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Entropy, Volume 26, Issue 6 (June 2024) – 84 articles

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18 pages, 482 KiB  
Article
Dual-Tower Counterfactual Session-Aware Recommender System
by Wenzhuo Song and Xiaoyu Xing
Entropy 2024, 26(6), 516; https://doi.org/10.3390/e26060516 - 14 Jun 2024
Viewed by 55
Abstract
In the complex dynamics of modern information systems such as e-commerce and streaming services, managing uncertainty and leveraging information theory are crucial in enhancing session-aware recommender systems (SARSs). This paper presents an innovative approach to SARSs that combines static long-term and dynamic short-term [...] Read more.
In the complex dynamics of modern information systems such as e-commerce and streaming services, managing uncertainty and leveraging information theory are crucial in enhancing session-aware recommender systems (SARSs). This paper presents an innovative approach to SARSs that combines static long-term and dynamic short-term preferences within a counterfactual causal framework. Our method addresses the shortcomings of current prediction models that tend to capture spurious correlations, leading to biased recommendations. By incorporating a counterfactual viewpoint, we aim to elucidate the causal influences of static long-term preferences on next-item selections and enhance the overall robustness of predictive models. We introduce a dual-tower architecture with a novel data augmentation process and a self-supervised training strategy, tailored to tackle inherent biases and unreliable correlations. Extensive experiments demonstrate the effectiveness of our approach, outperforming existing benchmarks and paving the way for more accurate and reliable session-based recommendations. Full article
(This article belongs to the Section Complexity)
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13 pages, 756 KiB  
Article
Underwater Wavelength Attack on Discrete Modulated Continuous-Variable Quantum Key Distribution
by Kangyi Feng, Yijun Wang, Yin Li, Yuang Wang, Zhiyue Zuo and Ying Guo
Entropy 2024, 26(6), 515; https://doi.org/10.3390/e26060515 - 14 Jun 2024
Viewed by 100
Abstract
The wavelength attack utilizes the dependence of beam splitters (BSs) on wavelength to cause legitimate users Alice and Bob to underestimate their excess noise so that Eve can steal more secret keys without being detected. Recently, the wavelength attack on Gaussian-modulated continuous-variable quantum [...] Read more.
The wavelength attack utilizes the dependence of beam splitters (BSs) on wavelength to cause legitimate users Alice and Bob to underestimate their excess noise so that Eve can steal more secret keys without being detected. Recently, the wavelength attack on Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) has been researched in both fiber and atmospheric channels. However, the wavelength attack may also pose a threat to the case of ocean turbulent channels, which are vital for the secure communication of both ocean sensor networks and submarines. In this work, we propose two wavelength attack schemes on underwater discrete modulated (DM) CV-QKD protocol, which is effective for the case with and without local oscillator (LO) intensity monitor, respectively. In terms of the transmittance properties of the fused biconical taper (FBT) BS, two sets of wavelengths are determined for Eve’s pulse manipulation, which are all located in the so-called blue–green band. The derived successful criterion shows that both attack schemes can control the estimated excess noise of Alice and Bob close to zero by selecting the corresponding condition parameters based on channel transmittance. Additionally, our numerical analysis shows that Eve can steal more bits when the wavelength attack controls the value of the estimated excess noise closer to zero. Full article
(This article belongs to the Special Issue Quantum Communications Networks: Trends and Challenges)
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11 pages, 1561 KiB  
Article
A Symmetric Form of the Clausius Statement of the Second Law of Thermodynamics
by Ti-Wei Xue, Tian Zhao and Zeng-Yuan Guo
Entropy 2024, 26(6), 514; https://doi.org/10.3390/e26060514 - 14 Jun 2024
Viewed by 102
Abstract
Bridgman once reflected on thermodynamics that the laws of thermodynamics were formulated in their present form by the great founders of thermodynamics, Kelvin and Clausius, before all the essential physical facts were in, and there has been no adequate reexamination of the fundamentals [...] Read more.
Bridgman once reflected on thermodynamics that the laws of thermodynamics were formulated in their present form by the great founders of thermodynamics, Kelvin and Clausius, before all the essential physical facts were in, and there has been no adequate reexamination of the fundamentals since. Thermodynamics still has unknown possibilities waiting to be explored. This paper begins with a brief review of Clausius’s work on the second law of thermodynamics and a reassessment of the content of Clausius’s statement. The review tells that what Clausius originally referred to as the second law of thermodynamics was, in fact, the theorem of equivalence of transformations (TET) in a reversible cycle. On this basis, a new symmetric form of Clausius’s TET is proposed. This theorem says that the two transformations, i.e., the transformation of heat to work and the transformation of work from high pressure to low pressure, should be equivalent in a reversible work-to-heat cycle. New thermodynamic cyclic laws are developed on the basis of the cycle with two work reservoirs (two pressures), which enriches the fundamental of the second law of thermodynamics. Full article
(This article belongs to the Special Issue Trends in the Second Law of Thermodynamics)
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12 pages, 274 KiB  
Article
Building Test Batteries Based on Analyzing Random Number Generator Tests within the Framework of Algorithmic Information Theory
by Boris Ryabko
Entropy 2024, 26(6), 513; https://doi.org/10.3390/e26060513 - 14 Jun 2024
Viewed by 91
Abstract
The problem of testing random number generators is considered and a new method for comparing the power of different statistical tests is proposed. It is based on the definitions of random sequence developed in the framework of algorithmic information theory and allows comparing [...] Read more.
The problem of testing random number generators is considered and a new method for comparing the power of different statistical tests is proposed. It is based on the definitions of random sequence developed in the framework of algorithmic information theory and allows comparing the power of different tests in some cases when the available methods of mathematical statistics do not distinguish between tests. In particular, it is shown that tests based on data compression methods using dictionaries should be included in test batteries. Full article
(This article belongs to the Special Issue Complexity, Entropy and the Physics of Information II)
14 pages, 1474 KiB  
Article
New Quantum Private Comparison Using Four-Particle Cluster State
by Min Hou, Yue Wu and Shibin Zhang
Entropy 2024, 26(6), 512; https://doi.org/10.3390/e26060512 - 14 Jun 2024
Viewed by 85
Abstract
Quantum private comparison (QPC) enables two users to securely conduct private comparisons in a network characterized by mutual distrust while guaranteeing the confidentiality of their private inputs. Most previous QPC protocols were primarily used to determine the equality of private information between two [...] Read more.
Quantum private comparison (QPC) enables two users to securely conduct private comparisons in a network characterized by mutual distrust while guaranteeing the confidentiality of their private inputs. Most previous QPC protocols were primarily used to determine the equality of private information between two users, which constrained their scalability. In this paper, we propose a QPC protocol that leverages the entanglement correlation between particles in a four-particle cluster state. This protocol can compare the information of two groups of users within one protocol execution, with each group consisting of two users. A semi-honest third party (TP), who will not deviate from the protocol execution or conspire with any participant, is involved in assisting users to achieve private comparisons. Users encode their inputs into specific angles of rotational operations performed on the received quantum sequence, which is then sent back to TP. Security analysis shows that both external attacks and insider threats are ineffective at stealing private data. Finally, we compare our protocol with some previously proposed QPC protocols. Full article
(This article belongs to the Special Issue Entropy, Quantum Information and Entanglement)
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29 pages, 1342 KiB  
Article
Exergoeconomic Analysis and Optimization of a Biomass Integrated Gasification Combined Cycle Based on Externally Fired Gas Turbine, Steam Rankine Cycle, Organic Rankine Cycle, and Absorption Refrigeration Cycle
by Jie Ren, Chen Xu, Zuoqin Qian, Weilong Huang and Baolin Wang
Entropy 2024, 26(6), 511; https://doi.org/10.3390/e26060511 - 12 Jun 2024
Viewed by 161
Abstract
Adopting biomass energy as an alternative to fossil fuels for electricity production presents a viable strategy to address the prevailing energy deficits and environmental concerns, although it faces challenges related to suboptimal energy efficiency levels. This study introduces a novel combined cooling and [...] Read more.
Adopting biomass energy as an alternative to fossil fuels for electricity production presents a viable strategy to address the prevailing energy deficits and environmental concerns, although it faces challenges related to suboptimal energy efficiency levels. This study introduces a novel combined cooling and power (CCP) system, incorporating an externally fired gas turbine (EFGT), steam Rankine cycle (SRC), absorption refrigeration cycle (ARC), and organic Rankine cycle (ORC), aimed at boosting the efficiency of biomass integrated gasification combined cycle systems. Through the development of mathematical models, this research evaluates the system’s performance from both thermodynamic and exergoeconomic perspectives. Results show that the system could achieve the thermal efficiency, exergy efficiency, and levelized cost of exergy (LCOE) of 70.67%, 39.13%, and 11.67 USD/GJ, respectively. The analysis identifies the combustion chamber of the EFGT as the component with the highest rate of exergy destruction. Further analysis on parameters indicates that improvements in thermodynamic performance are achievable with increased air compressor pressure ratio and gas turbine inlet temperature, or reduced pinch point temperature difference, while the LCOE can be minimized through adjustments in these parameters. Optimized operation conditions demonstrate a potential 5.7% reduction in LCOE at the expense of a 2.5% decrease in exergy efficiency when compared to the baseline scenario. Full article
(This article belongs to the Special Issue Thermodynamic Optimization of Industrial Energy Systems)
16 pages, 597 KiB  
Article
A Bayesian Measure of Model Accuracy
by Gabriel Hideki Vatanabe Brunello and Eduardo Yoshio Nakano
Entropy 2024, 26(6), 510; https://doi.org/10.3390/e26060510 - 12 Jun 2024
Viewed by 195
Abstract
Ensuring that the proposed probabilistic model accurately represents the problem is a critical step in statistical modeling, as choosing a poorly fitting model can have significant repercussions on the decision-making process. The primary objective of statistical modeling often revolves around predicting new observations, [...] Read more.
Ensuring that the proposed probabilistic model accurately represents the problem is a critical step in statistical modeling, as choosing a poorly fitting model can have significant repercussions on the decision-making process. The primary objective of statistical modeling often revolves around predicting new observations, highlighting the importance of assessing the model’s accuracy. However, current methods for evaluating predictive ability typically involve model comparison, which may not guarantee a good model selection. This work presents an accuracy measure designed for evaluating a model’s predictive capability. This measure, which is straightforward and easy to understand, includes a decision criterion for model rejection. The development of this proposal adopts a Bayesian perspective of inference, elucidating the underlying concepts and outlining the necessary procedures for application. To illustrate its utility, the proposed methodology was applied to real-world data, facilitating an assessment of its practicality in real-world scenarios. Full article
(This article belongs to the Section Multidisciplinary Applications)
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15 pages, 374 KiB  
Article
Violations of Hyperscaling in Finite-Size Scaling above the Upper Critical Dimension
by A. Peter Young
Entropy 2024, 26(6), 509; https://doi.org/10.3390/e26060509 - 12 Jun 2024
Viewed by 168
Abstract
We consider how finite-size scaling (FSS) is modified above the upper critical dimension, du=4, due to hyperscaling violations, which in turn arise from a dangerous irrelevant variable. In addition to the commonly studied case of periodic boundary conditions, we [...] Read more.
We consider how finite-size scaling (FSS) is modified above the upper critical dimension, du=4, due to hyperscaling violations, which in turn arise from a dangerous irrelevant variable. In addition to the commonly studied case of periodic boundary conditions, we also consider new effects that arise with free boundary conditions. Some numerical results are presented in addition to theoretical arguments. Full article
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12 pages, 996 KiB  
Article
Characterizing Complex Spatiotemporal Patterns from Entropy Measures
by Luan Orion Barauna, Rubens Andreas Sautter, Reinaldo Roberto Rosa, Erico Luiz Rempel and Alejandro C. Frery
Entropy 2024, 26(6), 508; https://doi.org/10.3390/e26060508 - 12 Jun 2024
Viewed by 176
Abstract
In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this [...] Read more.
In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method for classifying spatiotemporal processes based on entropy measurements. To test and validate the method, we selected five classes of similar processes related to the evolution of random patterns: (i) white noise; (ii) red noise; (iii) weak turbulence from reaction to diffusion; (iv) hydrodynamic fully developed turbulence; and (v) plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon permutation entropy (SHp) and a new approach based on Tsallis Spectral Permutation Entropy (Sqs). Notably, our observations reveal the segregation of reaction terms in this SHp×Sqs space, a result that identifies specific sectors for each class of dynamic process, and it can be used to train machine learning models for the automatic classification of complex spatiotemporal patterns. Full article
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24 pages, 3000 KiB  
Article
Fault Diagnosis of Wind Turbine Gearbox Based on Modified Hierarchical Fluctuation Dispersion Entropy of Tan-Sigmoid Mapping
by Xiang Wang and Yang Du
Entropy 2024, 26(6), 507; https://doi.org/10.3390/e26060507 - 11 Jun 2024
Viewed by 187
Abstract
Vibration monitoring and analysis are important methods in wind turbine gearbox fault diagnosis, and determining how to extract fault characteristics from the vibration signal is of primary importance. This paper presents a fault diagnosis approach based on modified hierarchical fluctuation dispersion entropy of [...] Read more.
Vibration monitoring and analysis are important methods in wind turbine gearbox fault diagnosis, and determining how to extract fault characteristics from the vibration signal is of primary importance. This paper presents a fault diagnosis approach based on modified hierarchical fluctuation dispersion entropy of tan-sigmoid mapping (MHFDE_TANSIG) and northern goshawk optimization–support vector machine (NGO–SVM) for wind turbine gearboxes. The tan-sigmoid (TANSIG) mapping function replaces the normal cumulative distribution function (NCDF) of the hierarchical fluctuation dispersion entropy (HFDE) method. Additionally, the hierarchical decomposition of the HFDE method is improved, resulting in the proposed MHFDE_TANSIG method. The vibration signals of wind turbine gearboxes are analyzed using the MHFDE_TANSIG method to extract fault features. The constructed fault feature set is used to intelligently recognize and classify the fault type of the gearboxes with the NGO–SVM classifier. The fault diagnosis methods based on MHFDE_TANSIG and NGO–SVM are applied to the experimental data analysis of gearboxes with different operating conditions. The results show that the fault diagnosis model proposed in this paper has the best performance with an average accuracy rate of 97.25%. Full article
(This article belongs to the Special Issue Entropy Applications in Condition Monitoring and Fault Diagnosis)
8 pages, 226 KiB  
Article
Multimodel Approaches Are Not the Best Way to Understand Multifactorial Systems
by Benjamin M. Bolker
Entropy 2024, 26(6), 506; https://doi.org/10.3390/e26060506 - 11 Jun 2024
Viewed by 182
Abstract
Information-theoretic (IT) and multi-model averaging (MMA) statistical approaches are widely used but suboptimal tools for pursuing a multifactorial approach (also known as the method of multiple working hypotheses) in ecology. (1) Conceptually, IT encourages ecologists to perform tests on sets of artificially simplified [...] Read more.
Information-theoretic (IT) and multi-model averaging (MMA) statistical approaches are widely used but suboptimal tools for pursuing a multifactorial approach (also known as the method of multiple working hypotheses) in ecology. (1) Conceptually, IT encourages ecologists to perform tests on sets of artificially simplified models. (2) MMA improves on IT model selection by implementing a simple form of shrinkage estimation (a way to make accurate predictions from a model with many parameters relative to the amount of data, by “shrinking” parameter estimates toward zero). However, other shrinkage estimators such as penalized regression or Bayesian hierarchical models with regularizing priors are more computationally efficient and better supported theoretically. (3) In general, the procedures for extracting confidence intervals from MMA are overconfident, providing overly narrow intervals. If researchers want to use limited data sets to accurately estimate the strength of multiple competing ecological processes along with reliable confidence intervals, the current best approach is to use full (maximal) statistical models (possibly with Bayesian priors) after making principled, a priori decisions about model complexity. Full article
23 pages, 3411 KiB  
Article
Code Similarity Prediction Model for Industrial Management Features Based on Graph Neural Networks
by Zhenhao Li, Hang Lei, Zhichao Ma and Fengyun Zhang
Entropy 2024, 26(6), 505; https://doi.org/10.3390/e26060505 - 9 Jun 2024
Viewed by 311
Abstract
The code of industrial management software typically features few system API calls and a high number of customized variables and structures. This makes the similarity of such codes difficult to compute using text features or traditional neural network methods. In this paper, we [...] Read more.
The code of industrial management software typically features few system API calls and a high number of customized variables and structures. This makes the similarity of such codes difficult to compute using text features or traditional neural network methods. In this paper, we propose an FSPS-GNN model, which is based on graph neural networks (GNNs), to address this problem. The model categorizes code features into two types, outer graph and inner graph, and conducts training and prediction with four stages—feature embedding, feature enhancement, feature fusion, and similarity prediction. Moreover, differently structured GNNs were used in the embedding and enhancement stages, respectively, to increase the interaction of code features. Experiments with code from three open-source projects demonstrate that the model achieves an average precision of 87.57% and an F0.5 Score of 89.12%. Compared to existing similarity-computation models based on GNNs, this model exhibits a Mean Squared Error (MSE) that is approximately 0.0041 to 0.0266 lower and an F0.5 Score that is 3.3259% to 6.4392% higher. It broadens the application scope of GNNs and offers additional insights for the study of code-similarity issues. Full article
11 pages, 282 KiB  
Article
Derivation of Bose’s Entropy Spectral Density from the Multiplicity of Energy Eigenvalues
by Arnaldo Spalvieri
Entropy 2024, 26(6), 504; https://doi.org/10.3390/e26060504 - 9 Jun 2024
Viewed by 250
Abstract
The modern textbook analysis of the thermal state of photons inside a three-dimensional reflective cavity is based on the three quantum numbers that characterize photon’s energy eigenvalues coming out when the boundary conditions are imposed. The crucial passage from the quantum numbers to [...] Read more.
The modern textbook analysis of the thermal state of photons inside a three-dimensional reflective cavity is based on the three quantum numbers that characterize photon’s energy eigenvalues coming out when the boundary conditions are imposed. The crucial passage from the quantum numbers to the continuous frequency is operated by introducing a three-dimensional continuous version of the three discrete quantum numbers, which leads to the energy spectral density and to the entropy spectral density. This standard analysis obscures the role of the multiplicity of energy eigenvalues associated to the same eigenfrequency. In this paper we review the past derivations of Bose’s entropy spectral density and present a new analysis of energy spectral density and entropy spectral density based on the multiplicity of energy eigenvalues. Our analysis explicitly defines the eigenfrequency distribution of energy and entropy and uses it as a starting point for the passage from the discrete eigenfrequencies to the continuous frequency. Full article
(This article belongs to the Section Thermodynamics)
15 pages, 283 KiB  
Article
Refinements and Extensions of Ziv’s Model of Perfect Secrecy for Individual Sequences
by Neri Merhav
Entropy 2024, 26(6), 503; https://doi.org/10.3390/e26060503 - 9 Jun 2024
Viewed by 212
Abstract
We refine and extend Ziv’s model and results regarding perfectly secure encryption of individual sequences. According to this model, the encrypter and the legitimate decrypter share a common secret key that is not shared with the unauthorized eavesdropper. The eavesdropper is aware of [...] Read more.
We refine and extend Ziv’s model and results regarding perfectly secure encryption of individual sequences. According to this model, the encrypter and the legitimate decrypter share a common secret key that is not shared with the unauthorized eavesdropper. The eavesdropper is aware of the encryption scheme and has some prior knowledge concerning the individual plaintext source sequence. This prior knowledge, combined with the cryptogram, is harnessed by the eavesdropper, who implements a finite-state machine as a mechanism for accepting or rejecting attempted guesses of the plaintext source. The encryption is considered perfectly secure if the cryptogram does not provide any new information to the eavesdropper that may enhance their knowledge concerning the plaintext beyond their prior knowledge. Ziv has shown that the key rate needed for perfect secrecy is essentially lower bounded by the finite-state compressibility of the plaintext sequence, a bound that is clearly asymptotically attained through Lempel–Ziv compression followed by one-time pad encryption. In this work, we consider some more general classes of finite-state eavesdroppers and derive the respective lower bounds on the key rates needed for perfect secrecy. These bounds are tighter and more refined than Ziv’s bound, and they are attained using encryption schemes that are based on different universal lossless compression schemes. We also extend our findings to the case where side information is available to the eavesdropper and the legitimate decrypter but may or may not be available to the encrypter. Full article
(This article belongs to the Collection Feature Papers in Information Theory)
9 pages, 599 KiB  
Article
Modelling Heterogeneous Anomalous Dynamics of Radiation-Induced Double-Strand Breaks in DNA during Non-Homologous End-Joining Pathway
by Nickolay Korabel, John W. Warmenhoven, Nicholas T. Henthorn, Samuel Ingram, Sergei Fedotov, Charlotte J. Heaven, Karen J. Kirkby, Michael J. Taylor and Michael J. Merchant
Entropy 2024, 26(6), 502; https://doi.org/10.3390/e26060502 - 8 Jun 2024
Viewed by 259
Abstract
The process of end-joining during nonhomologous repair of DNA double-strand breaks (DSBs) after radiation damage is considered. Experimental evidence has revealed that the dynamics of DSB ends exhibit subdiffusive motion rather than simple diffusion with rare directional movement. Traditional models often overlook the [...] Read more.
The process of end-joining during nonhomologous repair of DNA double-strand breaks (DSBs) after radiation damage is considered. Experimental evidence has revealed that the dynamics of DSB ends exhibit subdiffusive motion rather than simple diffusion with rare directional movement. Traditional models often overlook the rare long-range directed motion. To address this limitation, we present a heterogeneous anomalous diffusion model consisting of subdiffusive fractional Brownian motion interchanged with short periods of long-range movement. Our model sheds light on the underlying mechanisms of heterogeneous diffusion in DSB repair and could be used to quantify the DSB dynamics on a time scale inaccessible to single particle tracking analysis. The model predicts that the long-range movement of DSB ends is responsible for the misrepair of DSBs in the form of dicentric chromosome lesions. Full article
27 pages, 3937 KiB  
Article
Simultaneous Optimization and Integration of Multiple Process Heat Cascade and Site Utility Selection for the Design of a New Generation of Sugarcane Biorefinery
by Victor Fernandes Garcia and Adriano Viana Ensinas
Entropy 2024, 26(6), 501; https://doi.org/10.3390/e26060501 - 8 Jun 2024
Viewed by 176
Abstract
Biorefinery plays a crucial role in the decarbonization of the current economic model, but its high investments and costs make its products less competitive. Identifying the best technological route to maximize operational synergies is crucial for its viability. This study presents a new [...] Read more.
Biorefinery plays a crucial role in the decarbonization of the current economic model, but its high investments and costs make its products less competitive. Identifying the best technological route to maximize operational synergies is crucial for its viability. This study presents a new superstructure model based on mixed integer linear programming to identify an ideal biorefinery configuration. The proposed formulation considers the selection and process scale adjustment, utility selection, and heat integration by heat cascade integration from different processes. The formulation is tested by a study where the impact of new technologies on energy efficiency and the total annualized cost of a sugarcane biorefinery is evaluated. As a result, the energy efficiency of biorefinery increased from 50.25% to 74.5% with methanol production through bagasse gasification, mainly due to its high heat availability that can be transferred to the distillery, which made it possible to shift the bagasse flow from the cogeneration to gasification process. Additionally, the production of DME yields outcomes comparable to methanol production. However, CO2 hydrogenation negatively impacts profitability and energy efficiency due to the significant consumption and electricity cost. Nonetheless, it is advantageous for surface power density as it increases biofuel production without expanding the biomass area. Full article
(This article belongs to the Special Issue Thermodynamic Optimization of Industrial Energy Systems)
28 pages, 4312 KiB  
Article
Intermediate Judgments and Trust in Artificial Intelligence-Supported Decision-Making
by Scott Humr and Mustafa Canan
Entropy 2024, 26(6), 500; https://doi.org/10.3390/e26060500 - 8 Jun 2024
Viewed by 417
Abstract
Human decision-making is increasingly supported by artificial intelligence (AI) systems. From medical imaging analysis to self-driving vehicles, AI systems are becoming organically embedded in a host of different technologies. However, incorporating such advice into decision-making entails a human rationalization of AI outputs for [...] Read more.
Human decision-making is increasingly supported by artificial intelligence (AI) systems. From medical imaging analysis to self-driving vehicles, AI systems are becoming organically embedded in a host of different technologies. However, incorporating such advice into decision-making entails a human rationalization of AI outputs for supporting beneficial outcomes. Recent research suggests intermediate judgments in the first stage of a decision process can interfere with decisions in subsequent stages. For this reason, we extend this research to AI-supported decision-making to investigate how intermediate judgments on AI-provided advice may influence subsequent decisions. In an online experiment (N = 192), we found a consistent bolstering effect in trust for those who made intermediate judgments and over those who did not. Furthermore, violations of total probability were observed at all timing intervals throughout the study. We further analyzed the results by demonstrating how quantum probability theory can model these types of behaviors in human–AI decision-making and ameliorate the understanding of the interaction dynamics at the confluence of human factors and information features. Full article
(This article belongs to the Section Quantum Information)
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28 pages, 3502 KiB  
Review
On Casimir and Helmholtz Fluctuation-Induced Forces in Micro- and Nano-Systems: Survey of Some Basic Results
by Daniel Dantchev
Entropy 2024, 26(6), 499; https://doi.org/10.3390/e26060499 - 7 Jun 2024
Viewed by 404
Abstract
Fluctuations are omnipresent; they exist in any matter, due either to its quantum nature or to its nonzero temperature. In the current review, we briefly cover the quantum electrodynamic Casimir (QED) force as well as the critical Casimir (CC) and Helmholtz (HF) forces. [...] Read more.
Fluctuations are omnipresent; they exist in any matter, due either to its quantum nature or to its nonzero temperature. In the current review, we briefly cover the quantum electrodynamic Casimir (QED) force as well as the critical Casimir (CC) and Helmholtz (HF) forces. In the QED case, the medium is usually a vacuum and the massless excitations are photons, while in the CC and HF cases the medium is usually a critical or correlated fluid and the fluctuations of the order parameter are the cause of the force between the macroscopic or mesoscopic bodies immersed in it. We discuss the importance of the presented results for nanotechnology, especially for devising and assembling micro- or nano-scale systems. Several important problems for nanotechnology following from the currently available experimental findings are spelled out, and possible strategies for overcoming them are sketched. Regarding the example of HF, we explicitly demonstrate that when a given integral quantity characterizing the fluid is conserved, it has an essential influence on the behavior of the corresponding fluctuation-induced force. Full article
(This article belongs to the Collection Foundations of Statistical Mechanics)
17 pages, 463 KiB  
Article
A Semiparametric Bayesian Approach to Heterogeneous Spatial Autoregressive Models
by Ting Liu, Dengke Xu and Shiqi Ke
Entropy 2024, 26(6), 498; https://doi.org/10.3390/e26060498 - 7 Jun 2024
Viewed by 229
Abstract
Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed [...] Read more.
Many semiparametric spatial autoregressive (SSAR) models have been used to analyze spatial data in a variety of applications; however, it is a common phenomenon that heteroscedasticity often occurs in spatial data analysis. Therefore, when considering SSAR models in this paper, it is allowed that the variance parameters of the models can depend on the explanatory variable, and these are called heterogeneous semiparametric spatial autoregressive models. In order to estimate the model parameters, a Bayesian estimation method is proposed for heterogeneous SSAR models based on B-spline approximations of the nonparametric function. Then, we develop an efficient Markov chain Monte Carlo sampling algorithm on the basis of the Gibbs sampler and Metropolis–Hastings algorithm that can be used to generate posterior samples from posterior distributions and perform posterior inference. Finally, some simulation studies and real data analysis of Boston housing data have demonstrated the excellent performance of the proposed Bayesian method. Full article
(This article belongs to the Special Issue Markov Chain Monte Carlo for Bayesian Inference)
16 pages, 2640 KiB  
Article
Finite-Time Dynamics of an Entanglement Engine: Current, Fluctuations and Kinetic Uncertainty Relations
by Jeanne Bourgeois, Gianmichele Blasi, Shishir Khandelwal and Géraldine Haack
Entropy 2024, 26(6), 497; https://doi.org/10.3390/e26060497 - 7 Jun 2024
Viewed by 183
Abstract
Entanglement engines are autonomous quantum thermal machines designed to generate entanglement from the presence of a particle current flowing through the device. In this work, we investigate the functioning of a two-qubit entanglement engine beyond the steady-state regime. Within a master equation approach, [...] Read more.
Entanglement engines are autonomous quantum thermal machines designed to generate entanglement from the presence of a particle current flowing through the device. In this work, we investigate the functioning of a two-qubit entanglement engine beyond the steady-state regime. Within a master equation approach, we derive the time-dependent state, the particle current, as well as the associated current correlation functions. Our findings establish a direct connection between coherence and internal current, elucidating the existence of a critical current that serves as an indicator for entanglement in the steady state. We then apply our results to investigate kinetic uncertainty relations (KURs) at finite times. We demonstrate that there is more than one possible definition for KURs at finite times. Although the two definitions agree in the steady-state regime, they lead to different parameter ranges for violating KUR at finite times. Full article
(This article belongs to the Special Issue Advances in Quantum Thermodynamics)
12 pages, 588 KiB  
Article
Purported Self-Organized Criticality of the Cardiovascular Function: Methodological Considerations for Zipf’s Law Analysis
by Jacques-Olivier Fortrat
Entropy 2024, 26(6), 496; https://doi.org/10.3390/e26060496 - 7 Jun 2024
Viewed by 281
Abstract
Self-organized criticality is a universal theory for dynamical systems that has recently been applied to the cardiovascular system. Precise methodological approaches are essential for understanding the dynamics of cardiovascular self-organized criticality. This study examines how the duration and quality of data recording affect [...] Read more.
Self-organized criticality is a universal theory for dynamical systems that has recently been applied to the cardiovascular system. Precise methodological approaches are essential for understanding the dynamics of cardiovascular self-organized criticality. This study examines how the duration and quality of data recording affect the analysis of cardiovascular self-organized criticality, with a focus on the beat-by-beat heart rate variability time series obtained from seven healthy subjects in a standing position. Drawing a Zipf diagram, we evaluated the distribution of cardiovascular events of bradycardia and tachycardia. We identified tipping points for the distribution of both bradycardia and tachycardia events. By varying the recording durations (1, 2, 5, 10, 20, 30, and 40 min) and sampling frequencies (500, 250, and 100 Hz), we investigated their influence on the observed distributions. While shorter recordings can effectively capture cardiovascular events, they may underestimate the variables describing their distribution. Additionally, the tipping point of the Zipf distribution differs between bradycardia and tachycardia events. Comparisons of the distribution of bradycardia and tachycardia events should be conducted using long data recordings. Utilizing devices with lower sampling frequencies may compromise data fidelity. These insights contribute to refining experimental protocols and advancing our understanding of the complex dynamics underlying cardiovascular regulation. Full article
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58 pages, 131141 KiB  
Article
Neural Activity in Quarks Language: Lattice Field Theory for a Network of Real Neurons
by Giampiero Bardella, Simone Franchini, Liming Pan, Riccardo Balzan, Surabhi Ramawat, Emiliano Brunamonti, Pierpaolo Pani and Stefano Ferraina
Entropy 2024, 26(6), 495; https://doi.org/10.3390/e26060495 - 6 Jun 2024
Viewed by 468
Abstract
Brain–computer interfaces have seen extraordinary surges in developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This discrepancy becomes particularly pronounced when examining the collective [...] Read more.
Brain–computer interfaces have seen extraordinary surges in developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This discrepancy becomes particularly pronounced when examining the collective neural activity at the micro and meso scale, where a coherent formalization that adequately describes neural interactions is still lacking. Here, we introduce a mathematical framework to analyze systems of natural neurons and interpret the related empirical observations in terms of lattice field theory, an established paradigm from theoretical particle physics and statistical mechanics. Our methods are tailored to interpret data from chronic neural interfaces, especially spike rasters from measurements of single neuron activity, and generalize the maximum entropy model for neural networks so that the time evolution of the system is also taken into account. This is obtained by bridging particle physics and neuroscience, paving the way for particle physics-inspired models of the neocortex. Full article
(This article belongs to the Special Issue Entropy and Information in Biological Systems)
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11 pages, 589 KiB  
Article
The Information Length Concept Applied to Plasma Turbulence
by Johan Anderson, Kenji Imadera, Sara Moradi and Tariq Rafiq
Entropy 2024, 26(6), 494; https://doi.org/10.3390/e26060494 - 5 Jun 2024
Viewed by 260
Abstract
A methodology to study statistical properties of anomalous transport in fusion plasma is investigated. Three time traces generated by the full-f gyrokinetic code GKNET are analyzed for this purpose. The time traces consist of heat flux as a function of the radial position, [...] Read more.
A methodology to study statistical properties of anomalous transport in fusion plasma is investigated. Three time traces generated by the full-f gyrokinetic code GKNET are analyzed for this purpose. The time traces consist of heat flux as a function of the radial position, which is studied in a novel manner using statistical methods. The simulation data exhibit transport processes with both medium and long correlation length along the radius. A typical example of a phenomenon with long correlation length is avalanches. In order to investigate the evolution of the turbulent state, two basic configurations are studied, one flux-driven and one gradient-driven with decaying turbulence. The information length concept in tandem with Boltzmann–Gibbs and Tsallis entropy is used in the investigation. It is found that the dynamical states in both flux-driven and gradient-driven cases are surprisingly similar, but the Tsallis entropy reveals differences between them. This indicates that the types of probability distribution function are nevertheless quite different since the higher moments are significantly different. Full article
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15 pages, 562 KiB  
Article
Classical Modeling of a Lossy Gaussian Bosonic Sampler
by Mikhail V. Umanskii and Alexey N. Rubtsov
Entropy 2024, 26(6), 493; https://doi.org/10.3390/e26060493 - 5 Jun 2024
Viewed by 228
Abstract
Gaussian boson sampling (GBS) is considered a candidate problem for demonstrating quantum advantage. We propose an algorithm for the approximate classical simulation of a lossy GBS instance. The algorithm relies on the Taylor series expansion, and increasing the number of terms of the [...] Read more.
Gaussian boson sampling (GBS) is considered a candidate problem for demonstrating quantum advantage. We propose an algorithm for the approximate classical simulation of a lossy GBS instance. The algorithm relies on the Taylor series expansion, and increasing the number of terms of the expansion that are used in the calculation yields greater accuracy. The complexity of the algorithm is polynomial in the number of modes given the number of terms is fixed. We describe conditions for the input state squeezing parameter and loss level that provide the best efficiency for this algorithm (by efficient, we mean that the Taylor series converges quickly). In recent experiments that claim to have demonstrated quantum advantage, these conditions are satisfied; thus, this algorithm can be used to classically simulate these experiments. Full article
(This article belongs to the Topic Quantum Information and Quantum Computing, 2nd Volume)
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16 pages, 86910 KiB  
Article
Chaos-Assisted Dynamical Tunneling in Flat Band Superwires
by Anton M. Graf, Ke Lin, MyeongSeo Kim, Joonas Keski-Rahkonen, Alvar Daza and Eric J. Heller
Entropy 2024, 26(6), 492; https://doi.org/10.3390/e26060492 - 5 Jun 2024
Viewed by 270
Abstract
Recent theoretical investigations have revealed unconventional transport mechanisms within high Brillouin zones of two-dimensional superlattices. Electrons can navigate along channels we call superwires, gently guided without brute force confinement. Such dynamical confinement is caused by weak superlattice deflections, markedly different from the static [...] Read more.
Recent theoretical investigations have revealed unconventional transport mechanisms within high Brillouin zones of two-dimensional superlattices. Electrons can navigate along channels we call superwires, gently guided without brute force confinement. Such dynamical confinement is caused by weak superlattice deflections, markedly different from the static or energetic confinement observed in traditional wave guides or one-dimensional electron wires. The quantum properties of superwires give rise to elastic dynamical tunneling, linking disjoint regions of the corresponding classical phase space, and enabling the emergence of several parallel channels. This paper provides the underlying theory and mechanisms that facilitate dynamical tunneling assisted by chaos in periodic lattices. Moreover, we show that the mechanism of dynamical tunneling can be effectively conceptualized through the lens of a paraxial approximation. Our results further reveal that superwires predominantly exist within flat bands, emerging from eigenstates that represent linear combinations of conventional degenerate Bloch states. Finally, we quantify tunneling rates across various lattice configurations and demonstrate that tunneling can be suppressed in a controlled fashion, illustrating potential implications in future nanodevices. Full article
(This article belongs to the Special Issue Tunneling in Complex Systems)
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16 pages, 2683 KiB  
Article
Correlations of Cross-Entropy Loss in Machine Learning
by Richard Connor, Alan Dearle, Ben Claydon and Lucia Vadicamo
Entropy 2024, 26(6), 491; https://doi.org/10.3390/e26060491 - 3 Jun 2024
Viewed by 136
Abstract
Cross-entropy loss is crucial in training many deep neural networks. In this context, we show a number of novel and strong correlations among various related divergence functions. In particular, we demonstrate that, in some circumstances, (a) cross-entropy is almost perfectly correlated with the [...] Read more.
Cross-entropy loss is crucial in training many deep neural networks. In this context, we show a number of novel and strong correlations among various related divergence functions. In particular, we demonstrate that, in some circumstances, (a) cross-entropy is almost perfectly correlated with the little-known triangular divergence, and (b) cross-entropy is strongly correlated with the Euclidean distance over the logits from which the softmax is derived. The consequences of these observations are as follows. First, triangular divergence may be used as a cheaper alternative to cross-entropy. Second, logits can be used as features in a Euclidean space which is strongly synergistic with the classification process. This justifies the use of Euclidean distance over logits as a measure of similarity, in cases where the network is trained using softmax and cross-entropy. We establish these correlations via empirical observation, supported by a mathematical explanation encompassing a number of strongly related divergence functions. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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20 pages, 1971 KiB  
Article
Continuous-Time Quantum Walk in Glued Trees: Localized State-Mediated Almost Perfect Quantum-State Transfer
by Vincent Pouthier, Lucie Pepe and Saad Yalouz
Entropy 2024, 26(6), 490; https://doi.org/10.3390/e26060490 - 2 Jun 2024
Viewed by 212
Abstract
In this work, the dynamics of a quantum walker on glued trees is revisited to understand the influence of the architecture of the graph on the efficiency of the transfer between the two roots. Instead of considering regular binary trees, we focus our [...] Read more.
In this work, the dynamics of a quantum walker on glued trees is revisited to understand the influence of the architecture of the graph on the efficiency of the transfer between the two roots. Instead of considering regular binary trees, we focus our attention on leafier structures where each parent node could give rise to a larger number of children. Through extensive numerical simulations, we uncover a significant dependence of the transfer on the underlying graph architecture, particularly influenced by the branching rate (M) relative to the root degree (N). Our study reveals that the behavior of the walker is isomorphic to that of a particle moving on a finite-size chain. This chain exhibits defects that originate in the specific nature of both the roots and the leaves. Therefore, the energy spectrum of the chain showcases rich features, which lead to diverse regimes for the quantum-state transfer. Notably, the formation of quasi-degenerate localized states due to significant disparities between M and N triggers a localization process on the roots. Through analytical development, we demonstrate that these states play a crucial role in facilitating almost perfect quantum beats between the roots, thereby enhancing the transfer efficiency. Our findings offer valuable insights into the mechanisms governing quantum-state transfer on trees, with potential applications for the transfer of quantum information. Full article
(This article belongs to the Special Issue Quantum Walks for Quantum Technologies)
12 pages, 769 KiB  
Review
Entropy and the Limits to Growth
by Reiner Kümmel
Entropy 2024, 26(6), 489; https://doi.org/10.3390/e26060489 - 31 May 2024
Viewed by 201
Abstract
In its business-as-usual scenario, the 1972 Club-of-Rome report—The Limits to Growth—describes the collapse of the world economy around the year 2030, either because of the scarcity of natural resources or because of pollution. Mainstream economists, the high priests of secular societies, condemned it [...] Read more.
In its business-as-usual scenario, the 1972 Club-of-Rome report—The Limits to Growth—describes the collapse of the world economy around the year 2030, either because of the scarcity of natural resources or because of pollution. Mainstream economists, the high priests of secular societies, condemned it fiercely. Their gospel of perpetual economic growth, during which technological progress would solve all problems, promises a bright future for all mankind. On the other hand, engineers, natural scientists, and mathematicians realized that the breakdown scenario is due to the inclusion of the First and the Second Law of Thermodynamics in the Club-of-Rome’s world model. According to these laws, nothing happens in the world without energy conversion and entropy production. In 1865, Rudolph Clausius, the discoverer of entropy, published the laws as the constitution of the universe. Entropy is the physical measure of disorder. Without a proper understanding of energy and entropy in the economy, all efforts to achieve sustainability will fail. Full article
(This article belongs to the Section Complexity)
14 pages, 6693 KiB  
Article
Quantum Key Distribution with Displaced Thermal States
by Adam Walton, Anne Ghesquière and Benjamin T.H. Varcoe
Entropy 2024, 26(6), 488; https://doi.org/10.3390/e26060488 - 31 May 2024
Viewed by 172
Abstract
Secret key exchange relies on the creation of correlated signals, serving as the raw resource for secure communication. Thermal states exhibit Hanbury Brown and Twiss correlations, which offer a promising avenue for generating such signals. In this paper, we present an experimental implementation [...] Read more.
Secret key exchange relies on the creation of correlated signals, serving as the raw resource for secure communication. Thermal states exhibit Hanbury Brown and Twiss correlations, which offer a promising avenue for generating such signals. In this paper, we present an experimental implementation of a central broadcast thermal-state quantum key distribution (QKD) protocol in the microwave region. Our objective is to showcase a straightforward method of QKD utilizing readily available broadcasting equipment. Unlike conventional approaches to thermal-state QKD, we leverage displaced thermal states. These states enable us to share the output of a thermal source among Alice, Bob, and Eve via both waveguide channels and free space. Through measurement and conversion into bit strings, our protocol produces key-ready bit strings without the need for specialized equipment. By harnessing the inherent noise in thermal broadcasts, our setup facilitates the recovery of distinct bit strings by all parties involved. Full article
21 pages, 5733 KiB  
Article
A Circular-Linear Probabilistic Model Based on Nonparametric Copula with Applications to Directional Wind Energy Assessment
by Jie Liu and Zaizai Yan
Entropy 2024, 26(6), 487; https://doi.org/10.3390/e26060487 - 31 May 2024
Viewed by 135
Abstract
The joint probability density function of wind speed and wind direction serves as the mathematical basis for directional wind energy assessment. In this study, a nonparametric joint probability estimation system for wind velocity and direction based on copulas is proposed and empirically investigated [...] Read more.
The joint probability density function of wind speed and wind direction serves as the mathematical basis for directional wind energy assessment. In this study, a nonparametric joint probability estimation system for wind velocity and direction based on copulas is proposed and empirically investigated in Inner Mongolia, China. Optimal bandwidth algorithms and transformation techniques are used to determine the nonparametric copula method. Various parameter copula models and models without considering dependency relationships are introduced and compared with this approach. The results indicate a significant advantage of employing the nonparametric copula model for fitting joint probability distributions of both wind speed and wind direction, as well as conducting correlation analyses. By utilizing the proposed KDE-COP-CV model, it becomes possible to accurately and reliably analyze how wind power density fluctuates in relation to wind direction. This study reveals the researched region possesses abundant wind resources, with the highest wind power density being highly dependent on wind direction at maximum speeds. Wind resources in selected regions of Inner Mongolia are predominantly concentrated in the northwest and west directions. These findings can contribute to improving the accuracy of micro-siting for wind farms, as well as optimizing the design and capacity of wind turbine generators. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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