherent in the Tanner graphs of low-density parity-check (LDPC) codes constructed from balanced incomplete block designs (BIBDs). We begin by delineating the incidence structure of BIBDs and propose a methodology for constructing LDPC codes based [...] Read more.

In this paper, we investigate the cycle structure inherent in the Tanner graphs of low-density parity-check (LDPC) codes constructed from balanced incomplete block designs (BIBDs). We begin by delineating the incidence structure of BIBDs and propose a methodology for constructing LDPC codes based on these designs. By analyzing the incidence relations between points and blocks within a BIBD, we prove that the resulting LDPC codes possess a girth of 6. Subsequently, we provide a detailed analysis of the cycle structure of the constructed LDPC codes and introduce a systematic approach for enumerating their short cycles. Using this method, we determine the exact numbers of cycles of lengths 6 and 8. Simulation results demonstrate that the constructed LDPC codes exhibit excellent performance. Full article

(This article belongs to the Special Issue Advances in Modern Channel Coding)

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15 pages, 1473 KiB

Open AccessArticle

HECM-Plus: Hyper-Entropy Enhanced Cloud Models for Uncertainty-Aware Design Evaluation in Multi-Expert Decision Systems

by Jiaozi Pu and Zongxin Liu

Entropy 2025, 27(5), 475; https://doi.org/10.3390/e27050475 - 27 Apr 2025

Abstract

Uncertainty quantification in cloud models requires simultaneous characterization of fuzziness (via Entropy, En) and randomness (via Hyper-entropy, He), yet existing similarity measures often neglect the stochastic dispersion governed by He. To address this gap, we propose HECM-Plus, an algorithm integrating [...] Read more.

Uncertainty quantification in cloud models requires simultaneous characterization of fuzziness (via Entropy, En) and randomness (via Hyper-entropy, He), yet existing similarity measures often neglect the stochastic dispersion governed by He. To address this gap, we propose HECM-Plus, an algorithm integrating Expectation (Ex), En, and He to holistically model geometric and probabilistic uncertainties in cloud models. By deriving He-adjusted standard deviations through reverse cloud transformations, HECM-Plus reformulates the Hellinger distance to resolve conflicts in multi-expert evaluations where subjective ambiguity and stochastic randomness coexist. Experimental validation demonstrates three key advances: (1) Fuzziness–Randomness discrimination: HECM-Plus achieves balanced conceptual differentiation (δC₁/C₄ = 1.76, δC₂ = 1.66, δC₃ = 1.58) with linear complexity outperforming PDCM and HCCM by 10.3% and 17.2% in differentiation scores while resolving He-induced biases in HECM/ECM (C₁–C₄ similarity: 0.94 vs. 0.99) critical for stochastic dispersion modeling; (2) Robustness in time-series classification: It reduces the mean error by 6.8% (0.190 vs. 0.204, *p* < 0.05) with lower standard deviation (0.035 vs. 0.047) on UCI datasets, validating noise immunity; (3) Design evaluation application: By reclassifying controversial cases (e.g., reclassified from a “good” design (80.3/100 average) to “moderate” via cloud model using HECM-Plus), it resolves multi-expert disagreements in scoring systems. The main contribution of this work is the proposal of HECM-Plus, which resolves the limitation of HECM in neglecting He, thereby further enhancing the precision of normal cloud similarity measurements. The algorithm provides a practical tool for uncertainty-aware decision-making in multi-expert systems, particularly in multi-criteria design evaluation under conflicting standards. Future work will extend to dynamic expert weight adaptation and higher-order cloud interactions. Full article

(This article belongs to the Special Issue Entropy Method for Decision Making with Uncertainty)

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16 pages, 1467 KiB

Open AccessArticle

Quantum Phase Transition in the Coupled-Top Model: From Z₂ to U(1) Symmetry Breaking

by Wen-Jian Mao, Tian Ye, Liwei Duan and Yan-Zhi Wang

Entropy 2025, 27(5), 474; https://doi.org/10.3390/e27050474 - 27 Apr 2025

Abstract

We investigate the coupled-top model, which describes two large spins interacting along both x and y directions. By tuning coupling strengths along distinct directions, the system exhibits different symmetries, ranging from a discrete

Z_{2}

to a continuous U(1) symmetry. The anisotropic coupled-top [...] Read more.

We investigate the coupled-top model, which describes two large spins interacting along both x and y directions. By tuning coupling strengths along distinct directions, the system exhibits different symmetries, ranging from a discrete

Z_{2}

to a continuous U(1) symmetry. The anisotropic coupled-top model displays a discrete

Z_{2}

symmetry, and the symmetry breaking induced by strong coupling drives a quantum phase transition from a disordered paramagnetic phase to an ordered ferromagnetic or antiferromagnetic phase. In particular, the isotropic coupled-top model possesses a continuous U(1) symmetry, whose breaking gives rise to the Goldstone mode. The phase boundary can be well captured by the mean-field approach, characterized by the distinct behaviors of the order parameter. Higher-order quantum effects beyond the mean-field contribution can be achieved by mapping the large spins to bosonic operators via the Holstein–Primakoff transformation. For the anisotropic coupled-top model with

Z_{2}

symmetry, the energy gap closes, and both quantum fluctuations and entanglement entropy diverge near the critical point, signaling the onset of second-order quantum phase transitions. Strikingly, when U(1) symmetry is broken, the energy gap vanishes beyond the critical point, yielding a novel critical exponent of 1, rather than

1 / 2

for

Z_{2}

symmetry breaking. The rich symmetry structure of the coupled-top model underpins its role as a paradigmatic model for studying quantum phase transitions and exploring associated physical phenomena. Full article

(This article belongs to the Special Issue Entanglement Entropy and Quantum Phase Transition)

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24 pages, 3048 KiB

Open AccessArticle

Automatic Controversy Detection Based on Heterogeneous Signed Attributed Network and Deep Dual-Layer Self-Supervised Community Analysis

by Ying Li, Xiao Zhang, Yu Liang and Qianqian Li

Entropy 2025, 27(5), 473; https://doi.org/10.3390/e27050473 - 27 Apr 2025

Abstract

In this study, we propose a computational approach that applies text mining and deep learning to conduct controversy detection on social media platforms. Unlike previous research, our method integrates multidimensional and heterogeneous information from social media into a heterogeneous signed attributed network, encompassing [...] Read more.

In this study, we propose a computational approach that applies text mining and deep learning to conduct controversy detection on social media platforms. Unlike previous research, our method integrates multidimensional and heterogeneous information from social media into a heterogeneous signed attributed network, encompassing various users’ attributes, semantic information, and structural heterogeneity. We introduce a deep dual-layer self-supervised algorithm for community detection and analyze controversy within this network. A novel controversy metric is devised by considering three dimensions of controversy: community distinctions, betweenness centrality, and user representations. A comparison between our method and other classical controversy measures such as Random Walk, Biased Random Walk (BRW), BCC, EC, GMCK, MBLB, and community-based methods reveals that our model consistently produces more stable and accurate controversy scores. Additionally, we calculated the level of controversy and computed p-values for the detected communities on our crawled dataset Weibo, including #Microblog (3792), #Comment (45,741), #Retweet (36,126), and #User (61,327). Overall, our model had a comprehensive and nuanced understanding of controversy on social media platforms. To facilitate its use, we have developed a user-friendly web server. Full article

(This article belongs to the Section Complexity)

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