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Entropy, Volume 25, Issue 1 (January 2023) – 179 articles

Cover Story (view full-size image): A molecular electronic wavefunction prepared at a highly excited adiabatic state embedded in a densely quasi-degenerate manifold quickly begins to undergo continual nonadiabatic mixing with other states, each of which in turn further mixes with other states. The mixing is caused by the so-called nonadiabatic interactions due to a significant breakdown of the Born–Oppenheimer approximations. The resultant electronic wavepacket penetrates into the broader domain in the Hilbert space, and thus, the dynamics looks like a fractional Brownian motion. A monotonically increasing Shannon entropy and other indicators highlight the presence of quantum chaos in the electronic state of molecules. This intensive chaos brings about peculiar characteristics in the dynamics of molecules. View this paper
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16 pages, 7267 KiB  
Article
Numerical Investigation on the Effect of Section Width on the Performance of Air Ejector with Rectangular Section
by Ying Zhang, Jingming Dong, Shuaiyu Song, Xinxiang Pan, Nan He and Manfei Lu
Entropy 2023, 25(1), 179; https://doi.org/10.3390/e25010179 - 16 Jan 2023
Cited by 3 | Viewed by 2131
Abstract
Due to its simple structure and lack of moving parts, the supersonic air ejector has been widely applied in the fields of machinery, aerospace, and energy-saving. The performance of the ejector is influenced by the flow channel structure and the velocity of the [...] Read more.
Due to its simple structure and lack of moving parts, the supersonic air ejector has been widely applied in the fields of machinery, aerospace, and energy-saving. The performance of the ejector is influenced by the flow channel structure and the velocity of the jet, thus the confined jet is an important limiting factor for the performance of the supersonic air ejector. In order to investigate the effect of the confined jet on the performance of the ejector, an air ejector with a rectangular section was designed. The effects of the section width (Wc) on the entrainment ratio, velocity distribution, turbulent kinetic energy distribution, Mach number distribution, and vorticity distribution of the rectangular section air ejector were studied numerically. The numerical results indicated that the entrainment ratio of the rectangular section air ejector increased from 0.34 to 0.65 and the increment of the ER was 91.2% when the section width increased from 1 mm to 10 mm. As Wc increased, the region of the turbulent kinetic energy gradually expanded. The energy exchange between the primary fluid and the secondary fluid was mainly in the form of turbulent diffusion in the mixing chamber. In addition to Wc limiting the fluid flow in the rectangular section air ejector, the structure size of the rectangular section air ejector in the XOY plane also had a limiting effect on the internal fluid flow. In the rectangular section air ejector, the streamwise vortices played an important role in the mixing process. The increase of Wc would increase the distribution of the streamwise vortices in the constant-area section. Meanwhile, the distribution of the spanwise vortices would gradually decrease. Full article
(This article belongs to the Special Issue Entropy and Exergy Analysis in Ejector-Based Systems)
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29 pages, 7443 KiB  
Article
Multi-Level Thresholding Image Segmentation Based on Improved Slime Mould Algorithm and Symmetric Cross-Entropy
by Yuanyuan Jiang, Dong Zhang, Wenchang Zhu and Li Wang
Entropy 2023, 25(1), 178; https://doi.org/10.3390/e25010178 - 16 Jan 2023
Cited by 8 | Viewed by 3132
Abstract
Multi-level thresholding image segmentation divides an image into multiple regions of interest and is a key step in image processing and image analysis. Aiming toward the problems of the low segmentation accuracy and slow convergence speed of traditional multi-level threshold image segmentation methods, [...] Read more.
Multi-level thresholding image segmentation divides an image into multiple regions of interest and is a key step in image processing and image analysis. Aiming toward the problems of the low segmentation accuracy and slow convergence speed of traditional multi-level threshold image segmentation methods, in this paper, we present multi-level thresholding image segmentation based on an improved slime mould algorithm (ISMA) and symmetric cross-entropy for global optimization and image segmentation tasks. First, elite opposition-based learning (EOBL) was used to improve the quality and diversity of the initial population and accelerate the convergence speed. The adaptive probability threshold was used to adjust the selection probability of the slime mould to enhance the ability of the algorithm to jump out of the local optimum. The historical leader strategy, which selects the optimal historical information as the leader for the position update, was found to improve the convergence accuracy. Subsequently, 14 benchmark functions were used to evaluate the performance of ISMA, comparing it with other well-known algorithms in terms of the optimization accuracy, convergence speed, and significant differences. Subsequently, we tested the segmentation quality of the method proposed in this paper on eight grayscale images and compared it with other image segmentation criteria and well-known algorithms. The experimental metrics include the average fitness (mean), standard deviation (std), peak signal to noise ratio (PSNR), structure similarity index (SSIM), and feature similarity index (FSIM), which we utilized to evaluate the quality of the segmentation. The experimental results demonstrated that the improved slime mould algorithm is superior to the other compared algorithms, and multi-level thresholding image segmentation based on the improved slime mould algorithm and symmetric cross-entropy can be effectively applied to the task of multi-level threshold image segmentation. Full article
(This article belongs to the Special Issue Entropy in Soft Computing and Machine Learning Algorithms II)
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22 pages, 817 KiB  
Article
A Concise Account of Information as Meaning Ascribed to Symbols and Its Association with Conscious Mind
by Yunus A. Çengel
Entropy 2023, 25(1), 177; https://doi.org/10.3390/e25010177 - 16 Jan 2023
Cited by 3 | Viewed by 4757
Abstract
The term information is used in different meanings in different fields of study and daily life, causing misunderstanding and confusion. There is a need to clarify what information is and how it relates to knowledge. It is argued that information is meaning [...] Read more.
The term information is used in different meanings in different fields of study and daily life, causing misunderstanding and confusion. There is a need to clarify what information is and how it relates to knowledge. It is argued that information is meaning represented by physical symbols such as sights, sounds, and words. Knowledge is meaning that resides in a conscious mind. The basic building blocks of information are symbols and meaning, which cannot be reduced to one another. The symbols of information are the physical media of representation and the means of transmission of information. Without the associated meaning, the symbols of information have no significance since meaning is an ascribed and acquired quality and not an inherent property of the symbols. We can transmit symbols of information but cannot transmit meaning from one mind to another without a common protocol or convention. A concise and cohesive framework for information can be established on the common ground of the mind, meaning, and symbols trio. Using reasoned arguments, logical consistency, and conformity with common experiences and observations as the methodology, this paper offers valuable insights to facilitate clear understanding and unifies several definitions of information into one in a cohesive manner. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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11 pages, 1215 KiB  
Article
On Divided-Type Connectivity of Graphs
by Qiao Zhou, Xiaomin Wang and Bing Yao
Entropy 2023, 25(1), 176; https://doi.org/10.3390/e25010176 - 16 Jan 2023
Viewed by 1719
Abstract
The graph connectivity is a fundamental concept in graph theory. In particular, it plays a vital role in applications related to the modern interconnection graphs, e.g., it can be used to measure the vulnerability of the corresponding graph, and is an important metric [...] Read more.
The graph connectivity is a fundamental concept in graph theory. In particular, it plays a vital role in applications related to the modern interconnection graphs, e.g., it can be used to measure the vulnerability of the corresponding graph, and is an important metric for reliability and fault tolerance of the graph. Here, firstly, we introduce two types of divided operations, named vertex-divided operation and edge-divided operation, respectively, as well as their inverse operations vertex-coincident operation and edge-coincident operation, to find some methods for splitting vertices of graphs. Secondly, we define a new connectivity, which can be referred to as divided connectivity, which differs from traditional connectivity, and present an equivalence relationship between traditional connectivity and our divided connectivity. Afterwards, we explore the structures of graphs based on the vertex-divided connectivity. Then, as an application of our divided operations, we show some necessary and sufficient conditions for a graph to be an Euler’s graph. Finally, we propose some valuable and meaningful problems for further research. Full article
(This article belongs to the Section Statistical Physics)
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17 pages, 3459 KiB  
Article
Precision Machine Learning
by Eric J. Michaud, Ziming Liu and Max Tegmark
Entropy 2023, 25(1), 175; https://doi.org/10.3390/e25010175 - 15 Jan 2023
Cited by 16 | Viewed by 5930
Abstract
We explore unique considerations involved in fitting machine learning (ML) models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with increasing parameters and data. We find [...] Read more.
We explore unique considerations involved in fitting machine learning (ML) models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with increasing parameters and data. We find that neural networks (NNs) can often outperform classical approximation methods on high-dimensional examples, by (we hypothesize) auto-discovering and exploiting modular structures therein. However, neural networks trained with common optimizers are less powerful for low-dimensional cases, which motivates us to study the unique properties of neural network loss landscapes and the corresponding optimization challenges that arise in the high precision regime. To address the optimization issue in low dimensions, we develop training tricks which enable us to train neural networks to extremely low loss, close to the limits allowed by numerical precision. Full article
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18 pages, 3117 KiB  
Article
Long-Range Dependence Involutional Network for Logo Detection
by Xingzhuo Li, Sujuan Hou, Baisong Zhang, Jing Wang, Weikuan Jia and Yuanjie Zheng
Entropy 2023, 25(1), 174; https://doi.org/10.3390/e25010174 - 15 Jan 2023
Cited by 7 | Viewed by 2842
Abstract
Logo detection is one of the crucial branches in computer vision due to various real-world applications, such as automatic logo detection and recognition, intelligent transportation, and trademark infringement detection. Compared with traditional handcrafted-feature-based methods, deep learning-based convolutional neural networks (CNNs) can learn both [...] Read more.
Logo detection is one of the crucial branches in computer vision due to various real-world applications, such as automatic logo detection and recognition, intelligent transportation, and trademark infringement detection. Compared with traditional handcrafted-feature-based methods, deep learning-based convolutional neural networks (CNNs) can learn both low-level and high-level image features. Recent decades have witnessed the great feature representation capabilities of deep CNNs and their variants, which have been very good at discovering intricate structures in high-dimensional data and are thereby applicable to many domains including logo detection. However, logo detection remains challenging, as existing detection methods cannot solve well the problems of a multiscale and large aspect ratios. In this paper, we tackle these challenges by developing a novel long-range dependence involutional network (LDI-Net). Specifically, we designed a strategy that combines a new operator and a self-attention mechanism via rethinking the intrinsic principle of convolution called long-range dependence involution (LD involution) to alleviate the detection difficulties caused by large aspect ratios. We also introduce a multilevel representation neural architecture search (MRNAS) to detect multiscale logo objects by constructing a novel multipath topology. In addition, we implemented an adaptive RoI pooling module (ARM) to improve detection efficiency by addressing the problem of logo deformation. Comprehensive experiments on four benchmark logo datasets demonstrate the effectiveness and efficiency of the proposed approach. Full article
(This article belongs to the Topic Machine and Deep Learning)
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16 pages, 3179 KiB  
Article
From Nonlinear Dominant System to Linear Dominant System: Virtual Equivalent System Approach for Multiple Variable Self-Tuning Control System Analysis
by Jinghui Pan, Kaixiang Peng and Weicun Zhang
Entropy 2023, 25(1), 173; https://doi.org/10.3390/e25010173 - 15 Jan 2023
Viewed by 1600
Abstract
The stability and convergence analysis of a multivariable stochastic self-tuning system (STC) is very difficult because of its highly nonlinear structure. In this paper, based on the virtual equivalent system method, the structural nonlinear or nonlinear dominated multivariable self-tuning system is transformed into [...] Read more.
The stability and convergence analysis of a multivariable stochastic self-tuning system (STC) is very difficult because of its highly nonlinear structure. In this paper, based on the virtual equivalent system method, the structural nonlinear or nonlinear dominated multivariable self-tuning system is transformed into a structural linear or linear dominated system, thus simplifying the stability and convergence analysis of multivariable STC systems. For the control process of a multivariable stochastic STC system, parameter estimation is required, and there may be three cases of parameter estimation convergence, convergence to the actual value and divergence. For these three cases, this paper provides four theorems and two corollaries. Given the theorems and corollaries, it can be directly concluded that the convergence of parameter estimation is a sufficient condition for the stability and convergence of stochastic STC systems but not a necessary condition, and the four theorems and two corollaries proposed in this paper are independent of specific controller design strategies and specific parameter estimation algorithms. The virtual equivalent system theory proposed in this paper does not need specific control strategies, parameters and estimation algorithms but only needs the nature of the system itself, which can judge the stability and convergence of the self-tuning system and relax the dependence of the system stability convergence criterion on the system structure information. The virtual equivalent system method proposed in this paper is proved to be effective when the parameter estimation may have convergence, convergence to the actual value and divergence. Full article
(This article belongs to the Special Issue Nonlinear Control Systems with Recent Advances and Applications)
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24 pages, 12917 KiB  
Article
A Semantic-Enhancement-Based Social Network User-Alignment Algorithm
by Yuanhao Huang, Pengcheng Zhao, Qi Zhang, Ling Xing, Honghai Wu and Huahong Ma
Entropy 2023, 25(1), 172; https://doi.org/10.3390/e25010172 - 15 Jan 2023
Cited by 11 | Viewed by 2588
Abstract
User alignment can associate multiple social network accounts of the same user. It has important research implications. However, the same user has various behaviors and friends across different social networks. This will affect the accuracy of user alignment. In this paper, we aim [...] Read more.
User alignment can associate multiple social network accounts of the same user. It has important research implications. However, the same user has various behaviors and friends across different social networks. This will affect the accuracy of user alignment. In this paper, we aim to improve the accuracy of user alignment by reducing the semantic gap between the same user in different social networks. Therefore, we propose a semantically enhanced social network user alignment algorithm (SENUA). The algorithm performs user alignment based on user attributes, user-generated contents (UGCs), and user check-ins. The interference of local semantic noise can be reduced by mining the user’s semantic features for these three factors. In addition, we improve the algorithm’s adaptability to noise by multi-view graph-data augmentation. Too much similarity of non-aligned users can have a large negative impact on the user-alignment effect. Therefore, we optimize the embedding vectors based on multi-headed graph attention networks and multi-view contrastive learning. This can enhance the similar semantic features of the aligned users. Experimental results show that SENUA has an average improvement of 6.27% over the baseline method at hit-precision30. This shows that semantic enhancement can effectively improve user alignment. Full article
(This article belongs to the Special Issue Entropy in Machine Learning Applications)
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16 pages, 785 KiB  
Article
Willow Catkin Optimization Algorithm Applied in the TDOA-FDOA Joint Location Problem
by Jeng-Shyang Pan, Si-Qi Zhang, Shu-Chuan Chu, Hong-Mei Yang and Bin Yan
Entropy 2023, 25(1), 171; https://doi.org/10.3390/e25010171 - 14 Jan 2023
Cited by 8 | Viewed by 2214
Abstract
The heuristic optimization algorithm is a popular optimization method for solving optimization problems. A novel meta-heuristic algorithm was proposed in this paper, which is called the Willow Catkin Optimization (WCO) algorithm. It mainly consists of two processes: spreading seeds and aggregating seeds. In [...] Read more.
The heuristic optimization algorithm is a popular optimization method for solving optimization problems. A novel meta-heuristic algorithm was proposed in this paper, which is called the Willow Catkin Optimization (WCO) algorithm. It mainly consists of two processes: spreading seeds and aggregating seeds. In the first process, WCO tries to make the seeds explore the solution space to find the local optimal solutions. In the second process, it works to develop each optimal local solution and find the optimal global solution. In the experimental section, the performance of WCO is tested with 30 test functions from CEC 2017. WCO was applied in the Time Difference of Arrival and Frequency Difference of Arrival (TDOA-FDOA) co-localization problem of moving nodes in Wireless Sensor Networks (WSNs). Experimental results show the performance and applicability of the WCO algorithm. Full article
(This article belongs to the Special Issue Meta-Heuristic Optimizations for the Security and Energy Efficiency of Wireless Sensor Networks)
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13 pages, 10690 KiB  
Article
Can One Series of Self-Organized Nanoripples Guide Another Series of Self-Organized Nanoripples during Ion Bombardment: From the Perspective of Power Spectral Density Entropy?
by Hengbo Li, Jinyu Li, Gaoyuan Yang, Ying Liu, Frank Frost and Yilin Hong
Entropy 2023, 25(1), 170; https://doi.org/10.3390/e25010170 - 14 Jan 2023
Viewed by 1891
Abstract
Ion bombardment (IB) is a promising nanofabrication tool for self-organized nanostructures. When ions bombard a nominally flat solid surface, self-organized nanoripples can be induced on the irradiated target surface, which are called intrinsic nanoripples of the target material. The degree of ordering of [...] Read more.
Ion bombardment (IB) is a promising nanofabrication tool for self-organized nanostructures. When ions bombard a nominally flat solid surface, self-organized nanoripples can be induced on the irradiated target surface, which are called intrinsic nanoripples of the target material. The degree of ordering of nanoripples is an outstanding issue to be overcome, similar to other self-organization methods. In this study, the IB-induced nanoripples on bilayer systems with enhanced quality are revisited from the perspective of guided self-organization. First, power spectral density (PSD) entropy is introduced to evaluate the degree of ordering of the irradiated nanoripples, which is calculated based on the PSD curve of an atomic force microscopy image (i.e., the Fourier transform of the surface height. The PSD entropy can characterize the degree of ordering of nanoripples). The lower the PSD entropy of the nanoripples is, the higher the degree of ordering of the nanoripples. Second, to deepen the understanding of the enhanced quality of nanoripples on bilayer systems, the temporal evolution of the nanoripples on the photoresist (PR)/antireflection coating (ARC) and Au/ARC bilayer systems are compared with those of single PR and ARC layers. Finally, we demonstrate that a series of intrinsic IB-induced nanoripples on the top layer may act as a kind of self-organized template to guide the development of another series of latent IB-induced nanoripples on the underlying layer, aiming at improving the ripple ordering. The template with a self-organized nanostructure may alleviate the critical requirement for periodic templates with a small period of ~100 nm. The work may also provide inspiration for guided self-organization in other fields. Full article
(This article belongs to the Special Issue Recent Advances in Guided Self-Organization)
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16 pages, 3521 KiB  
Article
GRPAFusion: A Gradient Residual and Pyramid Attention-Based Multiscale Network for Multimodal Image Fusion
by Jinxin Wang, Xiaoli Xi, Dongmei Li, Fang Li and Guanxin Zhang
Entropy 2023, 25(1), 169; https://doi.org/10.3390/e25010169 - 14 Jan 2023
Cited by 7 | Viewed by 2114
Abstract
Multimodal image fusion aims to retain valid information from different modalities, remove redundant information to highlight critical targets, and maintain rich texture details in the fused image. However, current image fusion networks only use simple convolutional layers to extract features, ignoring global dependencies [...] Read more.
Multimodal image fusion aims to retain valid information from different modalities, remove redundant information to highlight critical targets, and maintain rich texture details in the fused image. However, current image fusion networks only use simple convolutional layers to extract features, ignoring global dependencies and channel contexts. This paper proposes GRPAFusion, a multimodal image fusion framework based on gradient residual and pyramid attention. The framework uses multiscale gradient residual blocks to extract multiscale structural features and multigranularity detail features from the source image. The depth features from different modalities were adaptively corrected for inter-channel responses using a pyramid split attention module to generate high-quality fused images. Experimental results on public datasets indicated that GRPAFusion outperforms the current fusion methods in subjective and objective evaluations. Full article
(This article belongs to the Special Issue Advances in Image Fusion)
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14 pages, 1592 KiB  
Article
Super-Exponential Growth in Models of a Binary String World
by Marco Villani and Roberto Serra
Entropy 2023, 25(1), 168; https://doi.org/10.3390/e25010168 - 13 Jan 2023
Cited by 1 | Viewed by 2247
Abstract
The Theory of the Adjacent Possible (TAP) equation has been proposed as an appropriate description of super-exponential growth phenomena, where a phase of slow growth is followed by a rapid increase, leading to a “hockey stick” curve. This equation, initially conceived to describe [...] Read more.
The Theory of the Adjacent Possible (TAP) equation has been proposed as an appropriate description of super-exponential growth phenomena, where a phase of slow growth is followed by a rapid increase, leading to a “hockey stick” curve. This equation, initially conceived to describe the growth in time of the number of new types of artifacts, has also been applied to several natural phenomena. A possible drawback is that it may overestimate the number of new artifact types, since it does not take into account the fact that interactions, among existing types, may produce types which have already been previously discovered. We introduce here a Binary String World (BSW) where new string types can be generated by interactions among (at most two) already existing types. We introduce a continuous limit of the TAP equation for the BSW; we solve it analytically and show that it leads to divergence in finite time. We also introduce a criterion to distinguish this type of behavior from the familiar exponential growth, which diverges only as t → ∝. In the BSW, it is possible to directly model the generation of new types, and to check whether the newborns are actually novel types, thus discarding the rediscoveries of already existing types. We show that the type of growth is still TAP-like, rather than exponential, although of course in simulations one never can observes true divergence. We also show that this property is robust with respect to some changes in the model, as long as it deals with types (and not with individuals). Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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15 pages, 2103 KiB  
Article
Image Registration for Visualizing Magnetic Flux Leakage Testing under Different Orientations of Magnetization
by Shengping Li, Jie Zhang, Gaofei Liu, Nanhui Chen, Lulu Tian, Libing Bai and Cong Chen
Entropy 2023, 25(1), 167; https://doi.org/10.3390/e25010167 - 13 Jan 2023
Viewed by 1770
Abstract
The Magnetic Flux Leakage (MFL) visualization technique is widely used in the surface defect inspection of ferromagnetic materials. However, the information of the images detected through the MFL method is incomplete when the defect (especially for the cracks) is complex, and some information [...] Read more.
The Magnetic Flux Leakage (MFL) visualization technique is widely used in the surface defect inspection of ferromagnetic materials. However, the information of the images detected through the MFL method is incomplete when the defect (especially for the cracks) is complex, and some information would be lost when magnetized unidirectionally. Then, the multidirectional magnetization method is proposed to fuse the images detected under different magnetization orientations. It causes a critical problem: the existing image registration methods cannot be applied to align the images because the images are different when detected under different magnetization orientations. This study presents a novel image registration method for MFL visualization to solve this problem. In order to evaluate the registration, and to fuse the information detected in different directions, the mutual information between the reference image and the MFL image calculated by the forward model is designed as a measure. Furthermore, Particle Swarm Optimization (PSO) is used to optimize the registration process. The comparative experimental results demonstrate that this method has a higher registration accuracy for the MFL images of complex cracks than the existing methods. Full article
(This article belongs to the Special Issue Application of Information Theory to Computer Vision and Image Processing)
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25 pages, 1812 KiB  
Article
A Pseudorandom Number Generator Based on the Chaotic Map and Quantum Random Walks
by Wenbo Zhao, Zhenhai Chang, Caochuan Ma and Zhuozhuo Shen
Entropy 2023, 25(1), 166; https://doi.org/10.3390/e25010166 - 13 Jan 2023
Cited by 11 | Viewed by 3046
Abstract
In this paper, a surjective mapping that satisfies the Li–Yorke chaos in the unit area is constructed and a perturbation algorithm (disturbing its parameters and inputs through another high-dimensional chaos) is proposed to enhance the randomness of the constructed chaotic system and expand [...] Read more.
In this paper, a surjective mapping that satisfies the Li–Yorke chaos in the unit area is constructed and a perturbation algorithm (disturbing its parameters and inputs through another high-dimensional chaos) is proposed to enhance the randomness of the constructed chaotic system and expand its key space. An algorithm for the composition of two systems (combining sequence based on quantum random walks with chaotic system’s outputs) is designed to improve the distribution of the system outputs and a compound chaotic system is ultimately obtained. The new compound chaotic system is evaluated using some test methods such as time series complexity, autocorrelation and distribution of output frequency. The test results showed that the new system has complex dynamic behavior such as high randomicity, unpredictability and uniform output distribution. Then, a new scheme for generating pseudorandom numbers is presented utilizing the composite chaotic system. The proposed pseudorandom number generator (PRNG) is evaluated using a series test suites such as NIST sp 800-22 soft and other tools or methods. The results of tests are promising, as the proposed PRNG passed all these tests. Thus, the proposed PRNG can be used in the information security field. Full article
(This article belongs to the Special Issue Information Network Mining and Applications)
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16 pages, 552 KiB  
Article
Fluctuation Theorem for Information Thermodynamics of Quantum Correlated Systems
by Jung Jun Park and Hyunchul Nha
Entropy 2023, 25(1), 165; https://doi.org/10.3390/e25010165 - 13 Jan 2023
Cited by 2 | Viewed by 1979
Abstract
We establish a fluctuation theorem for an open quantum bipartite system that explicitly manifests the role played by quantum correlation. Generally quantum correlations may substantially modify the universality of classical thermodynamic relations in composite systems. Our fluctuation theorem finds a non-equilibrium parameter of [...] Read more.
We establish a fluctuation theorem for an open quantum bipartite system that explicitly manifests the role played by quantum correlation. Generally quantum correlations may substantially modify the universality of classical thermodynamic relations in composite systems. Our fluctuation theorem finds a non-equilibrium parameter of genuinely quantum nature that sheds light on the emerging quantum information thermodynamics. Specifically we show that the statistics of quantum correlation fluctuation obtained in a time-reversed process can provide a useful insight into addressing work and heat in the resulting thermodynamic evolution. We illustrate these quantum thermodynamic relations by two examples of quantum correlated systems. Full article
(This article belongs to the Special Issue Quantum Thermodynamics: Fundamentals and Applications)
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12 pages, 398 KiB  
Article
Synchronization Transition of the Second-Order Kuramoto Model on Lattices
by Géza Ódor and Shengfeng Deng
Entropy 2023, 25(1), 164; https://doi.org/10.3390/e25010164 - 13 Jan 2023
Cited by 5 | Viewed by 2422
Abstract
The second-order Kuramoto equation describes the synchronization of coupled oscillators with inertia, which occur, for example, in power grids. On the contrary to the first-order Kuramoto equation, its synchronization transition behavior is significantly less known. In the case of Gaussian self-frequencies, it is [...] Read more.
The second-order Kuramoto equation describes the synchronization of coupled oscillators with inertia, which occur, for example, in power grids. On the contrary to the first-order Kuramoto equation, its synchronization transition behavior is significantly less known. In the case of Gaussian self-frequencies, it is discontinuous, in contrast to the continuous transition for the first-order Kuramoto equation. Herein, we investigate this transition on large 2D and 3D lattices and provide numerical evidence of hybrid phase transitions, whereby the oscillator phases θi exhibit a crossover, while the frequency is spread over a real phase transition in 3D. Thus, a lower critical dimension dlO=2 is expected for the frequencies and dlR=4 for phases such as that in the massless case. We provide numerical estimates for the critical exponents, finding that the frequency spread decays as ∼t−d/2 in the case of an aligned initial state of the phases in agreement with the linear approximation. In 3D, however, in the case of the initially random distribution of θi, we find a faster decay, characterized by ∼t−1.8(1) as the consequence of enhanced nonlinearities which appear by the random phase fluctuations. Full article
(This article belongs to the Special Issue Non-equilibrium Phase Transitions)
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11 pages, 275 KiB  
Article
Entropy, Graph Homomorphisms, and Dissociation Sets
by Ziyuan Wang, Jianhua Tu and Rongling Lang
Entropy 2023, 25(1), 163; https://doi.org/10.3390/e25010163 - 13 Jan 2023
Cited by 1 | Viewed by 1557
Abstract
Given two graphs G and H, the mapping of f:V(G)→V(H) is called a graph homomorphism from G to H if it maps the adjacent vertices of G to the adjacent vertices of [...] Read more.
Given two graphs G and H, the mapping of f:V(G)→V(H) is called a graph homomorphism from G to H if it maps the adjacent vertices of G to the adjacent vertices of H. For the graph G, a subset of vertices is called a dissociation set of G if it induces a subgraph of G containing no paths of order three, i.e., a subgraph of a maximum degree, which is at most one. Graph homomorphisms and dissociation sets are two generalizations of the concept of independent sets. In this paper, by utilizing an entropy approach, we provide upper bounds on the number of graph homomorphisms from the bipartite graph G to the graph H and the number of dissociation sets in a bipartite graph G. Full article
(This article belongs to the Special Issue Spectral Graph Theory, Topological Indices of Graph, and Entropy)
35 pages, 12354 KiB  
Article
Numerical Calculation of the Irreversible Entropy Production of Additively Manufacturable Off-Set Strip Fin Heat-Transferring Structures
by Marco Fuchs, Nico Lubos and Stephan Kabelac
Entropy 2023, 25(1), 162; https://doi.org/10.3390/e25010162 - 13 Jan 2023
Cited by 4 | Viewed by 1958
Abstract
In this manuscript, off-set strip fin structures are presented which are adapted to the possibilities of additive manufacturing. For this purpose, the geometric parameters, including fin height, fin spacing, fin length, and fin longitudinal displacement, are varied, and the Colburn j-factor and the [...] Read more.
In this manuscript, off-set strip fin structures are presented which are adapted to the possibilities of additive manufacturing. For this purpose, the geometric parameters, including fin height, fin spacing, fin length, and fin longitudinal displacement, are varied, and the Colburn j-factor and the Fanning friction factor are numerically calculated in the Reynolds number range of 80–920. The structures are classified with respect to their entropy production number according to Bejan. This method is compared with the results from partial differential equations for the calculation of the irreversible entropy production rate due to shear stresses and heat conduction. This study reveals that the chosen temperature difference leads to deviation in terms of entropy production due to heat conduction, whereas the dissipation by shear stresses shows only small deviations of less than 2%. It is further shown that the variation in fin height and fin spacing has only a small influence on heat transfer and pressure drop, while a variation in fin length and fin longitudinal displacement shows a larger influence. With respect to the entropy production number, short and long fins, as well as large fin spacing and fin longitudinal displacement, are shown to be beneficial. A detailed examination of a single structure shows that the entropy production rate due to heat conduction is dominated by the entropy production rate in the wall, while the fluid has only a minor influence. Full article
(This article belongs to the Special Issue Applications of CFD in Heat and Fluid Flow Processes)
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12 pages, 1209 KiB  
Article
Ray-Stretching Statistics and Hot-Spot Formation in Weak Random Disorder
by Sicong Chen and Lev Kaplan
Entropy 2023, 25(1), 161; https://doi.org/10.3390/e25010161 - 13 Jan 2023
Cited by 1 | Viewed by 1681
Abstract
Weak scattering in a random disordered medium and the associated extreme-event statistics are of great interest in various physical contexts. Here, in the context of non-relativistic particle motion through a weakly correlated random potential, we show how extreme events in particle densities are [...] Read more.
Weak scattering in a random disordered medium and the associated extreme-event statistics are of great interest in various physical contexts. Here, in the context of non-relativistic particle motion through a weakly correlated random potential, we show how extreme events in particle densities are strongly related to the stretching exponents, where the ’hot spots’ in the intensity profile correspond to minima in the stretching exponents. This strong connection is expected to be valid for different random potential distributions, as long as the disorder is correlated and weak, and is also expected to apply to other physical contexts, such as deep ocean waves. Full article
(This article belongs to the Special Issue Quantum Chaos—Dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday)
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12 pages, 457 KiB  
Article
Locality, Realism, Ergodicity and Randomness in Bell’s Experiment
by Alejandro Andrés Hnilo
Entropy 2023, 25(1), 160; https://doi.org/10.3390/e25010160 - 13 Jan 2023
Cited by 1 | Viewed by 1598
Abstract
Assuming that there is no way of sending signals propagating faster than light and that free will exists, the loophole-free observed violation of Bell’s inequalities demonstrates that at least one of three fundamental hypotheses involved in the derivation and observation of the inequalities [...] Read more.
Assuming that there is no way of sending signals propagating faster than light and that free will exists, the loophole-free observed violation of Bell’s inequalities demonstrates that at least one of three fundamental hypotheses involved in the derivation and observation of the inequalities is false: Locality, Realism, or Ergodicity. An experiment is proposed to obtain some evidence about which one is the false one. It is based on recording the time evolution of the rate of non-random series of outcomes that are generated in a specially designed Bell’s setup. The results of such experiment would be important not only to the foundations of Quantum Mechanics, but they would also have immediate practical impact on the efficient use of quantum-based random number generators and the security of Quantum Key Distribution using entangled states. Full article
(This article belongs to the Special Issue Quantum Mechanics and Its Foundations III)
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10 pages, 5152 KiB  
Article
EspEn Graph for the Spatial Analysis of Entropy in Images
by Ricardo Alonso Espinosa Medina
Entropy 2023, 25(1), 159; https://doi.org/10.3390/e25010159 - 12 Jan 2023
Viewed by 1862
Abstract
The quantification of entropy in images is a topic of interest that has had different applications in the field of agronomy, product generation and medicine. Some algorithms have been proposed for the quantification of the irregularity present in an image; however, the challenges [...] Read more.
The quantification of entropy in images is a topic of interest that has had different applications in the field of agronomy, product generation and medicine. Some algorithms have been proposed for the quantification of the irregularity present in an image; however, the challenges to overcome in the computational cost involved in large images and the reliable measurements in small images are still topics of discussion. In this research we propose an algorithm, EspEn Graph, which allows the quantification and graphic representation of the irregularity present in an image, revealing the location of the places where there are more or less irregular textures in the image. EspEn is used to calculate entropy because it presents reliable and stable measurements for small size images. This allows an image to be subdivided into small sections to calculate the entropy in each section and subsequently perform the conversion of values to graphically show the regularity present in an image. In conclusion, the EspEn Graph returns information on the spatial regularity that an image with different textures has and the average of these entropy values allows a reliable measure of the general entropy of the image. Full article
(This article belongs to the Special Issue Measures of Information II)
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39 pages, 738 KiB  
Article
On Regularized Systems of Equations for Gas Mixture Dynamics with New Regularizing Velocities and Diffusion Fluxes
by Alexander Zlotnik and Timofey Lomonosov
Entropy 2023, 25(1), 158; https://doi.org/10.3390/e25010158 - 12 Jan 2023
Cited by 6 | Viewed by 1608
Abstract
We deal with multidimensional regularized systems of equations for the one-velocity and one-temperature inert gas mixture dynamics consisting of the balance equations for the mass of components and the momentum and total energy of the mixture, with diffusion fluxes between the components as [...] Read more.
We deal with multidimensional regularized systems of equations for the one-velocity and one-temperature inert gas mixture dynamics consisting of the balance equations for the mass of components and the momentum and total energy of the mixture, with diffusion fluxes between the components as well as the viscosity and heat conductivity terms. The regularizations are kinetically motivated and aimed at constructing conditionally stable symmetric in space discretizations without limiters. We consider a new combined form of regularizing velocities containing the total pressure of the mixture. To confirm the physical correctness of the regularized systems, we derive the balance equation for the mixture entropy with the non-negative entropy production, under generalized assumptions on the diffusion fluxes. To confirm nice regularizing properties, we derive the systems of equations linearized at constant solutions and provide the existence, uniqueness and L2-dissipativity of weak solutions to an initial-boundary problem for them. For the original systems, we also discuss the related Petrovskii parabolicity property and its important corollaries. In addition, in the one-dimensional case, we also present the special three-point and symmetric finite-difference discretization in space of the regularized systems and prove that it inherits the entropy correctness property. We also give results of numerical experiments confirming that the discretization is able to simulate well various dynamic problems of contact between two different gases. Full article
(This article belongs to the Section Multidisciplinary Applications)
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16 pages, 1036 KiB  
Article
Dynamics of Quantum Networks in Noisy Environments
by Chang-Yue Zhang, Zhu-Jun Zheng, Shao-Ming Fei and Mang Feng
Entropy 2023, 25(1), 157; https://doi.org/10.3390/e25010157 - 12 Jan 2023
Cited by 1 | Viewed by 2109
Abstract
Noise exists inherently in realistic quantum systems and affects the evolution of quantum systems. We investigate the dynamics of quantum networks in noisy environments by using the fidelity of the quantum evolved states and the classical percolation theory. We propose an analytical framework [...] Read more.
Noise exists inherently in realistic quantum systems and affects the evolution of quantum systems. We investigate the dynamics of quantum networks in noisy environments by using the fidelity of the quantum evolved states and the classical percolation theory. We propose an analytical framework that allows us to characterize the stability of quantum networks in terms of quantum noises and network topologies. The calculation results of the framework determine the maximal time that quantum networks with different network topologies can maintain the ability to communicate under noise. We demonstrate the results of the framework through examples of specific graphs under amplitude damping and phase damping noises. We further consider the capacity of the quantum network in a noisy environment according to the proposed framework. The analytical framework helps us better understand the evolution time of a quantum network and provides a reference for designing large quantum networks. Full article
(This article belongs to the Special Issue New Advances in Quantum Communication and Networks)
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19 pages, 603 KiB  
Article
Lossless Image Coding Using Non-MMSE Algorithms to Calculate Linear Prediction Coefficients
by Grzegorz Ulacha and Mirosław Łazoryszczak
Entropy 2023, 25(1), 156; https://doi.org/10.3390/e25010156 - 12 Jan 2023
Cited by 5 | Viewed by 2198
Abstract
This paper presents a lossless image compression method with a fast decoding time and flexible adjustment of coder parameters affecting its implementation complexity. A comparison of several approaches for computing non-MMSE prediction coefficients with different levels of complexity was made. The data modeling [...] Read more.
This paper presents a lossless image compression method with a fast decoding time and flexible adjustment of coder parameters affecting its implementation complexity. A comparison of several approaches for computing non-MMSE prediction coefficients with different levels of complexity was made. The data modeling stage of the proposed codec was based on linear (calculated by the non-MMSE method) and non-linear (complemented by a context-dependent constant component removal block) predictions. Prediction error coding uses a two-stage compression: an adaptive Golomb code and a binary arithmetic code. The proposed solution results in 30% shorter decoding times and a lower bit average than competing solutions (by 7.9% relative to the popular JPEG-LS codec). Full article
(This article belongs to the Special Issue Advances in Information and Coding Theory)
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10 pages, 1036 KiB  
Article
Thermoelectric Cycle and the Second Law of Thermodynamics
by Ti-Wei Xue and Zeng-Yuan Guo
Entropy 2023, 25(1), 155; https://doi.org/10.3390/e25010155 - 12 Jan 2023
Cited by 5 | Viewed by 2758
Abstract
In 2019, Schilling et al. claimed that they achieved the supercooling of a body without external intervention in their thermoelectric experiments, thus arguing that the second law of thermodynamics was bent. Kostic suggested that their claim lacked full comprehension of the second law [...] Read more.
In 2019, Schilling et al. claimed that they achieved the supercooling of a body without external intervention in their thermoelectric experiments, thus arguing that the second law of thermodynamics was bent. Kostic suggested that their claim lacked full comprehension of the second law of thermodynamics. A review of history shows that what Clausius referred to as the second law of thermodynamics is the theorem of the equivalence of transformations (unfairly ignored historically) in a reversible heat–work cycle, rather than “heat can never pass from a cold to a hot body without some other change” that was only viewed by Clausius as a natural phenomenon. Here, we propose the theorem of the equivalence of transformations for reversible thermoelectric cycles. The analysis shows that the supercooling phenomenon Schilling et al. observed is achieved by a reversible combined power–refrigeration cycle. According to the theorem of equivalence of transformations in reversible thermoelectric cycles, the reduction in body temperature to below the ambient temperature requires the body itself to have a higher initial temperature than ambient as compensation. Not only does the supercooling phenomenon not bend the second law, but it provides strong evidence of the second law. Full article
(This article belongs to the Special Issue Exploring Fundamentals and Challenges of Heat, Entropy, and the Second Law of Thermodynamics: Honoring Professor Milivoje M. Kostic on the Occasion of His 70th Birthday)
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39 pages, 1240 KiB  
Article
Analysis of Kernel Matrices via the von Neumann Entropy and Its Relation to RVM Performances
by Lluís A. Belanche-Muñoz and Małgorzata Wiejacha
Entropy 2023, 25(1), 154; https://doi.org/10.3390/e25010154 - 12 Jan 2023
Cited by 1 | Viewed by 1863
Abstract
Kernel methods have played a major role in the last two decades in the modeling and visualization of complex problems in data science. The choice of kernel function remains an open research area and the reasons why some kernels perform better than others [...] Read more.
Kernel methods have played a major role in the last two decades in the modeling and visualization of complex problems in data science. The choice of kernel function remains an open research area and the reasons why some kernels perform better than others are not yet understood. Moreover, the high computational costs of kernel-based methods make it extremely inefficient to use standard model selection methods, such as cross-validation, creating a need for careful kernel design and parameter choice. These reasons justify the prior analyses of kernel matrices, i.e., mathematical objects generated by the kernel functions. This paper explores these topics from an entropic standpoint for the case of kernelized relevance vector machines (RVMs), pinpointing desirable properties of kernel matrices that increase the likelihood of obtaining good model performances in terms of generalization power, as well as relate these properties to the model’s fitting ability. We also derive a heuristic for achieving close-to-optimal modeling results while keeping the computational costs low, thus providing a recipe for efficient analysis when processing resources are limited. Full article
(This article belongs to the Special Issue Towards the Understanding of Kernel and Neural Learning Methods via Information-Theoretic Learning (ITL))
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16 pages, 1750 KiB  
Article
Entanglement of Signal Paths via Noisy Superconducting Quantum Devices
by Wenbo Shi and Robert Malaney
Entropy 2023, 25(1), 153; https://doi.org/10.3390/e25010153 - 12 Jan 2023
Cited by 2 | Viewed by 1958
Abstract
Quantum routers will provide for important functionality in emerging quantum networks, and the deployment of quantum routing in real networks will initially be realized on low-complexity (few-qubit) noisy quantum devices. A true working quantum router will represent a new application for quantum entanglement—the [...] Read more.
Quantum routers will provide for important functionality in emerging quantum networks, and the deployment of quantum routing in real networks will initially be realized on low-complexity (few-qubit) noisy quantum devices. A true working quantum router will represent a new application for quantum entanglement—the coherent superposition of multiple communication paths traversed by the same quantum signal. Most end-user benefits of this application are yet to be discovered, but a few important use-cases are now known. In this work, we investigate the deployment of quantum routing on low-complexity superconducting quantum devices. In such devices, we verify the quantum nature of the routing process as well as the preservation of the routed quantum signal. We also implement quantum random access memory, a key application of quantum routing, on these same devices. Our experiments then embed a five-qubit quantum error-correcting code within the router, outlining the pathway for error-corrected quantum routing. We detail the importance of the qubit-coupling map for a superconducting quantum device that hopes to act as a quantum router, and experimentally verify that optimizing the number of controlled-X gates decreases hardware errors that impact routing performance. Our results indicate that near-term realization of quantum routing using noisy superconducting quantum devices within real-world quantum networks is possible. Full article
(This article belongs to the Special Issue Quantum Entanglement and Its Application in Quantum Communication)
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12 pages, 1398 KiB  
Article
Heart Rate Complexity and Autonomic Modulation Are Associated with Psychological Response Inhibition in Healthy Subjects
by Francesco Riganello, Martina Vatrano, Paolo Tonin, Antonio Cerasa and Maria Daniela Cortese
Entropy 2023, 25(1), 152; https://doi.org/10.3390/e25010152 - 12 Jan 2023
Cited by 1 | Viewed by 2069
Abstract
Background: the ability to suppress/regulate impulsive reactions has been identified as common factor underlying the performance in all executive function tasks. We analyzed the HRV signals (power of high (HF) and low (LF) frequency, Sample Entropy (SampEn), and Complexity Index (CI)) during the [...] Read more.
Background: the ability to suppress/regulate impulsive reactions has been identified as common factor underlying the performance in all executive function tasks. We analyzed the HRV signals (power of high (HF) and low (LF) frequency, Sample Entropy (SampEn), and Complexity Index (CI)) during the execution of cognitive tests to assess flexibility, inhibition abilities, and rule learning. Methods: we enrolled thirty-six healthy subjects, recording five minutes of resting state and two tasks of increasing complexity based on 220 visual stimuli with 12 × 12 cm red and white squares on a black background. Results: at baseline, CI was negatively correlated with age, and LF was negatively correlated with SampEn. In Task 1, the CI and LF/HF were negatively correlated with errors. In Task 2, the reaction time positively correlated with the CI and the LF/HF ratio errors. Using a binary logistic regression model, age, CI, and LF/HF ratio classified performance groups with a sensitivity and specificity of 73 and 71%, respectively. Conclusions: this study performed an important initial exploration in defining the complex relationship between CI, sympathovagal balance, and age in regulating impulsive reactions during cognitive tests. Our approach could be applied in assessing cognitive decline, providing additional information on the brain-heart interaction. Full article
(This article belongs to the Special Issue Assessing Complexity in Physiological Systems through Biomedical Signals Analysis II)
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16 pages, 334 KiB  
Article
Stochastic Particle Creation: From the Dynamical Casimir Effect to Cosmology
by Matías Mantiñan, Francisco D. Mazzitelli and Leonardo G. Trombetta
Entropy 2023, 25(1), 151; https://doi.org/10.3390/e25010151 - 11 Jan 2023
Cited by 3 | Viewed by 1422
Abstract
We study a stochastic version of the dynamical Casimir effect, computing the particle creation inside a cavity produced by a random motion of one of its walls. We first present a calculation perturbative in the amplitude of the motion. We compare the stochastic [...] Read more.
We study a stochastic version of the dynamical Casimir effect, computing the particle creation inside a cavity produced by a random motion of one of its walls. We first present a calculation perturbative in the amplitude of the motion. We compare the stochastic particle creation with the deterministic counterpart. Then, we go beyond the perturbative evaluation using a stochastic version of the multiple scale analysis, that takes into account stochastic parametric resonance. We stress the relevance of the coupling between the different modes induced by the stochastic motion. In the single-mode approximation, the equations are formally analogous to those that describe the stochastic particle creation in a cosmological context, that we rederive using multiple scale analysis. Full article
(This article belongs to the Special Issue Quantum Nonstationary Systems)
16 pages, 662 KiB  
Article
Mining Mobile Network Fraudsters with Augmented Graph Neural Networks
by Xinxin Hu, Haotian Chen, Hongchang Chen, Xing Li, Junjie Zhang and Shuxin Liu
Entropy 2023, 25(1), 150; https://doi.org/10.3390/e25010150 - 11 Jan 2023
Cited by 10 | Viewed by 2944
Abstract
With the rapid evolution of mobile communication networks, the number of subscribers and their communication practices is increasing dramatically worldwide. However, fraudsters are also sniffing out the benefits. Detecting fraudsters from the massive volume of call detail records (CDR) in mobile communication networks [...] Read more.
With the rapid evolution of mobile communication networks, the number of subscribers and their communication practices is increasing dramatically worldwide. However, fraudsters are also sniffing out the benefits. Detecting fraudsters from the massive volume of call detail records (CDR) in mobile communication networks has become an important yet challenging topic. Fortunately, Graph neural network (GNN) brings new possibilities for telecom fraud detection. However, the presence of the graph imbalance and GNN oversmoothing problems makes fraudster detection unsatisfactory. To address these problems, we propose a new fraud detector. First, we transform the user features with the help of a multilayer perceptron. Then, a reinforcement learning-based neighbor sampling strategy is designed to balance the number of neighbors of different classes of users. Next, we perform user feature aggregation using GNN. Finally, we innovatively treat the above augmented GNN as weak classifier and integrate multiple weak classifiers using the AdaBoost algorithm. A balanced focal loss function is also used to monitor the model training error. Extensive experiments are conducted on two open real-world telecom fraud datasets, and the results show that the proposed method is significantly effective for the graph imbalance problem and the oversmoothing problem in telecom fraud detection. Full article
(This article belongs to the Special Issue Information Network Mining and Applications)
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