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Editor’s Choice Articles

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

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21 pages, 10983 KB  
Review
Machine Learning Advances in High-Entropy Alloys: A Mini-Review
by Yibo Sun and Jun Ni
Entropy 2024, 26(12), 1119; https://doi.org/10.3390/e26121119 - 20 Dec 2024
Cited by 7 | Viewed by 4149
Abstract
The efficacy of machine learning has increased exponentially over the past decade. The utilization of machine learning to predict and design materials has become a pivotal tool for accelerating materials development. High-entropy alloys are particularly intriguing candidates for exemplifying the potency of machine [...] Read more.
The efficacy of machine learning has increased exponentially over the past decade. The utilization of machine learning to predict and design materials has become a pivotal tool for accelerating materials development. High-entropy alloys are particularly intriguing candidates for exemplifying the potency of machine learning due to their superior mechanical properties, vast compositional space, and intricate chemical interactions. This review examines the general process of developing machine learning models. The advances and new algorithms of machine learning in the field of high-entropy alloys are presented in each part of the process. These advances are based on both improvements in computer algorithms and physical representations that focus on the unique ordering properties of high-entropy alloys. We also show the results of generative models, data augmentation, and transfer learning in high-entropy alloys and conclude with a summary of the challenges still faced in machine learning high-entropy alloys today. Full article
(This article belongs to the Special Issue Exploring Complexity: Short-Range Order in Medium and High-Entropy Materials)
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33 pages, 5394 KB  
Article
Carnot and the Archetype of Waterfalls
by Hans U. Fuchs, Elisabeth Dumont and Federico Corni
Entropy 2024, 26(12), 1066; https://doi.org/10.3390/e26121066 - 7 Dec 2024
Cited by 2 | Viewed by 1409
Abstract
Carnot treats Heat as a Force of Nature, with its typical fundamental characteristics of intensity and thermal tension (temperature and temperature difference), extension (amount of heat, i.e., caloric), and power. To suggest how the three aspects are related, he applies the imagery of [...] Read more.
Carnot treats Heat as a Force of Nature, with its typical fundamental characteristics of intensity and thermal tension (temperature and temperature difference), extension (amount of heat, i.e., caloric), and power. To suggest how the three aspects are related, he applies the imagery of waterfalls to causative thermal processes: heat powers motion in a heat engine just as falling water does when activating rotation in a water wheel. We understand Carnot’s waterfall imagery as an archetype of human reasoning—as an embodiment of how we experience and understand causative (agentive) phenomena. We project it onto the macroscopic phenomena identified in physical science and so unlock the power of analogical structure mapping between theories of fluids, electricity and magnetism, heat, substances, gravity, and linear and rotational motion. In particular, the notion of (motive) power of a waterfall lets us create imaginative explanations of the interactions of Forces of Nature and helps us construct a generalized energy principle. Two-hundred years after Carnot made us aware of it, his Waterfall Analogy is a powerful example of theory construction with roots deep in how we experience phenomena as caused by natural agents. Full article
(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)
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11 pages, 286 KB  
Article
Entropic Order Parameters for Categorical Symmetries in 2D-CFT
by Javier Molina-Vilaplana, Pablo Saura-Bastida and Germán Sierra
Entropy 2024, 26(12), 1064; https://doi.org/10.3390/e26121064 - 6 Dec 2024
Cited by 1 | Viewed by 730
Abstract
In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in (1+1)-d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states [...] Read more.
In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in (1+1)-d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of (1+1)-d theories with categorical symmetries. Full article
(This article belongs to the Special Issue Entanglement Entropy in Quantum Field Theory)
20 pages, 845 KB  
Article
Kinetic Theory of Self-Propelled Particles with Nematic Alignment
by Horst-Holger Boltz, Benjamin Kohler and Thomas Ihle
Entropy 2024, 26(12), 1054; https://doi.org/10.3390/e26121054 - 4 Dec 2024
Cited by 3 | Viewed by 2062
Abstract
We present the results from kinetic theory for a system of self-propelled particles with alignment interactions of higher-order symmetry, particularly nematic ones. To this end, we use the Landau equation approach, a systematic approximation to the BBGKY hierarchy for small effective couplings. Our [...] Read more.
We present the results from kinetic theory for a system of self-propelled particles with alignment interactions of higher-order symmetry, particularly nematic ones. To this end, we use the Landau equation approach, a systematic approximation to the BBGKY hierarchy for small effective couplings. Our calculations are presented in a pedagogical way with the explicit goal of serving as a tutorial from a physicists’ perspective into applying kinetic theory ideas beyond mean-field to active matter systems with essentially no prerequisites and yield predictions without free parameters that are in quantitative agreement with direct agent-based simulations Full article
(This article belongs to the Collection Foundations of Statistical Mechanics)
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32 pages, 686 KB  
Article
Opening the AI Black Box: Distilling Machine-Learned Algorithms into Code
by Eric J. Michaud, Isaac Liao, Vedang Lad, Ziming Liu, Anish Mudide, Chloe Loughridge, Zifan Carl Guo, Tara Rezaei Kheirkhah, Mateja Vukelić and Max Tegmark
Entropy 2024, 26(12), 1046; https://doi.org/10.3390/e26121046 - 2 Dec 2024
Cited by 2 | Viewed by 2970
Abstract
Can we turn AI black boxes into code? Although this mission sounds extremely challenging, we show that it is not entirely impossible by presenting a proof-of-concept method, MIPS, that can synthesize programs based on the automated mechanistic interpretability of neural networks trained to [...] Read more.
Can we turn AI black boxes into code? Although this mission sounds extremely challenging, we show that it is not entirely impossible by presenting a proof-of-concept method, MIPS, that can synthesize programs based on the automated mechanistic interpretability of neural networks trained to perform the desired task, auto-distilling the learned algorithm into Python code. We test MIPS on a benchmark of 62 algorithmic tasks that can be learned by an RNN and find it highly complementary to GPT-4: MIPS solves 32 of them, including 13 that are not solved by GPT-4 (which also solves 30). MIPS uses an integer autoencoder to convert the RNN into a finite state machine, then applies Boolean or integer symbolic regression to capture the learned algorithm. As opposed to large language models, this program synthesis technique makes no use of (and is therefore not limited by) human training data such as algorithms and code from GitHub. We discuss opportunities and challenges for scaling up this approach to make machine-learned models more interpretable and trustworthy. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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7 pages, 216 KB  
Article
A Characterization of Optimal Prefix Codes
by Spencer Congero and Kenneth Zeger
Entropy 2024, 26(12), 1000; https://doi.org/10.3390/e26121000 - 21 Nov 2024
Cited by 2 | Viewed by 962
Abstract
A property of prefix codes called strong monotonicity is introduced, and it is proven that for a given source, a prefix code is optimal if and only if it is complete and strongly monotone. Full article
(This article belongs to the Special Issue Advances in Information and Coding Theory, the Third Edition)
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19 pages, 903 KB  
Article
A Contemporary View on Carnot’s Réflexions
by Jan-Peter Meyn
Entropy 2024, 26(12), 1002; https://doi.org/10.3390/e26121002 - 21 Nov 2024
Cited by 1 | Viewed by 987
Abstract
Entropy and energy had not yet been introduced to physics by the time Carnot wrote his seminal Réflexions. Scholars continue to discuss what he really had in mind and what misconceptions he might have had. Actually, his work can be read as a [...] Read more.
Entropy and energy had not yet been introduced to physics by the time Carnot wrote his seminal Réflexions. Scholars continue to discuss what he really had in mind and what misconceptions he might have had. Actually, his work can be read as a correct introduction to the physics of heat engines when the term calorique is replaced by entropy and entropy is used as the other fundamental thermal quantity besides temperature. Carnot’s concepts of falling entropy as an analogy to the waterfall, and the separation of real thermal processes into reversible and irreversible processes are adopted. Some details of Carnot’s treatise are ignored, but the principal ideas are quoted and assumed without modification. With only two thermal quantities, temperature and entropy, modern heat engines can be explained in detail. Only after the principal function of heat engines is developed is energy introduced as physical quantity in order to compare thermal engines with mechanical and electrical engines and, specifically, to calculate efficiency. Full article
(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)
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12 pages, 359 KB  
Article
Statistical Properties of Superpositions of Coherent Phase States with Opposite Arguments
by Miguel Citeli de Freitas and Viktor V. Dodonov
Entropy 2024, 26(11), 977; https://doi.org/10.3390/e26110977 - 15 Nov 2024
Viewed by 913
Abstract
We calculate the second-order moments, the Robertson–Schrödinger uncertainty product, and the Mandel factor for various superpositions of coherent phase states with opposite arguments, comparing the results with similar superpositions of the usual (Klauder–Glauber–Sudarshan) coherent states. We discover that the coordinate variance in the [...] Read more.
We calculate the second-order moments, the Robertson–Schrödinger uncertainty product, and the Mandel factor for various superpositions of coherent phase states with opposite arguments, comparing the results with similar superpositions of the usual (Klauder–Glauber–Sudarshan) coherent states. We discover that the coordinate variance in the analog of even coherent states can show the most strong squeezing effect, close to the maximal possible squeezing for the given mean photon number. On the other hand, the Robertson–Schrödinger (RS) uncertainty product in superpositions of coherent phase states increases much slower (as function of the mean photon number) than in superpositions of the usual coherent states. A nontrivial behavior of the Mandel factor for small mean photon numbers is discovered in superpositions with unequal weights of two components. An exceptional nature of the even and odd superpositions is demonstrated. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness V)
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50 pages, 751 KB  
Article
Non-Equilibrium Quantum Brain Dynamics: Water Coupled with Phonons and Photons
by Akihiro Nishiyama, Shigenori Tanaka and Jack Adam Tuszynski
Entropy 2024, 26(11), 981; https://doi.org/10.3390/e26110981 - 15 Nov 2024
Viewed by 1463
Abstract
We investigate Quantum Electrodynamics (QED) of water coupled with sound and light, namely Quantum Brain Dynamics (QBD) of water, phonons and photons. We provide phonon degrees of freedom as additional quanta in the framework of QBD in this paper. We begin with the [...] Read more.
We investigate Quantum Electrodynamics (QED) of water coupled with sound and light, namely Quantum Brain Dynamics (QBD) of water, phonons and photons. We provide phonon degrees of freedom as additional quanta in the framework of QBD in this paper. We begin with the Lagrangian density QED with non-relativistic charged bosons, photons and phonons, and derive time-evolution equations of coherent fields and Kadanoff–Baym (KB) equations for incoherent particles. We next show an acoustic super-radiance solution in our model. We also introduce a kinetic entropy current in KB equations in 1st order approximation in the gradient expansion and show the H-theorem for self-energy in Hartree–Fock approximation. We finally derive conserved number density of charged bosons and conserved energy density in spatially homogeneous system. Full article
(This article belongs to the Section Quantum Information)
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13 pages, 4232 KB  
Article
Universality of Dynamical Symmetries in Chaotic Maps
by Marcos Acero, Sean Lyons, Andrés Aragoneses and Arjendu K. Pattanayak
Entropy 2024, 26(11), 969; https://doi.org/10.3390/e26110969 - 12 Nov 2024
Cited by 2 | Viewed by 1473
Abstract
Identifying signs of regularity and uncovering dynamical symmetries in complex and chaotic systems is crucial both for practical applications and for enhancing our understanding of complex dynamics. Recent approaches have quantified temporal correlations in time series, revealing hidden, approximate dynamical symmetries that provide [...] Read more.
Identifying signs of regularity and uncovering dynamical symmetries in complex and chaotic systems is crucial both for practical applications and for enhancing our understanding of complex dynamics. Recent approaches have quantified temporal correlations in time series, revealing hidden, approximate dynamical symmetries that provide insight into the systems under study. In this paper, we explore universality patterns in the dynamics of chaotic maps using combinations of complexity quantifiers. We also apply a recently introduced technique that projects dynamical symmetries into a “symmetry space”, providing an intuitive and visual depiction of these symmetries. Our approach unifies and extends previous results and, more importantly, offers a meaningful interpretation of universality by linking it with dynamical symmetries and their transitions. Full article
(This article belongs to the Special Issue Ordinal Patterns-Based Tools and Their Applications)
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8 pages, 275 KB  
Article
Modified Landauer Principle According to Tsallis Entropy
by Luis Herrera
Entropy 2024, 26(11), 931; https://doi.org/10.3390/e26110931 - 31 Oct 2024
Viewed by 1555
Abstract
The Landauer principle establishes a lower bound in the amount of energy that should be dissipated in the erasure of one bit of information. The specific value of this dissipated energy is tightly related to the definition of entropy. In this article, we [...] Read more.
The Landauer principle establishes a lower bound in the amount of energy that should be dissipated in the erasure of one bit of information. The specific value of this dissipated energy is tightly related to the definition of entropy. In this article, we present a generalization of the Landauer principle based on the Tsallis entropy. Some consequences resulting from such a generalization are discussed. These consequences include the modification to the mass ascribed to one bit of information, the generalization of the Landauer principle to the case when the system is embedded in a gravitational field, and the number of bits radiated in the emission of gravitational waves. Full article
(This article belongs to the Special Issue The Landauer Principle and Its Implementations in Physics, Chemistry and Biology: Current Status, Critics and Controversies)
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18 pages, 309 KB  
Article
Interval-Valued Random Matrices
by Abdolnasser Sadeghkhani and Ali Sadeghkhani
Entropy 2024, 26(11), 899; https://doi.org/10.3390/e26110899 - 23 Oct 2024
Viewed by 1192
Abstract
This paper introduces a novel approach that combines symbolic data analysis with matrix theory through the concept of interval-valued random matrices. This framework is designed to address the complexities of real-world data, offering enhanced statistical modeling techniques particularly suited for large and complex [...] Read more.
This paper introduces a novel approach that combines symbolic data analysis with matrix theory through the concept of interval-valued random matrices. This framework is designed to address the complexities of real-world data, offering enhanced statistical modeling techniques particularly suited for large and complex datasets where traditional methods may be inadequate. We develop both frequentist and Bayesian methods for the statistical inference of interval-valued random matrices, providing a comprehensive analytical framework. We conduct extensive simulations to compare the performance of these methods, demonstrating that Bayesian estimators outperform maximum likelihood estimators under the Frobenius norm loss function. The practical utility of our approach is further illustrated through an application to climatology and temperature data, highlighting the advantages of interval-valued random matrices in real-world scenarios. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
22 pages, 1739 KB  
Article
Approach Based on the Ordered Fuzzy Decision Making System Dedicated to Supplier Evaluation in Supply Chain Management
by Katarzyna Rudnik, Anna Chwastyk and Iwona Pisz
Entropy 2024, 26(10), 860; https://doi.org/10.3390/e26100860 - 12 Oct 2024
Cited by 6 | Viewed by 1854
Abstract
The selection of suppliers represents a pivotal aspect of supply chain management and has a considerable impact on the success and competitiveness of the organization in question. The selection of a suitable supplier is a multi-criteria decision making (MCDM) problem based on a [...] Read more.
The selection of suppliers represents a pivotal aspect of supply chain management and has a considerable impact on the success and competitiveness of the organization in question. The selection of a suitable supplier is a multi-criteria decision making (MCDM) problem based on a number of qualitative, quantitative, and even conflicting criteria. The aim of this paper is to propose a novel MCDM approach dedicated to the supplier evaluation problem using an ordered fuzzy decision making system. This study uses a fuzzy inference system based on IF–THEN rules with ordered fuzzy numbers (OFNs). The approach employs the concept of OFNs to account for potential uncertainty and subjectivity in the decision making process, and it also takes into account the trends of changes in assessment values and entropy in the final supplier evaluation. This paper’s principal contribution is the development of a knowledge base and the demonstration of its application in an ordered fuzzy expert system for multi-criteria supplier evaluation in a dynamic and uncertain environment. The proposed system takes into account the dynamic changes in the value of assessment parameters in the overall supplier assessment, allowing for the differentiation of suppliers based on current and historical data. The utilization of OFNs in a fuzzy model then allows for a reduction in the complexity of the knowledge base in comparison to a classical fuzzy system and makes it more accessible to users, as it requires only basic arithmetic operations in the inference process. This paper presents a comprehensive framework for the assessment of suppliers against a range of criteria, including local hiring, completeness, and defect factors. Furthermore, the potential to integrate sustainability and ESG (environmental, social, and corporate governance) criteria in the assessment process adds value to the decision making framework by adapting to current trends in supply chain management. Full article
(This article belongs to the Special Issue Handling Preference Information for Multiple-Criteria Decision-Making: Theory and Applications in Management, Economics and Finance)
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17 pages, 4033 KB  
Article
Motor Fault Diagnosis Based on Convolutional Block Attention Module-Xception Lightweight Neural Network
by Fengyun Xie, Qiuyang Fan, Gang Li, Yang Wang, Enguang Sun and Shengtong Zhou
Entropy 2024, 26(9), 810; https://doi.org/10.3390/e26090810 - 23 Sep 2024
Cited by 3 | Viewed by 1938
Abstract
Electric motors play a crucial role in self-driving vehicles. Therefore, fault diagnosis in motors is important for ensuring the safety and reliability of vehicles. In order to improve fault detection performance, this paper proposes a motor fault diagnosis method based on vibration signals. [...] Read more.
Electric motors play a crucial role in self-driving vehicles. Therefore, fault diagnosis in motors is important for ensuring the safety and reliability of vehicles. In order to improve fault detection performance, this paper proposes a motor fault diagnosis method based on vibration signals. Firstly, the vibration signals of each operating state of the motor at different frequencies are measured with vibration sensors. Secondly, the characteristic of Gram image coding is used to realize the coding of time domain information, and the one-dimensional vibration signals are transformed into grayscale diagrams to highlight their features. Finally, the lightweight neural network Xception is chosen as the main tool, and the attention mechanism Convolutional Block Attention Module (CBAM) is introduced into the model to enforce the importance of the characteristic information of the motor faults and realize their accurate identification. Xception is a type of convolutional neural network; its lightweight design maintains excellent performance while significantly reducing the model’s order of magnitude. Without affecting the computational complexity and accuracy of the network, the CBAM attention mechanism is added, and Gram’s corner field is combined with the improved lightweight neural network. The experimental results show that this model achieves a better recognition effect and faster iteration speed compared with the traditional Convolutional Neural Network (CNN), ResNet, and Xception networks. Full article
(This article belongs to the Special Issue Information-Theoretic Methods in Data Analytics)
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21 pages, 3199 KB  
Article
Developing an Early Warning System for Financial Networks: An Explainable Machine Learning Approach
by Daren Purnell, Jr., Amir Etemadi and John Kamp
Entropy 2024, 26(9), 796; https://doi.org/10.3390/e26090796 - 17 Sep 2024
Cited by 3 | Viewed by 4332
Abstract
Identifying the influential variables that provide early warning of financial network instability is challenging, in part due to the complexity of the system, uncertainty of a failure, and nonlinear, time-varying relationships between network participants. In this study, we introduce a novel methodology to [...] Read more.
Identifying the influential variables that provide early warning of financial network instability is challenging, in part due to the complexity of the system, uncertainty of a failure, and nonlinear, time-varying relationships between network participants. In this study, we introduce a novel methodology to select variables that, from a data-driven and statistical modeling perspective, represent these relationships and may indicate that the financial network is trending toward instability. We introduce a novel variable selection methodology that leverages Shapley values and modified Borda counts, in combination with statistical and machine learning methods, to create an explainable linear model to predict relationship value weights between network participants. We validate this new approach with data collected from the March 2023 Silicon Valley Bank Failure. The models produced using this novel method successfully identified the instability trend using only 14 input variables out of a possible 3160. The use of parsimonious linear models developed by this method has the potential to identify key financial stability indicators while also increasing the transparency of this complex system. Full article
(This article belongs to the Section Multidisciplinary Applications)
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19 pages, 377 KB  
Article
Modeling the Arrows of Time with Causal Multibaker Maps
by Aram Ebtekar and Marcus Hutter
Entropy 2024, 26(9), 776; https://doi.org/10.3390/e26090776 - 10 Sep 2024
Cited by 2 | Viewed by 3056
Abstract
Why do we remember the past, and plan the future? We introduce a toy model in which to investigate emergent time asymmetries: the causal multibaker maps. These are reversible discrete-time dynamical systems with configurable causal interactions. Imposing a suitable initial condition or “Past [...] Read more.
Why do we remember the past, and plan the future? We introduce a toy model in which to investigate emergent time asymmetries: the causal multibaker maps. These are reversible discrete-time dynamical systems with configurable causal interactions. Imposing a suitable initial condition or “Past Hypothesis”, and then coarse-graining, yields a Pearlean locally causal structure. While it is more common to speculate that the other arrows of time arise from the thermodynamic arrow, our model instead takes the causal arrow as fundamental. From it, we obtain the thermodynamic and epistemic arrows of time. The epistemic arrow concerns records, which we define to be systems that encode the state of another system at another time, regardless of the latter system’s dynamics. Such records exist of the past, but not of the future. We close with informal discussions of the evolutionary and agential arrows of time, and their relevance to decision theory. Full article
(This article belongs to the Special Issue Time and Temporal Asymmetries)
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10 pages, 699 KB  
Article
Quantum State Combinatorics
by Gregory D. Scholes
Entropy 2024, 26(9), 764; https://doi.org/10.3390/e26090764 - 6 Sep 2024
Cited by 1 | Viewed by 1214
Abstract
This paper concerns the analysis of large quantum states. It is a notoriously difficult problem to quantify separability of quantum states, and for large quantum states, it is unfeasible. Here we posit that when quantum states are large, we can deduce reasonable expectations [...] Read more.
This paper concerns the analysis of large quantum states. It is a notoriously difficult problem to quantify separability of quantum states, and for large quantum states, it is unfeasible. Here we posit that when quantum states are large, we can deduce reasonable expectations for the complex structure of non-classical multipartite correlations with surprisingly little information about the state. We show, with pegagogical examples, how known results from combinatorics can be used to reveal the expected structure of various correlations hidden in the ensemble described by a state. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering III)
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34 pages, 4915 KB  
Article
Natural Induction: Spontaneous Adaptive Organisation without Natural Selection
by Christopher L. Buckley, Tim Lewens, Michael Levin, Beren Millidge, Alexander Tschantz and Richard A. Watson
Entropy 2024, 26(9), 765; https://doi.org/10.3390/e26090765 - 6 Sep 2024
Cited by 5 | Viewed by 5817
Abstract
Evolution by natural selection is believed to be the only possible source of spontaneous adaptive organisation in the natural world. This places strict limits on the kinds of systems that can exhibit adaptation spontaneously, i.e., without design. Physical systems can show some properties [...] Read more.
Evolution by natural selection is believed to be the only possible source of spontaneous adaptive organisation in the natural world. This places strict limits on the kinds of systems that can exhibit adaptation spontaneously, i.e., without design. Physical systems can show some properties relevant to adaptation without natural selection or design. (1) The relaxation, or local energy minimisation, of a physical system constitutes a natural form of optimisation insomuch as it finds locally optimal solutions to the frustrated forces acting on it or between its components. (2) When internal structure ‘gives way’ or accommodates a pattern of forcing on a system, this constitutes learning insomuch, as it can store, recall, and generalise past configurations. Both these effects are quite natural and general, but in themselves insufficient to constitute non-trivial adaptation. However, here we show that the recurrent interaction of physical optimisation and physical learning together results in significant spontaneous adaptive organisation. We call this adaptation by natural induction. The effect occurs in dynamical systems described by a network of viscoelastic connections subject to occasional disturbances. When the internal structure of such a system accommodates slowly across many disturbances and relaxations, it spontaneously learns to preferentially visit solutions of increasingly greater quality (exceptionally low energy). We show that adaptation by natural induction thus produces network organisations that improve problem-solving competency with experience (without supervised training or system-level reward). We note that the conditions for adaptation by natural induction, and its adaptive competency, are different from those of natural selection. We therefore suggest that natural selection is not the only possible source of spontaneous adaptive organisation in the natural world. Full article
(This article belongs to the Section Entropy and Biology)
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9 pages, 926 KB  
Article
Testing the Pauli Exclusion Principle across the Periodic Table with the VIP-3 Experiment
by Simone Manti, Massimiliano Bazzi, Nicola Bortolotti, Cesidio Capoccia, Michael Cargnelli, Alberto Clozza, Luca De Paolis, Carlo Fiorini, Carlo Guaraldo, Mihail Iliescu, Matthias Laubenstein, Johann Marton, Fabrizio Napolitano, Kristian Piscicchia, Alessio Porcelli, Alessandro Scordo, Francesco Sgaramella, Diana Laura Sirghi, Florin Sirghi, Oton Vazquez Doce, Johann Zmeskal and Catalina Curceanuadd Show full author list remove Hide full author list
Entropy 2024, 26(9), 752; https://doi.org/10.3390/e26090752 - 2 Sep 2024
Cited by 1 | Viewed by 2300
Abstract
The Pauli exclusion principle (PEP), a cornerstone of quantum mechanics and whole science, states that in a system, two fermions can not simultaneously occupy the same quantum state. Several experimental tests have been performed to place increasingly stringent bounds on the validity of [...] Read more.
The Pauli exclusion principle (PEP), a cornerstone of quantum mechanics and whole science, states that in a system, two fermions can not simultaneously occupy the same quantum state. Several experimental tests have been performed to place increasingly stringent bounds on the validity of PEP. Among these, the series of VIP experiments, performed at the Gran Sasso Underground National Laboratory of INFN, is searching for PEP-violating atomic X-ray transitions in copper. In this paper, the upgraded VIP-3 setup is described, designed to extend these investigations to higher-Z elements such as zirconium, silver, palladium, and tin. We detail the enhanced design of this setup, including the implementation of cutting-edge, 1 mm thick, silicon drift detectors, which significantly improve the measurement sensitivity at higher energies. Additionally, we present calculations of expected PEP-violating energy shifts in the characteristic lines of these elements, performed using the multi-configurational Dirac–Fock method from first principles. The VIP-3 realization will contribute to ongoing research into PEP violation for different elements, offering new insights and directions for future studies. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering III)
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16 pages, 10566 KB  
Article
The Area Law of Molecular Entropy: Moving beyond Harmonic Approximation
by Amitava Roy, Tibra Ali and Vishwesh Venkatraman
Entropy 2024, 26(8), 688; https://doi.org/10.3390/e26080688 - 14 Aug 2024
Viewed by 2697
Abstract
This article shows that the gas-phase entropy of molecules is proportional to the area of the molecules, with corrections for the different curvatures of the molecular surface. The ability to estimate gas-phase entropy by the area law also allows us to calculate molecular [...] Read more.
This article shows that the gas-phase entropy of molecules is proportional to the area of the molecules, with corrections for the different curvatures of the molecular surface. The ability to estimate gas-phase entropy by the area law also allows us to calculate molecular entropy faster and more accurately than currently popular methods of estimating molecular entropy with harmonic oscillator approximation. The speed and accuracy of our method will open up new possibilities for the explicit inclusion of entropy in various computational biology methods. Full article
(This article belongs to the Section Multidisciplinary Applications)
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18 pages, 4026 KB  
Article
Generalized Kinetic Equations with Fractional Time-Derivative and Nonlinear Diffusion: H-Theorem and Entropy
by Ervin K. Lenzi, Michely P. Rosseto, Derik W. Gryczak, Luiz R. Evangelista, Luciano R. da Silva, Marcelo K. Lenzi and Rafael S. Zola
Entropy 2024, 26(8), 673; https://doi.org/10.3390/e26080673 - 8 Aug 2024
Cited by 1 | Viewed by 1321
Abstract
We investigate the H-theorem for a class of generalized kinetic equations with fractional time-derivative, hyperbolic term, and nonlinear diffusion. When the H-theorem is satisfied, we demonstrate that different entropic forms may emerge due to the equation’s nonlinearity. We obtain the entropy production related [...] Read more.
We investigate the H-theorem for a class of generalized kinetic equations with fractional time-derivative, hyperbolic term, and nonlinear diffusion. When the H-theorem is satisfied, we demonstrate that different entropic forms may emerge due to the equation’s nonlinearity. We obtain the entropy production related to these entropies and show that its form remains invariant. Furthermore, we investigate some behaviors for these equations from both numerical and analytical perspectives, showing a large class of behaviors connected with anomalous diffusion and their effects on entropy. Full article
(This article belongs to the Special Issue Theory and Applications of Hyperbolic Diffusion and Shannon Entropy)
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19 pages, 2444 KB  
Article
Fractional Telegrapher’s Equation under Resetting: Non-Equilibrium Stationary States and First-Passage Times
by Katarzyna Górska, Francisco J. Sevilla, Guillermo Chacón-Acosta and Trifce Sandev
Entropy 2024, 26(8), 665; https://doi.org/10.3390/e26080665 - 5 Aug 2024
Cited by 8 | Viewed by 1604
Abstract
We consider two different time fractional telegrapher’s equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the system approaches non-equilibrium stationary states, while the mean squared displacement saturates [...] Read more.
We consider two different time fractional telegrapher’s equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the system approaches non-equilibrium stationary states, while the mean squared displacement saturates due to the resetting mechanism. We also obtain the fractional telegraph process as a subordinated telegraph process by introducing operational time such that the physical time is considered as a Lévy stable process whose characteristic function is the Lévy stable distribution. We also analyzed the survival probability for the first-passage time problem and found the optimal resetting rate for which the corresponding mean first-passage time is minimal. Full article
(This article belongs to the Special Issue Theory and Applications of Hyperbolic Diffusion and Shannon Entropy)
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16 pages, 824 KB  
Article
Statistical Interdependence between Daily Precipitation and Extreme Daily Temperature in Regions of Mexico and Colombia
by Álvaro Zabaleta-Ortega, Teobaldis Mercado-Fernández, Israel Reyes-Ramírez, Fernando Angulo-Brown and Lev Guzmán-Vargas
Entropy 2024, 26(7), 558; https://doi.org/10.3390/e26070558 - 29 Jun 2024
Viewed by 1565
Abstract
We study the statistical interdependence between daily precipitation and daily extreme temperature for regions of Mexico (14 climatic stations, period 1960–2020) and Colombia (7 climatic stations, period 1973–2020) using linear (cross-correlation and coherence) and nonlinear (global phase synchronization index, mutual information, and cross-sample [...] Read more.
We study the statistical interdependence between daily precipitation and daily extreme temperature for regions of Mexico (14 climatic stations, period 1960–2020) and Colombia (7 climatic stations, period 1973–2020) using linear (cross-correlation and coherence) and nonlinear (global phase synchronization index, mutual information, and cross-sample entropy) synchronization metrics. The information shared between these variables is relevant and exhibits changes when comparing regions with different climatic conditions. We show that precipitation and temperature records from La Mojana are characterized by high persistence, while data from Mexico City exhibit lower persistence (less memory). We find that the information exchange and the level of coupling between the precipitation and temperature are higher for the case of the La Mojana region (Colombia) compared to Mexico City (Mexico), revealing that regions where seasonal changes are almost null and with low temperature gradients (less local variability) tend to display higher synchrony compared to regions where seasonal changes are very pronounced. The interdependence characterization between precipitation and temperature represents a robust option to characterize and analyze the collective dynamics of the system, applicable in climate change studies, as well as in changes not easily identifiable in future scenarios. Full article
(This article belongs to the Section Multidisciplinary Applications)
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18 pages, 10185 KB  
Article
Rise and Fall of Anderson Localization by Lattice Vibrations: A Time-Dependent Machine Learning Approach
by Yoel Zimmermann, Joonas Keski-Rahkonen, Anton M. Graf and Eric J. Heller
Entropy 2024, 26(7), 552; https://doi.org/10.3390/e26070552 - 28 Jun 2024
Cited by 1 | Viewed by 3145
Abstract
The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fröhlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum acoustics, emphasizing the wave nature of lattice vibrations, has enabled the exploration of previously [...] Read more.
The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fröhlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum acoustics, emphasizing the wave nature of lattice vibrations, has enabled the exploration of previously uncharted territories of electron–lattice interaction not accessible with conventional tools such as perturbation theory. In this context, our agenda here is two-fold. First, we showcase the application of machine learning methods to categorize various interaction regimes within the subtle interplay of electrons and the dynamical lattice landscape. Second, we shed light on a nebulous region of electron dynamics identified by the machine learning approach and then attribute it to transient localization, where strong lattice vibrations result in a momentary Anderson prison for electronic wavepackets, which are later released by the evolution of the lattice. Overall, our research illuminates the spectrum of dynamics within the Fröhlich model, such as transient localization, which has been suggested as a pivotal factor contributing to the mysteries surrounding strange metals. Furthermore, this paves the way for utilizing time-dependent perspectives in machine learning techniques for designing materials with tailored electron–lattice properties. Full article
(This article belongs to the Special Issue Recent Advances in the Theory of Disordered Systems)
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44 pages, 10685 KB  
Article
Evolutionary Implications of Self-Assembling Cybernetic Materials with Collective Problem-Solving Intelligence at Multiple Scales
by Benedikt Hartl, Sebastian Risi and Michael Levin
Entropy 2024, 26(7), 532; https://doi.org/10.3390/e26070532 - 21 Jun 2024
Cited by 5 | Viewed by 4981
Abstract
In recent years, the scientific community has increasingly recognized the complex multi-scale competency architecture (MCA) of biology, comprising nested layers of active homeostatic agents, each forming the self-orchestrated substrate for the layer above, and, in turn, relying on the structural and functional plasticity [...] Read more.
In recent years, the scientific community has increasingly recognized the complex multi-scale competency architecture (MCA) of biology, comprising nested layers of active homeostatic agents, each forming the self-orchestrated substrate for the layer above, and, in turn, relying on the structural and functional plasticity of the layer(s) below. The question of how natural selection could give rise to this MCA has been the focus of intense research. Here, we instead investigate the effects of such decision-making competencies of MCA agential components on the process of evolution itself, using in silico neuroevolution experiments of simulated, minimal developmental biology. We specifically model the process of morphogenesis with neural cellular automata (NCAs) and utilize an evolutionary algorithm to optimize the corresponding model parameters with the objective of collectively self-assembling a two-dimensional spatial target pattern (reliable morphogenesis). Furthermore, we systematically vary the accuracy with which the uni-cellular agents of an NCA can regulate their cell states (simulating stochastic processes and noise during development). This allows us to continuously scale the agents’ competency levels from a direct encoding scheme (no competency) to an MCA (with perfect reliability in cell decision executions). We demonstrate that an evolutionary process proceeds much more rapidly when evolving the functional parameters of an MCA compared to evolving the target pattern directly. Moreover, the evolved MCAs generalize well toward system parameter changes and even modified objective functions of the evolutionary process. Thus, the adaptive problem-solving competencies of the agential parts in our NCA-based in silico morphogenesis model strongly affect the evolutionary process, suggesting significant functional implications of the near-ubiquitous competency seen in living matter. Full article
(This article belongs to the Special Issue Complexity and Evolution, 2nd Edition)
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20 pages, 1986 KB  
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
Cited by 1 | Viewed by 1641
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)
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12 pages, 772 KB  
Review
Entropy and the Limits to Growth
by Reiner Kümmel
Entropy 2024, 26(6), 489; https://doi.org/10.3390/e26060489 - 31 May 2024
Cited by 1 | Viewed by 2754
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)
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17 pages, 815 KB  
Article
DAFT-Net: Dual Attention and Fast Tongue Contour Extraction Using Enhanced U-Net Architecture
by Xinqiang Wang, Wenhuan Lu, Hengxin Liu, Wei Zhang and Qiang Li
Entropy 2024, 26(6), 482; https://doi.org/10.3390/e26060482 - 31 May 2024
Cited by 1 | Viewed by 1366
Abstract
In most silent speech research, continuously observing tongue movements is crucial, thus requiring the use of ultrasound to extract tongue contours. Precisely and in real-time extracting ultrasonic tongue contours presents a major challenge. To tackle this challenge, the novel end-to-end lightweight network DAFT-Net [...] Read more.
In most silent speech research, continuously observing tongue movements is crucial, thus requiring the use of ultrasound to extract tongue contours. Precisely and in real-time extracting ultrasonic tongue contours presents a major challenge. To tackle this challenge, the novel end-to-end lightweight network DAFT-Net is introduced for ultrasonic tongue contour extraction. Integrating the Convolutional Block Attention Module (CBAM) and Attention Gate (AG) module with entropy-based optimization strategies, DAFT-Net establishes a comprehensive attention mechanism with dual functionality. This innovative approach enhances feature representation by replacing traditional skip connection architecture, thus leveraging entropy and information-theoretic measures to ensure efficient and precise feature selection. Additionally, the U-Net’s encoder and decoder layers have been streamlined to reduce computational demands. This process is further supported by information theory, thus guiding the reduction without compromising the network’s ability to capture and utilize critical information. Ablation studies confirm the efficacy of the integrated attention module and its components. The comparative analysis of the NS, TGU, and TIMIT datasets shows that DAFT-Net efficiently extracts relevant features, and it significantly reduces extraction time. These findings demonstrate the practical advantages of applying entropy and information theory principles. This approach improves the performance of medical image segmentation networks, thus paving the way for real-world applications. Full article
(This article belongs to the Section Multidisciplinary Applications)
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15 pages, 290 KB  
Article
Analytic Formulae for T Violation in Neutrino Oscillations
by Osamu Yasuda
Entropy 2024, 26(6), 472; https://doi.org/10.3390/e26060472 - 29 May 2024
Cited by 1 | Viewed by 1050
Abstract
Recently, a concept known as μTRISTAN, which involves the acceleration of μ+, has been proposed. This initiative has led to considerations of a new design for a neutrino factory. Additionally, leveraging the polarization of μ+, measurements of T [...] Read more.
Recently, a concept known as μTRISTAN, which involves the acceleration of μ+, has been proposed. This initiative has led to considerations of a new design for a neutrino factory. Additionally, leveraging the polarization of μ+, measurements of T violation in neutrino oscillations are also being explored. In this paper, we present analytical expressions for T violation in neutrino oscillations within the framework of standard three-flavor neutrino oscillations, a scenario involving nonstandard interactions, and a case of unitarity violation. We point out that examining the energy spectrum of T violation may be useful for probing new physics effects. Full article
(This article belongs to the Special Issue Particle Theory and Theoretical Cosmology—Dedicated to Professor Paul Howard Frampton on the Occasion of His 80th Birthday)
11 pages, 3522 KB  
Article
High-Throughput Polar Code Decoders with Information Bottleneck Quantization
by Claus Kestel, Lucas Johannsen and Norbert Wehn
Entropy 2024, 26(6), 462; https://doi.org/10.3390/e26060462 - 28 May 2024
Cited by 2 | Viewed by 1593
Abstract
In digital baseband processing, the forward error correction (FEC) unit belongs to the most demanding components in terms of computational complexity and power consumption. Hence, efficient implementation of FEC decoders is crucial for next-generation mobile broadband standards and an ongoing research topic. Quantization [...] Read more.
In digital baseband processing, the forward error correction (FEC) unit belongs to the most demanding components in terms of computational complexity and power consumption. Hence, efficient implementation of FEC decoders is crucial for next-generation mobile broadband standards and an ongoing research topic. Quantization has a significant impact on the decoder area, power consumption and throughput. Thus, lower bit widths are preferred for efficient implementations but degrade the error correction capability. To address this issue, a non-uniform quantization based on the Information Bottleneck (IB) method is proposed that enables a low bit width while maintaining the essential information. Many investigations on the use of the IB method for Low-density parity-check code) LDPC decoders exist and have shown its advantages from an implementation perspective. However, for polar code decoder implementations, there exists only one publication that is not based on the state-of-the-art Fast Simplified Successive-Cancellation (Fast-SSC) decoding algorithm, and only synthesis implementation results without energy estimation are shown. In contrast, our paper presents several optimized Fast-SSC polar code decoder implementations using IB-based quantization with placement and routing results using advanced 12 nm FinFET technology. Gains of up to 16% in area and 13% in energy efficiency are achieved with IB-based quantization at a Frame Error Rate (FER) of 10−7 and a polar code of N=1024,R=0.5 compared to state-of-the-art decoders. Full article
(This article belongs to the Special Issue Intelligent Information Processing and Coding for B5G Communications)
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15 pages, 659 KB  
Review
Ising Paradigm in Isobaric Ensembles
by Claudio A. Cerdeiriña and Jacobo Troncoso
Entropy 2024, 26(6), 438; https://doi.org/10.3390/e26060438 - 22 May 2024
Cited by 2 | Viewed by 1221
Abstract
We review recent work on Ising-like models with “compressible cells” of fluctuating volume that, as such, are naturally treated in NpT and μpT ensembles. Besides volumetric phenomena, local entropic effects crucially underlie the models. We focus on “compressible cell [...] Read more.
We review recent work on Ising-like models with “compressible cells” of fluctuating volume that, as such, are naturally treated in NpT and μpT ensembles. Besides volumetric phenomena, local entropic effects crucially underlie the models. We focus on “compressible cell gases” (CCG), namely, lattice gases with fluctuating cell volumes, and “compressible cell liquids” (CCL) with singly occupied cells and fluctuating cell volumes. CCGs contemplate singular diameters and “Yang–Yang features” predicted by the “complete scaling” formulation of asymmetric fluid criticality, with a specific version incorporating “ice-like” hydrogen bonding further describing the “singularity-free scenario” for the low-temperature unusual thermodynamics of supercooled water. In turn, suitable CCL variants constitute adequate prototypes of water-like liquid–liquid criticality and the freezing transition of a system of hard spheres. On incorporating vacant cells to such two-state CCL variants, one obtains three-state, BEG-like models providing a satisfactory description of water’s “second-critical-point scenario” and the whole phase behavior of a simple substance like argon. Future challenges comprise water’s crystal–fluid phase behavior and metastable states. Full article
(This article belongs to the Special Issue Matter-Aggregating Systems at a Classical vs. Quantum Interface)
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137 pages, 3333 KB  
Review
Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions
by Patrick Adelhardt, Jan A. Koziol, Anja Langheld and Kai P. Schmidt
Entropy 2024, 26(5), 401; https://doi.org/10.3390/e26050401 - 1 May 2024
Cited by 13 | Viewed by 3444
Abstract
Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum–optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical [...] Read more.
Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum–optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations. Full article
(This article belongs to the Special Issue Violations of Hyperscaling in Phase Transitions and Critical Phenomena—in Memory of Prof. Ralph Kenna)
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22 pages, 19924 KB  
Article
Thermodynamic Entropy-Based Fatigue Life Assessment Method for Nickel-Based Superalloy GH4169 at Elevated Temperature Considering Cyclic Viscoplasticity
by Shuiting Ding, Shuyang Xia, Zhenlei Li, Huimin Zhou, Shaochen Bao, Bolin Li and Guo Li
Entropy 2024, 26(5), 391; https://doi.org/10.3390/e26050391 - 30 Apr 2024
Viewed by 1678
Abstract
This paper develops a thermodynamic entropy-based life prediction model to estimate the low-cycle fatigue (LCF) life of the nickel-based superalloy GH4169 at elevated temperature (650 °C). The gauge section of the specimen was chosen as the thermodynamic system for modeling entropy generation within [...] Read more.
This paper develops a thermodynamic entropy-based life prediction model to estimate the low-cycle fatigue (LCF) life of the nickel-based superalloy GH4169 at elevated temperature (650 °C). The gauge section of the specimen was chosen as the thermodynamic system for modeling entropy generation within the framework of the Chaboche viscoplasticity constitutive theory. Furthermore, an explicitly numerical integration algorithm was compiled to calculate the cyclic stress–strain responses and thermodynamic entropy generation for establishing the framework for fatigue life assessment. A thermodynamic entropy-based life prediction model is proposed with a damage parameter based on entropy generation considering the influence of loading ratio. Fatigue lives for GH4169 at 650 °C under various loading conditions were estimated utilizing the proposed model, and the results showed good consistency with the experimental results. Finally, compared to the existing classical models, such as Manson–Coffin, Ostergren, Walker strain, and SWT, the thermodynamic entropy-based life prediction model provided significantly better life prediction results. Full article
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22 pages, 1210 KB  
Article
A Joint Communication and Computation Design for Probabilistic Semantic Communications
by Zhouxiang Zhao, Zhaohui Yang, Mingzhe Chen, Zhaoyang Zhang and H. Vincent Poor
Entropy 2024, 26(5), 394; https://doi.org/10.3390/e26050394 - 30 Apr 2024
Cited by 23 | Viewed by 5682
Abstract
In this paper, the problem of joint transmission and computation resource allocation for a multi-user probabilistic semantic communication (PSC) network is investigated. In the considered model, users employ semantic information extraction techniques to compress their large-sized data before transmitting them to a multi-antenna [...] Read more.
In this paper, the problem of joint transmission and computation resource allocation for a multi-user probabilistic semantic communication (PSC) network is investigated. In the considered model, users employ semantic information extraction techniques to compress their large-sized data before transmitting them to a multi-antenna base station (BS). Our model represents large-sized data through substantial knowledge graphs, utilizing shared probability graphs between the users and the BS for efficient semantic compression. The resource allocation problem is formulated as an optimization problem with the objective of maximizing the sum of the equivalent rate of all users, considering the total power budget and semantic resource limit constraints. The computation load considered in the PSC network is formulated as a non-smooth piecewise function with respect to the semantic compression ratio. To tackle this non-convex non-smooth optimization challenge, a three-stage algorithm is proposed, where the solutions for the received beamforming matrix of the BS, the transmit power of each user, and the semantic compression ratio of each user are obtained stage by stage. The numerical results validate the effectiveness of our proposed scheme. Full article
(This article belongs to the Special Issue Foundations of Goal-Oriented Semantic Communication in Intelligent Networks)
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24 pages, 1352 KB  
Article
Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers
by Luca Razzoli, Gabriele Cenedese, Maria Bondani and Giuliano Benenti
Entropy 2024, 26(4), 313; https://doi.org/10.3390/e26040313 - 2 Apr 2024
Cited by 10 | Viewed by 4359
Abstract
Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation due to its discrete nature. [...] Read more.
Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation due to its discrete nature. Current implementations, however, are usually characterized by quantum circuits of large size and depth, which leads to a higher computational cost and severely limits the number of time steps that can be reliably implemented on current quantum computers. In this work, we propose an efficient and scalable quantum circuit implementing the DTQW on the 2n-cycle based on the diagonalization of the conditional shift operator. For t time steps of the DTQW, the proposed circuit requires only O(n2+nt) two-qubit gates compared to the O(n2t) of the current most efficient implementation based on quantum Fourier transforms. We test the proposed circuit on an IBM quantum device for a Hadamard DTQW on the 4-cycle and 8-cycle characterized by periodic dynamics and by recurrent generation of maximally entangled single-particle states. Experimental results are meaningful well beyond the regime of few time steps, paving the way for reliable implementation and use on quantum computers. Full article
(This article belongs to the Special Issue Quantum Walks for Quantum Technologies)
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10 pages, 566 KB  
Article
Conformity and Mass Media Influence in the Sznajd Model on Regular Lattices
by Maciej Wołoszyn
Entropy 2024, 26(4), 307; https://doi.org/10.3390/e26040307 - 30 Mar 2024
Cited by 1 | Viewed by 1325
Abstract
The polarization of opinions and difficulties in reaching a consensus are central problems of many modern societies. Understanding the dynamics governing those processes is, therefore, one of the main aims of sociophysics. In this work, the Sznajd model of opinion dynamics is investigated [...] Read more.
The polarization of opinions and difficulties in reaching a consensus are central problems of many modern societies. Understanding the dynamics governing those processes is, therefore, one of the main aims of sociophysics. In this work, the Sznajd model of opinion dynamics is investigated with Monte Carlo simulations performed on four different regular lattices: triangular, honeycomb, and square with von Neumann or Moore neighborhood. The main objective is to discuss the interplay of the probability of convincing (conformity) and mass media (external) influence and to provide the details of the possible phase transitions. The results indicate that, while stronger bonds and openness to discussion and argumentation may help in reaching a consensus, external influence becomes destructive at different levels depending on the lattice. Full article
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16 pages, 633 KB  
Article
Influential Metrics Estimation and Dynamic Frequency Selection Based on Two-Dimensional Mapping for JPEG-Reversible Data Hiding
by Haiyong Wang and Chentao Lu
Entropy 2024, 26(4), 301; https://doi.org/10.3390/e26040301 - 29 Mar 2024
Viewed by 1344
Abstract
JPEG Reversible Data Hiding (RDH) is a method designed to extract hidden data from a marked image and perfectly restore the image to its original JPEG form. However, while existing RDH methods adaptively manage the visual distortion caused by embedded data, they often [...] Read more.
JPEG Reversible Data Hiding (RDH) is a method designed to extract hidden data from a marked image and perfectly restore the image to its original JPEG form. However, while existing RDH methods adaptively manage the visual distortion caused by embedded data, they often neglect the concurrent increase in file size. In rectifying this oversight, we have designed a new JPEG RDH scheme that addresses all influential metrics during the embedding phase and a dynamic frequency selection strategy with recoverable frequency order after data embedding. The process initiates with a pre-processing phase of blocks and the subsequent selection of frequencies. Utilizing a two-dimensional (2D) mapping strategy, we then compute the visual distortion and file size increment (FSI) for each image block by examining non-zero alternating current (AC) coefficient pairs (NZACPs) and their corresponding run lengths. Finally, we select appropriate block groups based on the influential metrics of each block group and proceed with data embedding by 2D histogram shifting (HS). Extensive experimentation demonstrates how our method’s efficiently and consistently outperformed existing techniques with a superior peak signal-to-noise Ratio (PSNR) and optimized FSI. Full article
(This article belongs to the Special Issue Information Theory and Coding for Image/Video Processing)
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17 pages, 1913 KB  
Article
Chaos in Opinion-Driven Disease Dynamics
by Thomas Götz, Tyll Krüger, Karol Niedzielewski, Radomir Pestow, Moritz Schäfer and Jan Schneider
Entropy 2024, 26(4), 298; https://doi.org/10.3390/e26040298 - 28 Mar 2024
Cited by 1 | Viewed by 2060
Abstract
During the COVID-19 pandemic, it became evident that the effectiveness of applying intervention measures is significantly influenced by societal acceptance, which, in turn, is affected by the processes of opinion formation. This article explores one among the many possibilities of coupled opinion–epidemic systems. [...] Read more.
During the COVID-19 pandemic, it became evident that the effectiveness of applying intervention measures is significantly influenced by societal acceptance, which, in turn, is affected by the processes of opinion formation. This article explores one among the many possibilities of coupled opinion–epidemic systems. The findings reveal either intricate periodic patterns or chaotic dynamics, leading to substantial fluctuations in opinion distribution and, consequently, significant variations in the total number of infections over time. Interestingly, the model exhibits a protective pattern. Full article
(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)
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14 pages, 12048 KB  
Article
Decoding the News Media Diet of Disinformation Spreaders
by Anna Bertani, Valeria Mazzeo and Riccardo Gallotti
Entropy 2024, 26(3), 270; https://doi.org/10.3390/e26030270 - 19 Mar 2024
Cited by 2 | Viewed by 2957
Abstract
In the digital era, information consumption is predominantly channeled through online news media and disseminated on social media platforms. Understanding the complex dynamics of the news media environment and users’ habits within the digital ecosystem is a challenging task that requires, at the [...] Read more.
In the digital era, information consumption is predominantly channeled through online news media and disseminated on social media platforms. Understanding the complex dynamics of the news media environment and users’ habits within the digital ecosystem is a challenging task that requires, at the same time, large databases and accurate methodological approaches. This study contributes to this expanding research landscape by employing network science methodologies and entropic measures to analyze the behavioral patterns of social media users sharing news pieces and dig into the diverse news consumption habits within different online social media user groups. Our analyses reveal that users are more inclined to share news classified as fake when they have previously posted conspiracy or junk science content and vice versa, creating a series of “misinformation hot streaks”. To better understand these dynamics, we used three different measures of entropy to gain insights into the news media habits of each user, finding that the patterns of news consumption significantly differ among users when focusing on disinformation spreaders as opposed to accounts sharing reliable or low-risk content. Thanks to these entropic measures, we quantify the variety and the regularity of the news media diet, finding that those disseminating unreliable content exhibit a more varied and, at the same time, a more regular choice of web-domains. This quantitative insight into the nuances of news consumption behaviors exhibited by disinformation spreaders holds the potential to significantly inform the strategic formulation of more robust and adaptive social media moderation policies. Full article
(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)
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12 pages, 319 KB  
Article
Magnetic Black Hole Thermodynamics in an Extended Phase Space with Nonlinear Electrodynamics
by Sergey Il’ich Kruglov
Entropy 2024, 26(3), 261; https://doi.org/10.3390/e26030261 - 14 Mar 2024
Cited by 3 | Viewed by 1746
Abstract
We study Einstein’s gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner–Nordström metric function [...] Read more.
We study Einstein’s gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner–Nordström metric function when the cosmological constant vanishes. The first law of black hole thermodynamics in an extended phase space is formulated and the magnetic potential and the thermodynamic conjugate to the coupling are obtained. We prove the generalized Smarr relation. The heat capacity and the Gibbs free energy are computed and the phase transitions are studied. It is shown that the electric fields of charged objects at the origin and the electrostatic self-energy are finite within the nonlinear electrodynamics proposed. Full article
(This article belongs to the Special Issue Trends in the Second Law of Thermodynamics)
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17 pages, 8787 KB  
Article
Multipole Approach to the Dynamical Casimir Effect with Finite-Size Scatterers
by Lucas Alonso, Guilherme C. Matos, François Impens, Paulo A. Maia Neto and Reinaldo de Melo e Souza
Entropy 2024, 26(3), 251; https://doi.org/10.3390/e26030251 - 12 Mar 2024
Cited by 2 | Viewed by 1780
Abstract
A mirror subjected to a fast mechanical oscillation emits photons out of the quantum vacuum—a phenomenon known as the dynamical Casimir effect (DCE). The mirror is usually treated as an infinite metallic surface. Here, we show that, in realistic experimental conditions (mirror size [...] Read more.
A mirror subjected to a fast mechanical oscillation emits photons out of the quantum vacuum—a phenomenon known as the dynamical Casimir effect (DCE). The mirror is usually treated as an infinite metallic surface. Here, we show that, in realistic experimental conditions (mirror size and oscillation frequency), this assumption is inadequate and drastically overestimates the DCE radiation. Taking the opposite limit, we use instead the dipolar approximation to obtain a simpler and more realistic treatment of DCE for macroscopic bodies. Our approach is inspired by a microscopic theory of DCE, which is extended to the macroscopic realm by a suitable effective Hamiltonian description of moving anisotropic scatterers. We illustrate the benefits of our approach by considering the DCE from macroscopic bodies of different geometries. Full article
(This article belongs to the Special Issue Quantum Nonstationary Systems)
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22 pages, 2092 KB  
Article
A Kalman Filtering Algorithm for Measurement Interruption Based on Polynomial Interpolation and Taylor Expansion
by Jianhua Cheng, Zili Wang, Bing Qi and He Wang
Entropy 2024, 26(3), 243; https://doi.org/10.3390/e26030243 - 10 Mar 2024
Viewed by 1702
Abstract
Combined SINS/GPS navigation systems have been widely used. However, when the traditional combined SINS/GPS navigation system travels between tall buildings, in the shade of trees, or through tunnels, the GPS encounters frequent signal blocking, which leads to the interruption of GPS signals, and [...] Read more.
Combined SINS/GPS navigation systems have been widely used. However, when the traditional combined SINS/GPS navigation system travels between tall buildings, in the shade of trees, or through tunnels, the GPS encounters frequent signal blocking, which leads to the interruption of GPS signals, and as a result, the combined SINS/GPS-based navigation method degenerates into a pure inertial guidance system, which will lead to the accumulation of navigation errors. In this paper, an adaptive Kalman filtering algorithm based on polynomial fitting and a Taylor expansion is proposed. Through the navigation information output from the inertial guidance system, the polynomial interpolation method is used to construct the velocity equation and position equation of the carrier, and then the Taylor expansion is used to construct the virtual measurement at the moment of the GPS signal interruption, which can make up for the impact of the lack of measurement information on the combined SINS/GPS navigation system when the GPS signal is interrupted. The results of computer simulation experiments and road measurement tests based on the loosely combined SINS/GPS navigation system show that when the carrier faces a GPS signal interruption situation, compared with a combined SINS/GPS navigation algorithm that does not take any rescue measures, our proposed combined SINS/GPS navigation algorithm possesses a higher accuracy in the attitude angle estimation, a higher accuracy in the velocity estimation, and a higher accuracy in the positional localization, and the system possesses higher stability. Full article
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22 pages, 23017 KB  
Article
Dynamical Analysis of an Improved Bidirectional Immunization SIR Model in Complex Network
by Shixiang Han, Guanghui Yan, Huayan Pei and Wenwen Chang
Entropy 2024, 26(3), 227; https://doi.org/10.3390/e26030227 - 2 Mar 2024
Cited by 3 | Viewed by 2186
Abstract
In order to investigate the impact of two immunization strategies—vaccination targeting susceptible individuals to reduce their infection rate and clinical medical interventions targeting infected individuals to enhance their recovery rate—on the spread of infectious diseases in complex networks, this study proposes a bilinear [...] Read more.
In order to investigate the impact of two immunization strategies—vaccination targeting susceptible individuals to reduce their infection rate and clinical medical interventions targeting infected individuals to enhance their recovery rate—on the spread of infectious diseases in complex networks, this study proposes a bilinear SIR infectious disease model that considers bidirectional immunization. By analyzing the conditions for the existence of endemic equilibrium points, we derive the basic reproduction numbers and outbreak thresholds for both homogeneous and heterogeneous networks. The epidemic model is then reconstructed and extensively analyzed using continuous-time Markov chain (CTMC) methods. This analysis includes the investigation of transition probabilities, transition rate matrices, steady-state distributions, and the transition probability matrix based on the embedded chain. In numerical simulations, a notable concordance exists between the outcomes of CTMC and mean-field (MF) simulations, thereby substantiating the efficacy of the CTMC model. Moreover, the CTMC-based model adeptly captures the inherent stochastic fluctuation in the disease transmission, which is consistent with the mathematical properties of Markov chains. We further analyze the relationship between the system’s steady-state infection density and the immunization rate through MCS. The results suggest that the infection density decreases with an increase in the immunization rate among susceptible individuals. The current research results will enhance our understanding of infectious disease transmission patterns in real-world scenarios, providing valuable theoretical insights for the development of epidemic prevention and control strategies. Full article
(This article belongs to the Section Complexity)
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17 pages, 972 KB  
Article
Quantum Implementation of the SAND Algorithm and Its Quantum Resource Estimation for Brute-Force Attack
by Hongyu Wu, Xiaoning Feng and Jiale Zhang
Entropy 2024, 26(3), 216; https://doi.org/10.3390/e26030216 - 29 Feb 2024
Viewed by 2161
Abstract
The SAND algorithm is a family of lightweight AND-RX block ciphers released by DCC in 2022. Our research focuses on assessing the security of SAND with a quantum computation model. This paper presents the first quantum implementation of SAND (including two versions of [...] Read more.
The SAND algorithm is a family of lightweight AND-RX block ciphers released by DCC in 2022. Our research focuses on assessing the security of SAND with a quantum computation model. This paper presents the first quantum implementation of SAND (including two versions of SAND, SAND-64 and SAND-128). Considering the depth-times-width metric, the quantum circuit implementation of the SAND algorithm demonstrates a relatively lower consumption of quantum resources than that of the quantum implementations of existing lightweight algorithms. A generalized Grover-based brute-force attack framework was implemented and employed to perform attacks on two versions of the SAND algorithm. This framework utilized the g-database algorithm, which considered different plaintext–ciphertext pairs in a unified manner, reducing quantum resource consumption. Our findings indicate that the SAND-128 algorithm achieved the NIST security level I, while the SAND-64 algorithm fell short of meeting the requirements of security level I. Full article
(This article belongs to the Section Quantum Information)
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15 pages, 448 KB  
Article
Ralph Kenna’s Scaling Relations in Critical Phenomena
by Leïla Moueddene, Arnaldo Donoso and Bertrand Berche
Entropy 2024, 26(3), 221; https://doi.org/10.3390/e26030221 - 29 Feb 2024
Cited by 8 | Viewed by 2351
Abstract
In this note, we revisit the scaling relations among “hatted critical exponents”, which were first derived by Ralph Kenna, Des Johnston, and Wolfhard Janke, and we propose an alternative derivation for some of them. For the scaling relation involving the behavior of the [...] Read more.
In this note, we revisit the scaling relations among “hatted critical exponents”, which were first derived by Ralph Kenna, Des Johnston, and Wolfhard Janke, and we propose an alternative derivation for some of them. For the scaling relation involving the behavior of the correlation function, we will propose an alternative form since we believe that the expression is erroneous in the work of Ralph and his collaborators. Full article
(This article belongs to the Special Issue Violations of Hyperscaling in Phase Transitions and Critical Phenomena—in Memory of Prof. Ralph Kenna)
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17 pages, 3100 KB  
Article
Fast Model Selection and Hyperparameter Tuning for Generative Models
by Luming Chen and Sujit K. Ghosh
Entropy 2024, 26(2), 150; https://doi.org/10.3390/e26020150 - 9 Feb 2024
Cited by 3 | Viewed by 2478
Abstract
Generative models have gained significant attention in recent years. They are increasingly used to estimate the underlying structure of high-dimensional data and artificially generate various kinds of data similar to those from the real world. The performance of generative models depends critically on [...] Read more.
Generative models have gained significant attention in recent years. They are increasingly used to estimate the underlying structure of high-dimensional data and artificially generate various kinds of data similar to those from the real world. The performance of generative models depends critically on a good set of hyperparameters. Yet, finding the right hyperparameter configuration can be an extremely time-consuming task. In this paper, we focus on speeding up the hyperparameter search through adaptive resource allocation, early stopping underperforming candidates quickly and allocating more computational resources to promising ones by comparing their intermediate performance. The hyperparameter search is formulated as a non-stochastic best-arm identification problem where resources like iterations or training time constrained by some predetermined budget are allocated to different hyperparameter configurations. A procedure which uses hypothesis testing coupled with Successive Halving is proposed to make the resource allocation and early stopping decisions and compares the intermediate performance of generative models by their exponentially weighted Maximum Means Discrepancy (MMD). The experimental results show that the proposed method selects hyperparameter configurations that lead to a significant improvement in the model performance compared to Successive Halving for a wide range of budgets across several real-world applications. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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20 pages, 518 KB  
Article
Asymptotic Expansion and Weak Approximation for a Stochastic Control Problem on Path Space
by Masaya Kannari, Riu Naito and Toshihiro Yamada
Entropy 2024, 26(2), 119; https://doi.org/10.3390/e26020119 - 29 Jan 2024
Viewed by 1602
Abstract
The paper provides a precise error estimate for an asymptotic expansion of a certain stochastic control problem related to relative entropy minimization. In particular, it is shown that the expansion error depends on the regularity of functionals on path space. An efficient numerical [...] Read more.
The paper provides a precise error estimate for an asymptotic expansion of a certain stochastic control problem related to relative entropy minimization. In particular, it is shown that the expansion error depends on the regularity of functionals on path space. An efficient numerical scheme based on a weak approximation with Monte Carlo simulation is employed to implement the asymptotic expansion in multidimensional settings. Throughout numerical experiments, it is confirmed that the approximation error of the proposed scheme is consistent with the theoretical rate of convergence. Full article
(This article belongs to the Special Issue Monte Carlo Simulation in Statistical Physics)
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13 pages, 2878 KB  
Article
Modeling Misinformation Spread in a Bounded Confidence Model: A Simulation Study
by Yujia Wu and Peng Guo
Entropy 2024, 26(2), 99; https://doi.org/10.3390/e26020099 - 23 Jan 2024
Cited by 1 | Viewed by 2306
Abstract
Misinformation has posed significant threats to all aspects of people’s lives. One of the most active areas of research in misinformation examines how individuals are misinformed. In this paper, we study how and to what extent agents are misinformed in an extended bounded [...] Read more.
Misinformation has posed significant threats to all aspects of people’s lives. One of the most active areas of research in misinformation examines how individuals are misinformed. In this paper, we study how and to what extent agents are misinformed in an extended bounded confidence model, which consists of three parts: (i) online selective neighbors whose opinions differ from their own but not by more than a certain confidence level; (ii) offline neighbors, in a Watts–Strogatz small-world network, whom an agent has to communicate with even though their opinions are far different from their own; and (iii) a Bayesian analysis. Furthermore, we introduce two types of epistemically irresponsible agents: agents who hide their honest opinions and focus on disseminating misinformation and agents who ignore the messages received and follow the crowd mindlessly. Simulations show that, in an environment with only online selective neighbors, the misinforming is more successful with broader confidence intervals. Having offline neighbors contributes to being cautious of misinformation, while employing a Bayesian analysis helps in discovering the truth. Moreover, the agents who are only willing to listen to the majority, regardless of the truth, unwittingly help to bring about the success of misinformation attempts, and they themselves are, of course, misled to a greater extent. Full article
(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics)
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15 pages, 7064 KB  
Article
Study on Microstructure and High Temperature Stability of WTaVTiZrx Refractory High Entropy Alloy Prepared by Laser Cladding
by Xiaoyu Ding, Weigui Wang, Haojie Zhang, Xueqin Tian, Laima Luo, Yucheng Wu and Jianhua Yao
Entropy 2024, 26(1), 73; https://doi.org/10.3390/e26010073 - 15 Jan 2024
Cited by 3 | Viewed by 2167
Abstract
The extremely harsh environment of the high temperature plasma imposes strict requirements on the construction materials of the first wall in a fusion reactor. In this work, a refractory alloy system, WTaVTiZrx, with low activation and high entropy, was theoretically designed [...] Read more.
The extremely harsh environment of the high temperature plasma imposes strict requirements on the construction materials of the first wall in a fusion reactor. In this work, a refractory alloy system, WTaVTiZrx, with low activation and high entropy, was theoretically designed based on semi-empirical formula and produced using a laser cladding method. The effects of Zr proportions on the metallographic microstructure, phase composition, and alloy chemistry of a high-entropy alloy cladding layer were investigated using a metallographic microscope, XRD (X-ray diffraction), SEM (scanning electron microscope), and EDS (energy dispersive spectrometer), respectively. The high-entropy alloys have a single-phase BCC structure, and the cladding layers exhibit a typical dendritic microstructure feature. The evolution of microstructure and mechanical properties of the high-entropy alloys, with respect to annealing temperature, was studied to reveal the performance stability of the alloy at a high temperature. The microstructure of the annealed samples at 900 °C for 5–10 h did not show significant changes compared to the as-cast samples, and the microhardness increased to 988.52 HV, which was higher than that of the as-cast samples (725.08 HV). When annealed at 1100 °C for 5 h, the microstructure remained unchanged, and the microhardness increased. However, after annealing for 10 h, black substances appeared in the microstructure, and the microhardness decreased, but it was still higher than the matrix. When annealed at 1200 °C for 5–10 h, the microhardness did not increase significantly compared to the as-cast samples, and after annealing for 10 h, the microhardness was even lower than that of the as-cast samples. The phase of the high entropy alloy did not change significantly after high-temperature annealing, indicating good phase stability at high temperatures. After annealing for 10 h, the microhardness was lower than that of the as-cast samples. The phase of the high entropy alloy remained unchanged after high-temperature annealing, demonstrating good phase stability at high temperatures. Full article
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15 pages, 331 KB  
Article
The Onset of Parisi’s Complexity in a Mismatched Inference Problem
by Francesco Camilli, Pierluigi Contucci and Emanuele Mingione
Entropy 2024, 26(1), 42; https://doi.org/10.3390/e26010042 - 30 Dec 2023
Cited by 2 | Viewed by 1812
Abstract
We show that a statistical mechanics model where both the Sherringhton–Kirkpatrick and Hopfield Hamiltonians appear, which is equivalent to a high-dimensional mismatched inference problem, is described by a replica symmetry-breaking Parisi solution. Full article
(This article belongs to the Special Issue A Journey Through Complex Landscapes—Dedicated to Professor Giorgio Parisi to Celebrate the Nobel Prize & His 75th Birthday)
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