Entropy

16 pages, 2475 KiB

Open AccessArticle

Control of Inhibition-Stabilized Oscillations in Wilson-Cowan Networks with Homeostatic Plasticity

by Camille Godin, Matthew R. Krause, Pedro G. Vieira, Christopher C. Pack and Jean-Philippe Thivierge

Entropy 2025, 27(2), 215; https://doi.org/10.3390/e27020215 - 19 Feb 2025

Abstract

Interactions between excitatory and inhibitory neurons in the cerebral cortex give rise to different regimes of activity and modulate brain oscillations. A prominent regime in the cortex is the inhibition-stabilized network (ISN), defined by strong recurrent excitation balanced by inhibition. While theoretical models [...] Read more.

Interactions between excitatory and inhibitory neurons in the cerebral cortex give rise to different regimes of activity and modulate brain oscillations. A prominent regime in the cortex is the inhibition-stabilized network (ISN), defined by strong recurrent excitation balanced by inhibition. While theoretical models have captured the response of brain circuits in the ISN state, their connectivity is typically hard-wired, leaving unanswered how a network may self-organize to an ISN state and dynamically switch between ISN and non-ISN states to modulate oscillations. Here, we introduce a mean-rate model of coupled Wilson-Cowan equations, link ISN and non-ISN states to Kolmogorov-Sinai entropy, and demonstrate how homeostatic plasticity (HP) allows the network to express both states depending on its level of tonic activity. This mechanism enables the model to capture a broad range of experimental effects, including (i) a paradoxical decrease in inhibitory activity, (ii) a phase offset between excitation and inhibition, and (iii) damped gamma oscillations. Further, the model accounts for experimental work on asynchronous quenching, where an external input suppresses intrinsic oscillations. Together, findings show that oscillatory activity is modulated by the dynamical regime of the network under the control of HP, thus advancing a framework that bridges neural dynamics, entropy, oscillations, and synaptic plasticity. Full article

(This article belongs to the Section Entropy and Biology)

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6 pages, 206 KiB

Open AccessArticle

Lacunary Series and Strong Approximation

by István Berkes

Entropy 2025, 27(2), 214; https://doi.org/10.3390/e27020214 - 19 Feb 2025

Abstract

Strong approximation, introduced by Strassen (1964), is one of the most powerful methods to prove limit theorems in probability and statistics. In this paper we use strong approximation of lacunary series with conditionally independent sequences to prove uniform and permutation-invariant limit theorems for [...] Read more.

Strong approximation, introduced by Strassen (1964), is one of the most powerful methods to prove limit theorems in probability and statistics. In this paper we use strong approximation of lacunary series with conditionally independent sequences to prove uniform and permutation-invariant limit theorems for such series. Full article

(This article belongs to the Special Issue The Random Walk Path of Pál Révész in Probability)

25 pages, 5127 KiB

Open AccessArticle

Fault Root Cause Analysis Based on Liang–Kleeman Information Flow and Graphical Lasso

by Xiangdong Liu, Jie Liu, Xiaohua Yang, Zhiqiang Wu, Ying Wei, Zhuoran Xu and Juan Wen

Entropy 2025, 27(2), 213; https://doi.org/10.3390/e27020213 - 19 Feb 2025

Abstract

Root cause analysis is used to find the specific fault location and cause of a fault during system fault diagnosis. It is an important step in fault diagnosis. The root cause analysis method based on causality starts from the origin of the causal [...] Read more.

Root cause analysis is used to find the specific fault location and cause of a fault during system fault diagnosis. It is an important step in fault diagnosis. The root cause analysis method based on causality starts from the origin of the causal connection between transactions and infers the location and cause of the mechanism failure by analyzing the causal impact of variables between systems, which has methodological advantages. Causal analysis methods based on transfer entropy are proven to have biases in calculation results, so there is a phenomenon of calculating false causal relationships, which leads to the problem of insufficient accuracy in root cause analysis. Liang–Kleeman information flow (LKIF) is a kind of information entropy that can effectively carry out causal inference, which can avoid obtaining wrong causal relationships. We propose a root cause analysis method that combines graphical lasso and information flow. In view of the large amount of redundant information in industrial data due to the coupling effect of industrial systems, graphical lasso (Glasso) is a high-precision dimensionality reduction method suitable for large-scale and high-dimensional datasets. To ensure the timeliness of root cause analysis, graphical lasso uses dimensionality reduction of the data. Then, LKIF is used to calculate the information flow intensity of each relevant variable, infer the causal relationship between the variable pairs, and trace the root cause of the fault. On the Tennessee Eastman simulation platform, root cause analysis was performed on all faults, and two root cause analysis solutions, transfer entropy and information flow, were compared. Experimental results show that the LKIF–Glasso method can effectively detect the root cause of faults and display the propagation of faults throughout the process. It further shows that information flow has a better effect in root cause analysis than transfer entropy. And through the root cause analysis of the step failure of the stripper, the reason why information flow is superior to transfer entropy is explained in detail. Full article

(This article belongs to the Special Issue Entropy-Based Fault Diagnosis: From Theory to Applications)

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15 pages, 3884 KiB

Open AccessArticle

Research on Development Progress and Test Evaluation of Post-Quantum Cryptography

by Meng Zhang, Jing Wang, Junsen Lai, Mingfu Dong, Zhenzhong Zhu, Ryan Ma and Jun Yang

Entropy 2025, 27(2), 212; https://doi.org/10.3390/e27020212 - 18 Feb 2025

Abstract

With the rapid development of quantum computing technology, traditional cryptographic systems are facing unprecedented challenges. Post-Quantum Cryptography (PQC), as a new cryptographic technology that can resist attacks from quantum computers, has received widespread attention in recent years. This paper first analyzes the threat [...] Read more.

With the rapid development of quantum computing technology, traditional cryptographic systems are facing unprecedented challenges. Post-Quantum Cryptography (PQC), as a new cryptographic technology that can resist attacks from quantum computers, has received widespread attention in recent years. This paper first analyzes the threat of quantum computing to existing cryptographic systems, then introduces in detail the main technical routes of PQC and its standardization process. Then, a testing and evaluation system for PQC is proposed and relevant tests are carried out. Finally, suggestions for future development are put forward. Full article

(This article belongs to the Special Issue Quantum Information: Working towards Applications)

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11 pages, 1005 KiB

Open AccessArticle

OTFS Radar Waveform Design Based on Information Theory

by Qilong Miao, Ling Kuang, Ge Zhang and Yu Shao

Entropy 2025, 27(2), 211; https://doi.org/10.3390/e27020211 - 17 Feb 2025

Abstract

In this work, we consider the waveform design for radar systems based on orthogonal time–frequency space (OTFS). The conditional mutual information (CMI), chosen as a promising metric for assessing the radar cognitive capability, serves as the criterion for OTFS waveform design. After formulating [...] Read more.

In this work, we consider the waveform design for radar systems based on orthogonal time–frequency space (OTFS). The conditional mutual information (CMI), chosen as a promising metric for assessing the radar cognitive capability, serves as the criterion for OTFS waveform design. After formulating the OTFS waveform design problem based on maximizing CMI, we propose an equivalent waveform processing approach by minimizing the autocorrelation sidelobes and cross-correlations (ASaCC) of the OTFS transmitting matrix. Simulation results demonstrate that superior performance in target information extraction is achieved by the optimized OTFS waveforms compared to random waveforms. Full article

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

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26 pages, 3014 KiB

Open AccessArticle

Beamforming Design for STAR-RIS-Assisted NOMA with Binary and Coupled Phase-Shifts

by Yongfei Liu, Yuhuan Wang and Weizhang Xu

Entropy 2025, 27(2), 210; https://doi.org/10.3390/e27020210 - 17 Feb 2025

Abstract

This paper investigates the joint optimization of active and passive beamforming in simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-assisted non-orthogonal multiple access (NOMA) systems, with the aim of maximizing system throughput and improving overall performance. To achieve this goal, we propose an [...] Read more.

This paper investigates the joint optimization of active and passive beamforming in simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-assisted non-orthogonal multiple access (NOMA) systems, with the aim of maximizing system throughput and improving overall performance. To achieve this goal, we propose an iterative and efficient algorithmic framework. For active beamforming optimization, the fractional programming (FP) method is employed to reformulate the non-convex optimization problem into a convex problem, making it more tractable. Additionally, Nesterov’s extrapolation technique is introduced to enhance the convergence rate and reduce computational overhead. For the phase optimization of the STAR-RIS, a binary phase design method is proposed, which reformulates the binary phase optimization problem as a segmentation problem on the unit circle. This approach enables a closed form solution that can be derived in linear time. Simulation results demonstrate that the proposed algorithmic framework outperforms existing benchmark algorithms in terms of both system throughput and computational efficiency, verifying its effectiveness and practicality in STAR-RIS-assisted NOMA systems. Full article

(This article belongs to the Special Issue Entropy and Time–Frequency Signal Processing)

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19 pages, 4812 KiB

Open AccessArticle

Exploring Causal Network Complexity in Industrial Linkages: A Comparative Study

by Yongmei Ding, Chao Huang and Xubo Feng

Entropy 2025, 27(2), 209; https://doi.org/10.3390/e27020209 - 17 Feb 2025

Abstract

Industrial linkages play a crucial role in sustaining industrial agglomerations, driving economic growth, and shaping the spatial architecture of economic systems. This study explores the complexity of causal networks within the industrial ecosystems of China and the United States, using high-frequency economic data [...] Read more.

Industrial linkages play a crucial role in sustaining industrial agglomerations, driving economic growth, and shaping the spatial architecture of economic systems. This study explores the complexity of causal networks within the industrial ecosystems of China and the United States, using high-frequency economic data to compare the interdependencies and causal structures across key sectors. By employing the partial cross mapping (PCM) technique, we capture the dynamic interactions and intricate linkages among industries, providing a detailed analysis of inter-industry causality. Utilizing data from 32 Chinese industries and 11 United States industries spanning 2015 to 2023, our findings reveal that the United States, as a global leader in technology and finance, exhibits a diversified and service-oriented industrial structure, where financial and technology sectors are pivotal to economic propagation. In contrast, China’s industrial network shows higher centrality in heavy industries and manufacturing sectors, underscoring its focus on industrial output and export-led growth. A comparative analysis of the network topology and resilience highlights that China’s industrial structure enhances network stability and interconnectivity, fostering robust inter-industry linkages, whereas the limited nodal points in the United States network constrain its resilience. These insights into causal network complexity offer a comprehensive perspective on the structural dynamics and resilience of the economic systems in both countries. Full article

(This article belongs to the Section Complexity)

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28 pages, 6007 KiB

Open AccessArticle

Improving the CRCC-DHR Reliability: An Entropy-Based Mimic-Defense-Resource Scheduling Algorithm

by Xinghua Wu, Mingzhe Wang, Yun Cai, Xiaolin Chang and Yong Liu

Entropy 2025, 27(2), 208; https://doi.org/10.3390/e27020208 - 16 Feb 2025

Abstract

With more China railway business information systems migrating to the China Railway Cloud Center (CRCC), the attack surface is expanding and there are increasing security threats for the CRCC to deal with. Cyber Mimic Defense (CMD) technology, as an active defense strategy, can [...] Read more.

With more China railway business information systems migrating to the China Railway Cloud Center (CRCC), the attack surface is expanding and there are increasing security threats for the CRCC to deal with. Cyber Mimic Defense (CMD) technology, as an active defense strategy, can counter these threats by constructing a Dynamic Heterogeneous Redundancy (DHR) architecture. However, there are at least two challenges posed to the DHR deployment, namely, the limited number of available schedulable heterogeneous resources and memorization-based attacks. This paper aims to address these two challenges to improve the CRCC-DHR reliability and then facilitate the DHR deployment. By reliability, we mean that the CRCC-DHR with the limited number of available heterogeneous resources can effectively resist memorization-based attacks. We first propose three metrics for assessing the reliability of the CRCC-DHR architecture. Then, we propose an incomplete-information-based game model to capture the relationships between attackers and defenders. Finally, based on the proposed metrics and the captured relationship, we propose a redundant-heterogeneous-resources scheduling algorithm, called the Entropy Weight Scheduling Algorithm (REWS). We evaluate the capability of REWS with the three existing algorithms through simulations. The results show that REWS can achieve a better reliability than the other algorithms. In addition, REWS demonstrates a lower time complexity compared with the existing algorithms. Full article

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

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60 pages, 715 KiB

Open AccessArticle

New Formulas of Feedback Capacity for AGN Channels with Memory: A Time-Domain Sufficient Statistic Approach

by Charalambos D. Charalambous, Christos Kourtellaris and Stelios Louka

Entropy 2025, 27(2), 207; https://doi.org/10.3390/e27020207 - 15 Feb 2025

Abstract

Recently, several papers identified technical issues related to equivalent time-domain and frequency-domain “characterization of the n–block or transmission” feedback capacity formula and its asymptotic limit, the feedback capacity, of additive Gaussian noise (AGN) channels, first introduce by Cover and Pombra in 1989 [...] Read more.

Recently, several papers identified technical issues related to equivalent time-domain and frequency-domain “characterization of the n–block or transmission” feedback capacity formula and its asymptotic limit, the feedback capacity, of additive Gaussian noise (AGN) channels, first introduce by Cover and Pombra in 1989 (IEEE Transactions on Information Theory). The main objective of this paper is to derive new results on the Cover and Pombra characterization of the n–block feedback capacity formula, and to clarify the main points of confusion regarding the time-domain results that appeared in the literature. The first part of this paper derives new equivalent time-domain sequential characterizations of feedback capacity of AGN channels driven by non-stationary and non-ergodic Gaussian noise. It is shown that the optimal channel input processes of the new equivalent sequential characterizations are expressed as functionals of a sufficient statistic and a Gaussian orthogonal innovations process. Further, the Cover and Pombra n–block capacity formula is expressed as a functional of two generalized matrix difference Riccati equations (DREs) of the filtering theory of Gaussian systems, contrary to results that appeared in the literature and involve only one DRE. It is clarified that prior literature deals with a simpler problem that presupposes the state of the noise is known to the encoder and the decoder. In the second part of this paper, the existence of the asymptotic limit of the n–block feedback capacity formula is shown to be equivalent to the convergence properties of solutions of the two generalized DREs. Further, necessary and or sufficient conditions are identified for the existence of asymptotic limits, for stable and unstable Gaussian noise, when the optimal input distributions are asymptotically time-invariant but not necessarily stationary. This paper contains an in-depth analysis, with various examples, and identifies the technical conditions on the feedback code and state space noise realization, so that the time-domain capacity formulas that appeared in the literature, for AGN channels with stationary noises, are indeed correct. Full article

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

18 pages, 1334 KiB

Open AccessArticle

Transient Dynamics and Homogenization in Incoherent Collision Models

by Göktuğ Karpat and Barış Çakmak

Entropy 2025, 27(2), 206; https://doi.org/10.3390/e27020206 - 15 Feb 2025

Abstract

Collision models have attracted significant attention in recent years due to their versatility to simulate open quantum systems in different dynamical regimes. They have been used to study various interesting phenomena such as the dynamical emergence of non-Markovian memory effects and the spontaneous [...] Read more.

Collision models have attracted significant attention in recent years due to their versatility to simulate open quantum systems in different dynamical regimes. They have been used to study various interesting phenomena such as the dynamical emergence of non-Markovian memory effects and the spontaneous establishment of synchronization in open quantum systems. In such models, the repeated pairwise interactions between the system and the environment and also the possible coupling between different environmental units are typically modeled using the coherent partial SWAP (PSWAP) operation as it is known to be a universal homogenizer. In this study, we investigate the dynamical behavior of incoherent collision models, where the interactions between different units are modeled by the incoherent controlled SWAP (CSWAP) operation, which is also a universal homogenizer. Even though the asymptotic dynamics of the open system in cases of both coherent and incoherent swap interactions appear to be identical, its transient dynamics turns out to be significantly different. Here, we present a comparative analysis of the consequences of having coherent or incoherent couplings in collision models, namely, PSWAP or CSWAP interactions, respectively, for the emergence of memory effects for a single-qubit system and for the onset synchronization between a pair of qubits, both of which are strictly determined by the transient dynamics of the open system. Full article

(This article belongs to the Special Issue Simulation of Open Quantum Systems)

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15 pages, 3219 KiB

Open AccessArticle

Earthquake Forecasting Based on b Value and Background Seismicity Rate in Yunnan Province, China

by Yuchen Zhang, Rui Wang, Haixia Shi, Miao Miao, Jiancang Zhuang, Ying Chang, Changsheng Jiang, Lingyuan Meng, Danning Li, Lifang Liu, Youjin Su, Zhenguo Zhang and Peng Han

Entropy 2025, 27(2), 205; https://doi.org/10.3390/e27020205 - 15 Feb 2025

Abstract

Characterized by frequent earthquakes and a dense population, Yunnan Province, China, faces significant seismic hazards and is a hot place for earthquake forecasting research. In a previous study, we evaluated the performance of the b value for 5-year seismic forecasting during 2000–2019 and [...] Read more.

Characterized by frequent earthquakes and a dense population, Yunnan Province, China, faces significant seismic hazards and is a hot place for earthquake forecasting research. In a previous study, we evaluated the performance of the b value for 5-year seismic forecasting during 2000–2019 and made a forward prediction of M ≥ 5.0 earthquakes in 2020–2024. In this study, with the forecast period having passed, we first revisit the results and assess the forward prediction performance. Then, the background seismicity rate, which may also offer valuable long-term forecasting information, is incorporated into earthquake prediction for Yunnan Province. To assess the effectiveness of the prediction, the Molchan Error Diagram (MED), Probability Gain (PG), and Probability Difference (PD) are employed. Using a 25-year catalog, the spatial b value and background seismicity rate across five temporal windows are calculated, and 86 M ≥ 5.0 earthquakes as prediction samples are examined. The predictive performance of the background seismicity rate and b value is comprehensively tested and shown to be useful for 5-year forecasting in Yunnan. The performance of the b value exhibits a positive correlation with the predicted earthquake magnitude. The synergistic effect of combining these two predictors is also revealed. Finally, using the threshold corresponding to the maximum PD, we integrate the forecast information of background seismicity rates and the b value. A forward prediction is derived for the period from January 2025 to December 2029. This study can be helpful for disaster preparedness and risk management in Yunnan Province, China. Full article

(This article belongs to the Special Issue Time Series Analysis in Earthquake Complex Networks)

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(a) The b value from January 2015 to December 2019 and earthquakes with M ≥ 5.0 from January 2020 to December 2024. The dot and star are scaled to the magnitude. (b) Temporal distribution of earthquakes in Yunnan Province from January 2000 to December 2024. (c) Temporal distribution of earthquakes in Yunnan Province from January 2020 to December 2024. (d) The MED of forecast performance based on the b value in (a). The marked numbers are the serial numbers in <a href="#entropy-27-00205-t001" class="html-table">Table 1</a>, and the size of the cross markers is scaled to the magnitude. Full article ">Figure 2
The b value and background seismicity rate. (a–e) b value; (f,j) background seismicity rate. Results in (a,f) using catalog in 2000–2004 and forecasting moderate–large earthquakes in 2005–2009; (b,g) using catalog in 2005–2009 and forecasting moderate–large earthquakes in 2010–2014; (c,h) using catalog in 2010–2014 and forecasting moderate–large earthquakes in 2015–2019; (d,i) using catalog in 2015–2019 and forecasting moderate–large earthquakes in 2020–2024; (e,j) using catalog in 2020–2024. A dot represents an earthquake with 5.0 ≤ M < 5.5. A star represents an earthquake with M ≥ 5.5. The sizes of the dots and stars are scaled to magnitude. Full article ">Figure 3
Forecast performance based on b value and background seismicity rate during 2005–2024. (a–c) show the results of earthquakes with M ≥ 5.5. (a) MED; (b) PG; (c) PD. (d–f) are the results of earthquakes with M ≥ 5.0. (d) MED; (e) PG; (f) PD. The number of earthquake samples is <math display="inline"><semantics> <mrow> <mo>=</mo> <mn>29</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>N</mi> </mrow> <mrow> <mi>M</mi> <mo>≥</mo> <mn>5.0</mn> </mrow> </msub> <mo>=</mo> <mn>86</mn> </mrow> </semantics></math>. Full article ">Figure 4
The variation in forecast performance with earthquake magnitude. (a) Variation in maximum PG with the forecast magnitude; (b) variation in maximum PD with the forecast magnitude; (c) variation in S with the forecast magnitude. Full article ">Figure 5
Forecast performance by combining b value and background seismicity rate during 2005–2024. The x-axis is the alarming rate of background seismicity corresponding to <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>t</mi> <mi>h</mi> <mi>r</mi> </mrow> <mrow> <mi>μ</mi> </mrow> </msub> </mrow> </semantics></math>, and the y-axis is the alarming rate of the b value corresponding to <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>t</mi> <mi>h</mi> <mi>r</mi> </mrow> <mrow> <mi>b</mi> </mrow> </msub> </mrow> </semantics></math>. (a) PG for M ≥ 5.5 earthquakes; (b) PD for M ≥ 5.5 earthquakes; (c) PG for M ≥ 5.0 earthquakes; (d) PD for M ≥ 5.0 earthquakes. The location of the maximum value (PG or PD) in each figure is marked with dots and detailed in <a href="#entropy-27-00205-t002" class="html-table">Table 2</a>. The cross in (b) is located at the alarming rate corresponding to the maximum PD in <a href="#entropy-27-00205-f003" class="html-fig">Figure 3</a>c. Full article ">Figure 6
Alarmed regions for the period from January 2025 to December 2029 based on b value and background seismicity rate obtained during 2020–2024. (a) Alarmed area based on b value and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>t</mi> <mi>h</mi> <mi>r</mi> <mo>_</mo> <mi>P</mi> <mi>D</mi> </mrow> <mrow> <mi>b</mi> </mrow> </msub> </mrow> </semantics></math>, with 0.38 alarming rate; (b) alarmed area based on background seismicity rate and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>t</mi> <mi>h</mi> <mi>r</mi> <mo>_</mo> <mi>P</mi> <mi>D</mi> </mrow> <mrow> <mi>μ</mi> </mrow> </msub> </mrow> </semantics></math>, with 0.42 alarming rate; (c) alarmed area based on b value and background seismicity rate, with 0.20 alarming rate. The red edge squares show the alarmed grid cells. Full article ">

27 pages, 3309 KiB

Open AccessArticle

Quantum Thermometry for Ultra-Low Temperatures Using Probe and Ancilla Qubit Chains

by Asghar Ullah, Vipul Upadhyay and Özgür E. Müstecaplıoğlu

Entropy 2025, 27(2), 204; https://doi.org/10.3390/e27020204 - 14 Feb 2025

Abstract

We propose a scheme to enhance the range and precision of ultra-low temperature measurements by employing a probe qubit coupled to a chain of ancilla qubits. Specifically, we analyze a qubit chain governed by Heisenberg

X X

and Dzyaloshinskii–Moriya (DM) interactions. The precision [...] Read more.

We propose a scheme to enhance the range and precision of ultra-low temperature measurements by employing a probe qubit coupled to a chain of ancilla qubits. Specifically, we analyze a qubit chain governed by Heisenberg

X X

and Dzyaloshinskii–Moriya (DM) interactions. The precision limits of temperature measurements are characterized by evaluating quantum Fisher information (QFI). Our findings demonstrate that the achievable precision bounds, as well as the number of peaks in the QFI as a function of temperature, can be controlled by adjusting the number of ancilla qubits and the system’s model parameters. These results are interpreted in terms of the influence of energy transitions on the range and the number of QFI peaks as a function of temperature. This study highlights the potential of the probe qubit–ancilla chain system as a powerful and precise tool for quantum thermometry in the ultra-low temperature regime. Full article

(This article belongs to the Special Issue Simulation of Open Quantum Systems)

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20 pages, 844 KiB

Open AccessArticle

Maximum Entropy-Minimum Residual Model: An Optimum Solution to Comprehensive Evaluation and Multiple Attribute Decision Making

by Qi-Yi Tang and Yu-Xuan Lin

Entropy 2025, 27(2), 203; https://doi.org/10.3390/e27020203 - 14 Feb 2025

Abstract

To assess a subject with multiple factors or attributes, a comprehensive evaluation index, or say a composite indicator, is often constructed to make a holistic judgement. The key problem is to assign weights to the factors. There are various weighting methods in the [...] Read more.

To assess a subject with multiple factors or attributes, a comprehensive evaluation index, or say a composite indicator, is often constructed to make a holistic judgement. The key problem is to assign weights to the factors. There are various weighting methods in the literature, but a gold standard is lacking. Some weighting methods may lead to a trivial weight assignment that is one factor having a weight equal to 1 and the others all zero, while some methods generate a solution contradicting intuitive judgement, or even infeasible to calculate. This paper proposes a new model to generate weights based on the maximum entropy-minimum residual (MEMR) principle, directly estimating the relationship between factor weights and the composite indicator. The MEMR composite indicator extracts the common feature of multiple factors while preserving their diversity. This paper compares the MEMR model with other commonly used weighting methods in various case studies. The MEMR model has more robust, consistent, and interpretable results than others and is suitable for all comprehensive evaluation cases involving quantitative factors. The optimization technique of the proposed MEMR model and the related statistical tests are included as a package in the DPS (data processing system) software V21.05 for the convenience of application in all fields. Full article

(This article belongs to the Special Issue Number Theoretic Methods in Statistics: Theory and Applications)

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15 pages, 1714 KiB

Open AccessArticle

SAluMC: Thwarting Side-Channel Attacks via Random Number Injection in RISC-V

by Shibo Dang, Yunlong Shao, Zhida Li, Adetokunbo Makanju and Thomas Aaron Gulliver

Entropy 2025, 27(2), 202; https://doi.org/10.3390/e27020202 - 14 Feb 2025

Abstract

As processor performance advances, the cache has become an essential component of computer architecture. Moreover, the rapid digital transformation of daily life has resulted in electronic devices storing greater amounts of sensitive information. Thus, device users are becoming more concerned about the security [...] Read more.

As processor performance advances, the cache has become an essential component of computer architecture. Moreover, the rapid digital transformation of daily life has resulted in electronic devices storing greater amounts of sensitive information. Thus, device users are becoming more concerned about the security of their personal information, so improving processor performance is no longer the sole priority. Hardware vulnerabilities are generally more difficult to detect and address compared to software viruses and related threats. A common technique for exploiting hardware vulnerabilities is through side-channel attacks. They can bypass software security to extract personal information directly from hardware components like the cache or registers. This paper introduces a novel architecture for the arithmetic logic unit (ALU) and associated memory controller (MC) based on the RISC-V microarchitecture to mitigate side-channel attacks. The proposed approach employs hardware-generated random numbers and has minimal design costs, negligible impact on the original system structure, seamless integration, and easy modification of internal components. Results are presented that show it is effective against side-channel attacks. Full article

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

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16 pages, 7069 KiB

Open AccessArticle

Tradeoffs Between Richness and Bias of Augmented Data in Long-Tail Recognition

by Wei Dai, Yanbiao Ma, Jiayi Chen, Xiaohua Chen and Shuo Li

Entropy 2025, 27(2), 201; https://doi.org/10.3390/e27020201 - 14 Feb 2025

Abstract

In long-tail scenarios, models have a very high demand for high-quality data. Information augmentation, as an important class of data-centric methods, has been proposed to improve model performance by expanding the richness and quantity of samples in tail classes. However, the underlying mechanisms [...] Read more.

In long-tail scenarios, models have a very high demand for high-quality data. Information augmentation, as an important class of data-centric methods, has been proposed to improve model performance by expanding the richness and quantity of samples in tail classes. However, the underlying mechanisms behind the effectiveness of information augmentation methods remain underexplored. This has led to reliance on empirical and intricate fine-tuning in the use of information augmentation for long-tail recognition tasks. In this work, we simultaneously consider the richness gain and distribution shift introduced by information augmentation methods and propose effective information gain (EIG) to explore the mechanisms behind the effectiveness of these methods. We find that when the value of the effective information gain appropriately balances the richness gain and distribution shift, the performance of information augmentation methods is fully realized. Comprehensive experiments on long-tail benchmark datasets CIFAR-10-LT, CIFAR-100-LT, and ImageNet-LT demonstrate that using effective information gain to filter augmented data can further enhance model performance without any modifications to the model’s architecture. Therefore, in addition to proposing new model architectures, data-centric approaches also hold significant potential in the field of long-tail recognition. Full article

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

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In the traditional development cycle of AI models, researchers primarily focus on improving the model’s architecture or training techniques to enhance the performance of long-tail recognition. The common research paradigm involves assessing performance differences between different models, given training and test data. Data-centric long-tail learning, on the other hand, should keep the model constant and concentrate on improving the quality of the dataset. Full article ">Figure 2
(A) The data manifold corresponding to a class has boundaries, and samples outside the manifold boundaries may not exist in the real world, such as dogs with long wings. (B) Grid regions represent the diversity gain in features brought about by augmented samples. Full article ">Figure 3
Remix improves upon Mixup by modifying the synthesized labels so that when samples from head classes and tail classes are mixed, the resulting label is <math display="inline"><semantics> <mrow> <mn>100</mn> <mo>%</mo> </mrow> </semantics></math> contributed by the tail class. CMO uses CutMix to paste patches from tail class samples onto head class samples, thereby generating augmented samples. OFA decomposes sample features into class-specific and class-generic features and combines the tail class’s specific features with the head class’s generic features to generate augmented samples for the tail class. FDC observes that similar classes have similar distribution statistics (variances) and, thus, transfers the variance of the most similar head class to the tail class to re-estimate the distribution, sampling augmented samples from the new distribution. Full article ">Figure 4
The performances of information augmentation with different FDGs in CIFAR-10-LT. Full article ">Figure 5
The performances of information augmentation with different FDGs in CIFAR-100-LT. Full article ">Figure 6
Variation curve of the optimal EIG for augmented data across 10 CIFAR-10-LT datasets with different imbalance factors (IF = <math display="inline"><semantics> <mrow> <mi>i</mi> <mo>∗</mo> <mn>10</mn> <mo>(</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mn>10</mn> <mo>)</mo> </mrow> </semantics></math>). Full article ">Figure 7
(Left): Using the EIG to select augmented samples generated by Remix, CMO, OFA, and FDC in ImageNet-LT significantly improves the overall model performance. (Right): Performance improvement in tail classes, using EIG-selected augmented data. Full article ">

16 pages, 2425 KiB

Open AccessArticle

Adaptive Trust Evaluation Model Based on Entropy Weight Method for Sensing Terminal Process

by Tao Li and Yanyi Zhang

Entropy 2025, 27(2), 200; https://doi.org/10.3390/e27020200 - 14 Feb 2025

Abstract

Remote sensing (RS) has been widely used for data acquisition, monitoring, control, and intelligent decision-making. However, most of them are unattended and easily become the target of attack, which means there are still some risks in the sensing terminal processes. Therefore, trust evaluation [...] Read more.

Remote sensing (RS) has been widely used for data acquisition, monitoring, control, and intelligent decision-making. However, most of them are unattended and easily become the target of attack, which means there are still some risks in the sensing terminal processes. Therefore, trust evaluation of the processes associated with the sensing terminal is necessary. The existing trust evaluation model based on the sensing terminal process has some defects, such as low performance, low precision, and difficulty in effectively identifying malicious processes in the sensing terminal. In this paper, an adaptive trust evaluation model based on the entropy weight method is proposed to detect the sensing terminal process (PB-ATEM). By establishing two kinds of trust values, the direct trust value and the reciprocal trust value, we can comprehensively judge whether the process is trustworthy. For the direct trust value, we can dynamically capture the auto-correlation value of processes and establish a dynamic reward and punishment function to improve the response to malicious processes. For reciprocal trust values, k-means cluster analysis is used to classify processes, and the optimal entropy weight method is proposed to calculate the direct trust weight and reciprocal trust weight of each process more accurately, which accelerates the exposure of malicious processes. Finally, these two trust values are weighted to obtain the integrated trust value. The simulation results show that PB-ATEM can respond quickly to malicious processes. Compared with the existing trust evaluation models, it has higher detection accuracy and better ability to identify malicious processes. Full article

(This article belongs to the Special Issue Information-Theoretic Cryptography and Security)

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12 pages, 1184 KiB

Open AccessArticle

Three-Phase Confusion Learning

by Filippo Caleca, Simone Tibaldi and Elisa Ercolessi

Entropy 2025, 27(2), 199; https://doi.org/10.3390/e27020199 - 14 Feb 2025

Abstract

The use of Neural Networks in quantum many-body theory has undergone a formidable rise in recent years. Among the many possible applications, their pattern recognition power can be utilized when dealing with the study of equilibrium phase diagrams. Learning by Confusion has emerged [...] Read more.

The use of Neural Networks in quantum many-body theory has undergone a formidable rise in recent years. Among the many possible applications, their pattern recognition power can be utilized when dealing with the study of equilibrium phase diagrams. Learning by Confusion has emerged as an interesting and unbiased scheme within this context. This technique involves systematically reassigning labels to the data in various ways, followed by training and testing the Neural Network. While random labeling results in low accuracy, the method reveals a peak in accuracy when the data are correctly and meaningfully partitioned, even if the correct labeling is initially unknown. Here, we propose a generalization of this confusion scheme for systems with more than two phases, for which it was originally proposed. Our construction relies on the use of a slightly different Neural Network: from a binary classifier, we move to a ternary one, which is more suitable to detect systems exhibiting three phases. After introducing this construction, we test it on free and interacting Kitaev chains and on the one-dimensional Extended Hubbard model, consistently achieving results that are compatible with previous works. Our work opens the way to wider use of Learning by Confusion, demonstrating once more the usefulness of Machine Learning to address quantum many-body problems. Full article

(This article belongs to the Section Statistical Physics)

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30 pages, 4693 KiB

Open AccessArticle

A Perturbative Approach to the Solution of the Thirring Quantum Cellular Automaton

by Alessandro Bisio, Paolo Perinotti, Andrea Pizzamiglio and Saverio Rota

Entropy 2025, 27(2), 198; https://doi.org/10.3390/e27020198 - 13 Feb 2025

Abstract

The Thirring Quantum Cellular Automaton (QCA) describes the discrete time dynamics of local fermionic modes that evolve according to one step of the Dirac cellular automaton, followed by the most general on-site number-preserving interaction, and serves as the QCA counterpart of the Thirring [...] Read more.

The Thirring Quantum Cellular Automaton (QCA) describes the discrete time dynamics of local fermionic modes that evolve according to one step of the Dirac cellular automaton, followed by the most general on-site number-preserving interaction, and serves as the QCA counterpart of the Thirring model in quantum field theory. In this work, we develop perturbative techniques for the QCA path sum approach, expanding both the number of interaction vertices and the mass parameter of the Thirring QCA. By classifying paths within the regimes of very light and very heavy particles, we computed the transition amplitudes in the two- and three-particle sectors to the first few orders. Our investigation into the properties of the Thirring QCA, addressing the combinatorial complexity of the problem, yielded some useful results applicable to the many-particle sector of any on-site number-preserving interactions in one spatial dimension. Full article

(This article belongs to the Special Issue Recent Advances and Challenges in Quantum Cellular Automata)

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21 pages, 5719 KiB

Open AccessArticle

Exergy Analysis of a Convective Heat Pump Dryer Integrated with a Membrane Energy Recovery Ventilator

by Anand Balaraman, Md Ashiqur Rahman, Davide Ziviani and David M. Warsinger

Entropy 2025, 27(2), 197; https://doi.org/10.3390/e27020197 - 13 Feb 2025

Abstract

To increase energy efficiency, heat pump dryers and membrane dryers have been proposed to replace conventional fossil fuel dryers. Both conventional and heat pump dryers require substantial energy for condensing and reheating, while “active” membrane systems require vacuum pumps that are insufficiently developed. [...] Read more.

To increase energy efficiency, heat pump dryers and membrane dryers have been proposed to replace conventional fossil fuel dryers. Both conventional and heat pump dryers require substantial energy for condensing and reheating, while “active” membrane systems require vacuum pumps that are insufficiently developed. Lower temperature dehumidification systems make efficient use of membrane energy recovery ventilators (MERVs) that do not need vacuum pumps, but their high heat losses and lack of vapor selectivity have prevented their use in industrial drying. In this work, we propose an insulating membrane energy recovery ventilator for moisture removal from drying exhaust air, thereby reducing sensible heat loss from the dehumidification process and reheating energy. The second law analysis of the proposed system is carried out and compared with a baseline convective heat pump dryer. Irreversibilities in each component under different ambient temperatures (5–35 °C) and relative humidity (5–95%) are identified. At an ambient temperature of 35 °C, the proposed system substantially reduces sensible heat loss (47–60%) in the dehumidification process, resulting in a large reduction in condenser load (45–50%) compared to the baseline system. The evaporator in the proposed system accounts for up to 59% less irreversibility than the baseline system. A maximum of 24.5% reduction in overall exergy input is also observed. The highest exergy efficiency of 10.2% is obtained at an ambient condition of 35 °C and 5% relative humidity, which is more than twice the efficiency of the baseline system under the same operating condition. Full article

(This article belongs to the Special Issue Thermodynamic Optimization of Energy Systems)

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20 pages, 932 KiB

Open AccessArticle

Gradient-Based Multiple Robust Learning Calibration on Data Missing-Not-at-Random via Bi-Level Optimization

by Shuxia Gong and Chen Ma

Entropy 2025, 27(2), 196; https://doi.org/10.3390/e27020196 - 13 Feb 2025

Abstract

Recommendation systems (RS) have become integral to numerous digital platforms and applications, ranging from e-commerce to content streaming field. A critical problem in RS is that the ratings are missing not at random (MNAR), which is due to the users always giving feedback [...] Read more.

Recommendation systems (RS) have become integral to numerous digital platforms and applications, ranging from e-commerce to content streaming field. A critical problem in RS is that the ratings are missing not at random (MNAR), which is due to the users always giving feedback on items with self-selection. The biased selection of rating data results in inaccurate rating prediction for all user-item pairs. Doubly robust (DR) learning has been studied in many tasks in RS, which is unbiased when either a single imputation or a single propensity model is accurate. In addition, multiple robust (MR) has been proposed with multiple imputation models and propensity models, and is unbiased when there exists a linear combination of these imputation models and propensity models is correct. However, we claim that the imputed errors and propensity scores are miscalibrated in the MR method. In this paper, we propose a gradient-based calibrated multiple robust learning method to enhance the debiasing performance and reliability of the rating prediction model. Specifically, we propose to use bi-level optimization to solve the weights and model coefficients of each propensity and imputation model in MR framework. Moreover, we adopt the differentiable expected calibration error as part of the objective to optimize the model calibration quality directly. Experiments on three real-world datasets show that our method outperforms the state-of-the-art baselines. Full article

(This article belongs to the Special Issue Causal Inference in Recommender Systems)

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10 pages, 448 KiB

Open AccessArticle

Revisiting Endoreversible Carnot Engine: Extending the Yvon Engine

by Xiu-Hua Zhao and Yu-Han Ma

Entropy 2025, 27(2), 195; https://doi.org/10.3390/e27020195 - 13 Feb 2025

Abstract

Curzon and Ahlborn’s 1975 paper, a pioneering work that inspired the birth of the field of finite-time thermodynamics, unveiled the efficiency at maximum power (EMP) of the endoreversible Carnot heat engine, now commonly referred to as the Curzon–Ahlborn (CA) engine. Historically, despite the [...] Read more.

Curzon and Ahlborn’s 1975 paper, a pioneering work that inspired the birth of the field of finite-time thermodynamics, unveiled the efficiency at maximum power (EMP) of the endoreversible Carnot heat engine, now commonly referred to as the Curzon–Ahlborn (CA) engine. Historically, despite the significance of the CA engine, similar findings had emerged at an earlier time, such as the Yvon engine proposed by J. Yvon in 1955 that shares the exact same EMP, that is, the CA efficiency

η_{CA}

. However, the special setup of the Yvon engine has circumscribed its broader influence. This paper extends the Yvon engine model to achieve a level of generality comparable to that of the CA engine. With the power expression of the extended Yvon engine, we directly explain the universality that

η_{CA}

is independent of the heat transfer coefficients between the working substance and the heat reservoirs. A rigorous comparison reveals that the extended Yvon engine and CA engine represent the steady-state and cyclic forms of the endoreversible Carnot heat engine, respectively, and are equivalent. Full article

(This article belongs to the Special Issue The First Half Century of Finite-Time Thermodynamics)

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Figure 1
Steady-state (a,b) and cyclic (c,d) endoreversible heat engines. (a) In the original Yvon engine, finite heat flux (denoted as <math display="inline"><semantics> <mover accent="true"> <mi>Q</mi> <mo>˙</mo> </mover> </semantics></math>) occurs only at the high-temperature end, where there is a temperature difference between the working substance and the hot reservoir. (b) The extended Yvon engine introduces temperature differences, and thus, heat fluxes, between the working substance and both the hot and cold reservoirs. (c,d) show the entropy (S)–temperature (T) diagrams of the endoreversible Carnot engine cycles with finite heat fluxes (denoted as <math display="inline"><semantics> <mover accent="true"> <mi>q</mi> <mo>˙</mo> </mover> </semantics></math>) along the high-temperature and both isothermal branches, respectively. Full article ">Figure 2
Trade-off relations between power and efficiency for the Curzon-Ahlborn engine with <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi mathvariant="normal">C</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (dash-dotted curve), <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi mathvariant="normal">C</mi> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math> (dashed curve), and <math display="inline"><semantics> <mrow> <msub> <mi>η</mi> <mi mathvariant="normal">C</mi> </msub> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math> (solid curve). The triangles and circle mark the maximum power and maximum efficiency, respectively. Full article ">

11 pages, 546 KiB

Open AccessTechnical Note

The Density Profile of a Neutron Star

by Allan D. Woodbury

Entropy 2025, 27(2), 194; https://doi.org/10.3390/e27020194 - 13 Feb 2025

Abstract

The problem posed in this study is to determine the density distribution within an ideal spherically symmetric neutron star based on only two constraints: the volumetrically averaged density and a moment of inertia factor, f. In order to deal with the above, [...] Read more.

The problem posed in this study is to determine the density distribution within an ideal spherically symmetric neutron star based on only two constraints: the volumetrically averaged density and a moment of inertia factor, f. In order to deal with the above, it is recognized that space within these objects is heavily curved, and thus lengths, densities, and the moment of inertia have to be adjusted for relativistic effects. For the first time, the minimum relative entropy methodology (MRE) is used to find the expected value of a series of effective densities within a neutron star. In numerical experiments, we use the data from the star PSR J0737-3039A, which has a mass of

2.6 \times 10^{30}

kg and a radius of 13.75 km. Here, the factor f is based on a range of values of moments of inertia (MOI): 1.30–1.63

\times 10^{45}

g cm². For

f = 0.324

, at no time do densities cross over

1 \times 10^{15}

gm/cc. For the most part, densities >

6 \times 10^{14}

gm/cc are shown at radial dimensions of less than about 4 km. When

f = 0.258

, densities closer to the core are pushed higher, as one might expect, and peak at slightly over

4 \times 10^{15}

gm/cc. If recent values of MOI are more appropriate at

1.15 \times 10^{45}

g cm², this then suggests core densities greater than

4 \times 10^{15}

gm/cc. These various density models lead to quantitative statements about qualitative interpretations, and as time goes on, any internal density models should satisfy the two constraints posed. Also, since the model presented here is probabilistic, it can be established that density at a certain depth is constrained within a certain confidence limit. The expected values of densities for PSR J0737-3039A are in reasonable agreement with current conceptual neutron star models but are highly sensitive to assumed MOI values. It is emphasized that the probabilities and the mean values of density obtained are conditional on the imposed moments, namely,

M

and f, and also the radius

R

. Full article

(This article belongs to the Section Multidisciplinary Applications)

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Figure 1
Conceptual model of a neutron star and its interior. Credit NASA/B. Link, <a href="https://heasarc.gsfc.nasa.gov" target="_blank">https://heasarc.gsfc.nasa.gov</a>. Full article ">Figure 2
Star J0737-3039A. Expected values of density for different values of moment of inertia (MOI) factors, f. The dashed line is the expected value of prior probability, which is a uniform prior <math display="inline"><semantics> <mrow> <mn>2.4</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>14</mn> </msup> </mrow> </semantics></math> gm/cc in the radial direction. Full article ">Figure 3
SR J0737-3039A. Expected values of density for two different values of moment of inertia factor f. The dashed line is the expected value of prior probability, which, in this case, is a zoned conceptual model loosely based on the conceptual model of <a href="#entropy-27-00194-f001" class="html-fig">Figure 1</a>. Full article ">Figure 4
Assumed conceptual model of a neutron star studied by [<a href="#B20-entropy-27-00194" class="html-bibr">20</a>]. The expected value of density for assumed values of moment of inertia factor f. The dashed line is the expected value of prior probability from nuclear model V18. The dashed line is a uniform prior in the radial direction. Full article ">

17 pages, 5697 KiB

Open AccessArticle

Alkali Halide Aqueous Solutions Under Pressure: A Non-Equilibrium Molecular Dynamics Investigation of Thermal Transport and Thermodiffusion

by Guansen Zhao and Fernando Bresme

Entropy 2025, 27(2), 193; https://doi.org/10.3390/e27020193 - 13 Feb 2025

Abstract

Thermal gradients induce thermodiffusion in aqueous solutions, a non-equilibrium effect arising from the coupling of thermal and mass fluxes. While thermal transport processes have garnered significant attention under standard conditions, thermal transport at high pressures and temperatures, typical of the Earth’s crust, has [...] Read more.

Thermal gradients induce thermodiffusion in aqueous solutions, a non-equilibrium effect arising from the coupling of thermal and mass fluxes. While thermal transport processes have garnered significant attention under standard conditions, thermal transport at high pressures and temperatures, typical of the Earth’s crust, has escaped scrutiny. Non-equilibrium thermodynamics theory and non-equilibrium molecular dynamics simulations provide an excellent means to quantify thermal transport under extreme conditions and establish a connection between the behaviour of the solutions and their microscopic structure. Here, we investigate the thermal conductivity and thermal diffusion of NaCl and LiCl solutions in the GPa pressure regime, targeting temperatures between 300 K and 1000 K at 1 molal concentration. We employ non-equilibrium molecular dynamics simulations along with the Madrid-2019 and TIP4P/2005 force fields. The thermal conductivity of the solutions increases significantly with pressure, and following the behaviour observed at standard pressure, the thermal conductivity is lower than that of pure water. The reduction in thermal conductivity is significant in the GPa pressure regime, ∼3% for 1 molal NaCl and LiCl solutions. We demonstrate that under GPa pressure conditions, the solutions feature thermophobic behaviour, with ions migrating towards colder regions. The pronounced impact of pressure is more evident in LiCl solutions, which display a thermophilic to thermophobic “transition” at pressures above 0.25 GPa. We discuss a correlation between the solution’s thermophobicity and the disruption of the water hydrogen bond structure at high pressure, where the water structure resembles that observed in simple liquids. Full article

(This article belongs to the Special Issue The Entropy Production—as Cornerstone in Applied Nonequilibrium Thermodynamics—Dedicated to Professor Signe Kjelstrup on the Occasion of Her 75th Birthday)

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20 pages, 8250 KiB

Open AccessArticle

Fault Diagnosis of Wind Turbine Gearbox Based on Improved Multivariate Variational Mode Decomposition and Ensemble Refined Composite Multivariate Multiscale Dispersion Entropy

by Xin Xia, Xiaolu Wang and Weilin Chen

Entropy 2025, 27(2), 192; https://doi.org/10.3390/e27020192 - 13 Feb 2025

Abstract

Wind turbine planetary gearboxes have complex structures and operating environments, which makes it difficult to extract fault features effectively. In addition, it is difficult to achieve efficient fault diagnosis. To improve the efficiency of feature extraction and fault diagnosis, a fault diagnosis method [...] Read more.

Wind turbine planetary gearboxes have complex structures and operating environments, which makes it difficult to extract fault features effectively. In addition, it is difficult to achieve efficient fault diagnosis. To improve the efficiency of feature extraction and fault diagnosis, a fault diagnosis method based on improved multivariate variational mode decomposition (IMVMD) and ensemble refined composite multivariate multiscale dispersion entropy (ERCmvMDE) with multi-channel vibration data is proposed. Firstly, the IMVMD is proposed to obtain the optimal parameters of the MVMD, which would make the MVMD more effective. Secondly, the ERCmvMDE is proposed to extract rich and effective feature information. Finally, the fault diagnosis of the planetary gearbox is achieved using the least squares support vector machine (LSSVM) with features consisting of ERCmvMDE. Simulations and experimental studies indicate that the proposed method performs feature extraction well and obtains higher fault diagnosis accuracy. Full article

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

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17 pages, 221 KiB

Open AccessReview

Complexity, Uncertainty, and Entropy: Applications to Food Sensory Perception and Other Complex Phenomena

by Luka Sturtewagen, Harald van Mil and Erik van der Linden

Entropy 2025, 27(2), 191; https://doi.org/10.3390/e27020191 - 13 Feb 2025

Abstract

Complexity has been studied in various areas of science, such as ecology and sensory science. One important aspect is the quantification of the complexity of a system. There exist a multitude of different approaches. One approach relates complexity to information, with its measure [...] Read more.

Complexity has been studied in various areas of science, such as ecology and sensory science. One important aspect is the quantification of the complexity of a system. There exist a multitude of different approaches. One approach relates complexity to information, with its measure introduced by Shannon. This is equal to the negative value of entropy, or uncertainty. In this review, we discuss the different approaches that are used to quantify and measure complexity in the realm of food sensory perception. We address how the food sensory field could benefit from an approach that is based on an information-theoretical footing, to allow for one quantitative measure, thus improving comparison and reproducibility among different laboratories. Reversely, the review is intended to inspire the physics community to explore complex phenomena, such as sensory perception, in terms of a general information-theoretical measure, such as entropy and other fields. Full article

(This article belongs to the Special Issue The Entropy Production—as Cornerstone in Applied Nonequilibrium Thermodynamics—Dedicated to Professor Signe Kjelstrup on the Occasion of Her 75th Birthday)

21 pages, 1531 KiB

Open AccessArticle

Dual-Regularized Feature Selection for Class-Specific and Global Feature Associations

by Chenchen Wang, Jun Wang, Yanfei Li, Chengkai Piao and Jinmao Wei

Entropy 2025, 27(2), 190; https://doi.org/10.3390/e27020190 - 13 Feb 2025

Abstract

Understanding feature associations is vital for selecting the most informative features. Existing methods primarily focus on global feature associations, which capture overall relationships across all samples. However, they often overlook class-specific feature interactions, which are essential for capturing locality features that may only [...] Read more.

Understanding feature associations is vital for selecting the most informative features. Existing methods primarily focus on global feature associations, which capture overall relationships across all samples. However, they often overlook class-specific feature interactions, which are essential for capturing locality features that may only be significant within certain classes. In this paper, we propose Dual-Regularized Feature Selection (DRFS), which incorporates two feature association regularizers to address both class-specific and global feature relationships. The class-specific regularizer captures the local geometric structure of features within each class. Meanwhile, the global regularizer utilizes a global feature similarity matrix to eliminate redundant features across classes. By combining these regularizers, DRFS selects features that preserve both local interactions within each class and global discriminative power, with each regularizer complementing the other to enhance feature selection. Experimental results on eight public real-world datasets demonstrate that DRFS outperforms existing methods in classification accuracy. Full article

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

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13 pages, 2862 KiB

Open AccessArticle

Solving Flexible Job-Shop Scheduling Problems Based on Quantum Computing

by Kaihan Fu, Jianjun Liu, Miao Chen and Huiying Zhang

Entropy 2025, 27(2), 189; https://doi.org/10.3390/e27020189 - 13 Feb 2025

Abstract

Flexible job-shop scheduling problems (FJSPs) represent one of the most complex combinatorial optimization challenges. Modern production systems and control processes demand rapid decision-making in scheduling. To address this challenge, we propose a quantum computing approach for solving FJSPs. We propose a quadratic unconstrained [...] Read more.

Flexible job-shop scheduling problems (FJSPs) represent one of the most complex combinatorial optimization challenges. Modern production systems and control processes demand rapid decision-making in scheduling. To address this challenge, we propose a quantum computing approach for solving FJSPs. We propose a quadratic unconstrained binary optimization (QUBO) model to minimize the makespan of FJSPs, with the scheduling scheme encoded in the ground state of the Hamiltonian operator. The model is solved using a coherent Ising machine (CIM). Numerical experiments are conducted to evaluate and validate the performance and effectiveness of the CIM. The results demonstrate that quantum computing holds significant potential for solving FJSPs more efficiently than traditional computational methods. Full article

(This article belongs to the Special Issue Quantum Information: Working towards Applications)

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21 pages, 335 KiB

Open AccessArticle

On the Global Practical Exponential Stability of h-Manifolds for Impulsive Reaction–Diffusion Cohen–Grossberg Neural Networks with Time-Varying Delays

by Gani Stamov, Trayan Stamov, Ivanka Stamova and Cvetelina Spirova

Entropy 2025, 27(2), 188; https://doi.org/10.3390/e27020188 - 12 Feb 2025

Abstract

In this paper, we focus on h-manifolds related to impulsive reaction–diffusion Cohen–Grossberg neural networks with time-varying delays. By constructing a new Lyapunov-type function and a comparison principle, sufficient conditions that guarantee the global practical exponential stability of specific states are established. The [...] Read more.

In this paper, we focus on h-manifolds related to impulsive reaction–diffusion Cohen–Grossberg neural networks with time-varying delays. By constructing a new Lyapunov-type function and a comparison principle, sufficient conditions that guarantee the global practical exponential stability of specific states are established. The states of interest are determined by the so-called h-manifolds, i.e., manifolds defined by a specific function h, which is essential for various applied problems in imposing constraints on their dynamics. The established criteria are less restrictive for the variable domain and diffusion coefficients. The effect of some uncertain parameters on the stability behavior is also considered and a robust practical stability analysis is proposed. In addition, the obtained h-manifolds’ practical stability results are applied to a bidirectional associative memory (BAM) neural network model with impulsive perturbations and time-varying delays. Appropriate examples are discussed. Full article

(This article belongs to the Special Issue Dynamics in Complex Neural Networks, 2nd Edition)

13 pages, 359 KiB

Open AccessArticle

Entropic Probability and Context States

by Benjamin Schumacher and Michael D. Westmoreland

Entropy 2025, 27(2), 187; https://doi.org/10.3390/e27020187 - 12 Feb 2025

Abstract

In a previous paper, we introduced an axiomatic system for information thermodynamics, deriving an entropy function that includes both thermodynamic and information components. From this function, we derived an entropic probability distribution for certain uniform collections of states. Here, we extend the concept [...] Read more.

In a previous paper, we introduced an axiomatic system for information thermodynamics, deriving an entropy function that includes both thermodynamic and information components. From this function, we derived an entropic probability distribution for certain uniform collections of states. Here, we extend the concept of entropic probability to more general collections, augmenting the states by reservoir and context states. This leads to an abstract concept of free energy and establishes a relation between free energy, information erasure, and generalized work. Full article

(This article belongs to the Section Thermodynamics)

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15 pages, 1088 KiB

Open AccessArticle

A Novel Evaluation of Income Class Boundaries Using Inflection Points of Probability Density Functions: A Case Study of Brazil

by Rafael Bittencourt, Hernane Borges de Barros Pereira, Marcelo A. Moret, Ivan C. Da Cunha Lima and Serge Galam

Entropy 2025, 27(2), 186; https://doi.org/10.3390/e27020186 - 12 Feb 2025

Abstract

Categorizing a population into different income classes is important for creating effective policies and analyzing markets. Our study develops a statistical method based on a nationwide survey of income distribution. We use these data to create a cumulative distribution function with a metalogistic [...] Read more.

Categorizing a population into different income classes is important for creating effective policies and analyzing markets. Our study develops a statistical method based on a nationwide survey of income distribution. We use these data to create a cumulative distribution function with a metalogistic distribution and its probability density function. We propose a new way to divide the population into income classes by using the inflection points of the probability density function as the class boundaries. As a case study, we apply this method to income data from Brazil between 2012 and 2022. We identify five income classes, with both their boundaries and the distribution of the population changing over time. To check our approach, we calculate the Gini coefficient and find that our results closely match official figures, with a root mean square deviation of less than 1%. By using individual income instead of family income, we avoid distortions caused by the fact that poorer families tend to be larger than wealthier ones. In the end, we identify five main income classes, with their boundaries shifting each year, reflecting the changing nature of income distribution in society. Full article

(This article belongs to the Special Issue Computational and Statistical Physics Approaches for Complex Systems and Social Phenomena, 3rd Edition)

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Figure 1
Mean absolute error (MAE) for each year from 2012 to 2022, for metalog quantile functions with different numbers of parameters (from <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> up to <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>). Full article ">Figure 2
Quantile probability function of the logarithm of monthly per capita income for the population segments in <a href="#entropy-27-00186-t001" class="html-table">Table 1</a>. The curves are derived from fitting a metalogistic distribution function with <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>. Full article ">Figure 3
The figure presents the average Lorenz curve derived from the metalogistic treatment with <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> for the period 2012–2022. The Gini coefficient associated with this curve is <math display="inline"><semantics> <mrow> <mi>G</mi> <mo>=</mo> <mn>0.528</mn> </mrow> </semantics></math>. Full article ">Figure 4
Metalogistic PDF for the presidential terms: the last three years of 2011–2014 (a), 2015–2018 (b), and 2019–2022 (c). Full article ">Figure 5
Second derivative of the PDF through the years 2012 (a) up to 2022 (k). The ascending PDF rates are represented in blue, while the descending rates are in red. The points where the curves change colors show the inflection points that define the boundaries of classes in our model. Full article ">Figure 6
The bar plots illustrate the distribution of the population across different income classes (a) and the income thresholds defining each class (b) from 2012 to 2022. Full article ">

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Entropy, Volume 27, Issue 2 (February 2025) – 119 articles

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