Journal Description
Entropy
Entropy
is an international and interdisciplinary peer-reviewed open access journal of entropy and information studies, published monthly online by MDPI. The International Society for the Study of Information (IS4SI) and Spanish Society of Biomedical Engineering (SEIB) are affiliated with Entropy and their members receive a discount on the article processing charge.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), Inspec, PubMed, PMC, Astrophysics Data System, and other databases.
- Journal Rank: JCR - Q2 (Physics, Multidisciplinary) / CiteScore - Q1 (Mathematical Physics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 20.8 days after submission; acceptance to publication is undertaken in 2.9 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about Entropy.
- Companion journals for Entropy include: Foundations, Thermo and MAKE.
Impact Factor:
2.7 (2022);
5-Year Impact Factor:
2.6 (2022)
Latest Articles
Efficient Quantum Private Comparison Based on GHZ States
Entropy 2024, 26(5), 413; https://doi.org/10.3390/e26050413 (registering DOI) - 10 May 2024
Abstract
Quantum private comparison (QPC) is a fundamental cryptographic protocol that allows two parties to compare the equality of their private inputs without revealing any information about those inputs to each other. In recent years, QPC protocols utilizing various quantum resources have been proposed.
[...] Read more.
Quantum private comparison (QPC) is a fundamental cryptographic protocol that allows two parties to compare the equality of their private inputs without revealing any information about those inputs to each other. In recent years, QPC protocols utilizing various quantum resources have been proposed. However, these QPC protocols have lower utilization of quantum resources and qubit efficiency. To address this issue, we propose an efficient QPC protocol based on GHZ states, which leverages the unique properties of GHZ states and rotation operations to achieve secure and efficient private comparison. The secret information is encoded in the rotation angles of rotation operations performed on the received quantum sequence transmitted along the circular mode. This results in the multiplexing of quantum resources and enhances the utilization of quantum resources. Our protocol does not require quantum key distribution (QKD) for sharing a secret key to ensure the security of the inputs, resulting in no consumption of quantum resources for key sharing. One GHZ state can be compared to three bits of classical information in each comparison, leading to qubit efficiency reaching 100%. Compared with the existing QPC protocol, our protocol does not require quantum resources for sharing a secret key. It also demonstrates enhanced performance in qubit efficiency and the utilization of quantum resources.
Full article
(This article belongs to the Special Issue Quantum Computation, Communication and Cryptography)
Open AccessArticle
Finite-Temperature Correlation Functions Obtained from Combined Real- and Imaginary-Time Propagation of Variational Thawed Gaussian Wavepackets
by
Jens Aage Poulsen and Gunnar Nyman
Entropy 2024, 26(5), 412; https://doi.org/10.3390/e26050412 - 10 May 2024
Abstract
We apply the so-called variational Gaussian wavepacket approximation (VGA) for conducting both real- and imaginary-time dynamics to calculate thermal correlation functions. By considering strongly anharmonic systems, such as a quartic potential and a double-well potential at high and low temperatures, it is shown
[...] Read more.
We apply the so-called variational Gaussian wavepacket approximation (VGA) for conducting both real- and imaginary-time dynamics to calculate thermal correlation functions. By considering strongly anharmonic systems, such as a quartic potential and a double-well potential at high and low temperatures, it is shown that this method is partially able to account for tunneling. This is contrary to other popular many-body methods, such as ring polymer molecular dynamics and the classical Wigner method, which fail in this respect. It is a historical peculiarity that no one has considered the VGA method for representing both the Boltzmann operator and the real-time propagation. This method should be well suited for molecular systems containing many atoms.
Full article
(This article belongs to the Special Issue Tunneling in Complex Systems)
►▼
Show Figures
Figure 1
Open AccessArticle
Does Quantum Mechanics Require “Conspiracy”?
by
Ovidiu Cristinel Stoica
Entropy 2024, 26(5), 411; https://doi.org/10.3390/e26050411 - 9 May 2024
Abstract
Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an
[...] Read more.
Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an extremely restricted subspace of the Hilbert space that seems “conspiratorial”, in the sense that (1) it seems to depend on future events that involve records (including measurement settings) and on the dynamical law (normally thought to be independent of the initial conditions), and (2) it violates Statistical Independence, even when it is valid in the context of Bell’s theorem. To solve the puzzle, I build a model in which, by changing the dynamical law, the same initial conditions can lead to different histories in which the validity of records is relative to the new dynamical law. This relative validity of the records may restore causality, but the initial conditions still must depend, at least partially, on the dynamical law. While violations of Statistical Independence are often seen as non-scientific, they turn out to be needed to ensure the validity of records and our own memories and, by this, of science itself. A Past Hypothesis is needed to ensure the existence of records and turns out to require violations of Statistical Independence. It is not excluded that its explanation, still unknown, ensures such violations in the way needed by local interpretations of quantum mechanics. I suggest that an as-yet unknown law or superselection rule may restrict the full tensor-product Hilbert space to the very special subspace required by the validity of records and the Past Hypothesis.
Full article
(This article belongs to the Section Quantum Information)
Open AccessArticle
Geometric Algebra Jordan–Wigner Transformation for Quantum Simulation
by
Grégoire Veyrac and Zeno Toffano
Entropy 2024, 26(5), 410; https://doi.org/10.3390/e26050410 - 8 May 2024
Abstract
►▼
Show Figures
Quantum simulation qubit models of electronic Hamiltonians rely on specific transformations in order to take into account the fermionic permutation properties of electrons. These transformations (principally the Jordan–Wigner transformation (JWT) and the Bravyi–Kitaev transformation) correspond in a quantum circuit to the introduction of
[...] Read more.
Quantum simulation qubit models of electronic Hamiltonians rely on specific transformations in order to take into account the fermionic permutation properties of electrons. These transformations (principally the Jordan–Wigner transformation (JWT) and the Bravyi–Kitaev transformation) correspond in a quantum circuit to the introduction of a supplementary circuit level. In order to include the fermionic properties in a more straightforward way in quantum computations, we propose to use methods issued from Geometric Algebra (GA), which, due to its commutation properties, are well adapted for fermionic systems. First, we apply the Witt basis method in GA to reformulate the JWT in this framework and use this formulation to express various quantum gates. We then rewrite the general one and two-electron Hamiltonian and use it for building a quantum simulation circuit for the Hydrogen molecule. Finally, the quantum Ising Hamiltonian, widely used in quantum simulation, is reformulated in this framework.
Full article
Figure 1
Open AccessArticle
Entropy-Aided Meshing-Order Modulation Analysis for Wind Turbine Planetary Gear Weak Fault Detection under Variable Rotational Speed
by
Shaodan Zhi, Hengshan Wu, Haikuo Shen, Tianyang Wang and Hongfei Fu
Entropy 2024, 26(5), 409; https://doi.org/10.3390/e26050409 - 8 May 2024
Abstract
As one of the most vital energy conversation systems, the safe operation of wind turbines is very important; however, weak fault and time-varying speed may challenge the conventional monitoring strategies. Thus, an entropy-aided meshing-order modulation method is proposed for detecting the optimal frequency
[...] Read more.
As one of the most vital energy conversation systems, the safe operation of wind turbines is very important; however, weak fault and time-varying speed may challenge the conventional monitoring strategies. Thus, an entropy-aided meshing-order modulation method is proposed for detecting the optimal frequency band, which contains the weak fault-related information. Specifically, the variable rotational frequency trend is first identified and extracted based on the time–frequency representation of the raw signal by constructing a novel scaling-basis local reassigning chirplet transform (SLRCT). A new entropy-aided meshing-order modulation (EMOM) indicator is then constructed to locate the most sensitive modulation frequency area according to the extracted fine speed trend with the help of order tracking technique. Finally, the raw vibration signal is bandpass filtered via the corresponding optimal frequency band with the highest EMOM indicator. The order components resulting from the weak fault can be highlighted to accomplish weak fault detection. The effectiveness of the proposed EMOM analysis-based method has been tested using the experimental data of three different gear fault types of different fault levels from a planetary test rig.
Full article
(This article belongs to the Special Issue Signal Processing for Fault Detection and Diagnosis in Electric Machines and Energy Conversion Systems)
Open AccessArticle
Investigation of Thermo-Hydraulics in a Lid-Driven Square Cavity with a Heated Hemispherical Obstacle at the Bottom
by
Farhan Lafta Rashid, Abbas Fadhil Khalaf, Arman Ameen and Mudhar A. Al-Obaidi
Entropy 2024, 26(5), 408; https://doi.org/10.3390/e26050408 - 8 May 2024
Abstract
Lid-driven cavity (LDC) flow is a significant area of study in fluid mechanics due to its common occurrence in engineering challenges. However, using numerical simulations (ANSYS Fluent) to accurately predict fluid flow and mixed convective heat transfer features, incorporating both a moving top
[...] Read more.
Lid-driven cavity (LDC) flow is a significant area of study in fluid mechanics due to its common occurrence in engineering challenges. However, using numerical simulations (ANSYS Fluent) to accurately predict fluid flow and mixed convective heat transfer features, incorporating both a moving top wall and a heated hemispherical obstruction at the bottom, has not yet been attempted. This study aims to numerically demonstrate forced convection in a lid-driven square cavity (LDSC) with a moving top wall and a heated hemispherical obstacle at the bottom. The cavity is filled with a Newtonian fluid and subjected to a specific set of velocities (5, 10, 15, and 20 m/s) at the moving wall. The finite volume method is used to solve the governing equations using the Boussinesq approximation and the parallel flow assumption. The impact of various cavity geometries, as well as the influence of the moving top wall on fluid flow and heat transfer within the cavity, are evaluated. The results of this study indicate that the movement of the wall significantly disrupts the flow field inside the cavity, promoting excellent mixing between the flow field below the moving wall and within the cavity. The static pressure exhibits fluctuations, with the highest value observed at the top of the cavity of 1 m width (adjacent to the moving wall) and the lowest at 0.6 m. Furthermore, dynamic pressure experiences a linear increase until reaching its peak at 0.7 m, followed by a steady decrease toward the moving wall. The velocity of the internal surface fluctuates unpredictably along its length while other parameters remain relatively stable.
Full article
(This article belongs to the Special Issue Modern Trends in Multi-Phase Flow and Heat Transfer)
Open AccessArticle
Minimizing Computation and Communication Costs of Two-Sided Secure Distributed Matrix Multiplication under Arbitrary Collusion Pattern
by
Jin Li, Nan Liu and Wei Kang
Entropy 2024, 26(5), 407; https://doi.org/10.3390/e26050407 - 8 May 2024
Abstract
This paper studies the problem of minimizing the total cost, including computation cost and communication cost, in the system of two-sided secure distributed matrix multiplication (SDMM) under an arbitrary collusion pattern. In order to perform SDMM, the two input matrices are split into
[...] Read more.
This paper studies the problem of minimizing the total cost, including computation cost and communication cost, in the system of two-sided secure distributed matrix multiplication (SDMM) under an arbitrary collusion pattern. In order to perform SDMM, the two input matrices are split into some blocks, blocks of random matrices are appended to protect the security of the two input matrices, and encoded copies of the blocks are distributed to all computing nodes for matrix multiplication calculation. Our aim is to minimize the total cost, overall matrix splitting factors, number of appended random matrices, and distribution vector, while satisfying the security constraint of the two input matrices, the decodability constraint of the desired result of the multiplication, the storage capacity of the computing nodes, and the delay constraint. First, a strategy of appending zeros to the input matrices is proposed to overcome the divisibility problem of matrix splitting. Next, the optimization problem is divided into two subproblems with the aid of alternating optimization (AO), where a feasible solution can be obtained. In addition, some necessary conditions for the problem to be feasible are provided. Simulation results demonstrate the superiority of our proposed scheme compared to the scheme without appending zeros and the scheme with no alternating optimization.
Full article
(This article belongs to the Special Issue Information-Theoretic Cryptography and Security)
►▼
Show Figures
Figure 1
Open AccessArticle
Relativistic Roots of κ-Entropy
by
Giorgio Kaniadakis
Entropy 2024, 26(5), 406; https://doi.org/10.3390/e26050406 (registering DOI) - 7 May 2024
Abstract
The axiomatic structure of the -statistcal theory is proven. In addition to the first three standard Khinchin–Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom and the scaling axiom. It is shown that both the
[...] Read more.
The axiomatic structure of the -statistcal theory is proven. In addition to the first three standard Khinchin–Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom and the scaling axiom. It is shown that both the -entropy and its special limiting case, the classical Boltzmann–Gibbs–Shannon entropy, follow unambiguously from the above new set of five axioms. It has been emphasized that the statistical theory that can be built from -entropy has a validity that goes beyond physics and can be used to treat physical, natural, or artificial complex systems. The physical origin of the self-duality and scaling axioms has been investigated and traced back to the first principles of relativistic physics, i.e., the Galileo relativity principle and the Einstein principle of the constancy of the speed of light. It has been shown that the -formalism, which emerges from the -entropy, can treat both simple (few-body) and complex (statistical) systems in a unified way. Relativistic statistical mechanics based on -entropy is shown that preserves the main features of classical statistical mechanics (kinetic theory, molecular chaos hypothesis, maximum entropy principle, thermodynamic stability, H-theorem, and Lesche stability). The answers that the -statistical theory gives to the more-than-a-century-old open problems of relativistic physics, such as how thermodynamic quantities like temperature and entropy vary with the speed of the reference frame, have been emphasized.
Full article
(This article belongs to the Special Issue Twenty Years of Kaniadakis Entropy: Current Trends and Future Perspectives)
Open AccessArticle
Chaos Synchronization of Integrated Five-Section Semiconductor Lasers
by
Yuanyuan Guo, Yao Du, Hua Gao, Min Tan, Tong Zhao, Zhiwei Jia, Pengfa Chang and Longsheng Wang
Entropy 2024, 26(5), 405; https://doi.org/10.3390/e26050405 - 6 May 2024
Abstract
►▼
Show Figures
We proposed and verified a scheme of chaos synchronization for integrated five-section semiconductor lasers with matching parameters. The simulation results demonstrated that the integrated five-section semiconductor laser could generate a chaotic signal within a large parameter range of the driving currents of five
[...] Read more.
We proposed and verified a scheme of chaos synchronization for integrated five-section semiconductor lasers with matching parameters. The simulation results demonstrated that the integrated five-section semiconductor laser could generate a chaotic signal within a large parameter range of the driving currents of five sections. Subsequently, chaos synchronization between two integrated five-section semiconductor lasers with matched parameters was realized by using a common noise signal as a driver. Moreover, it was found that the synchronization was sensitive to the current mismatch in all five sections, indicating that the driving currents of the five sections could be used as keys of chaotic optical communication. Therefore, this synchronization scheme provides a candidate to increase the dimension of key space and enhances the security of the system.
Full article
Figure 1
Open AccessArticle
Importance of Characteristic Features and Their Form for Data Exploration
by
Urszula Stańczyk, Beata Zielosko and Grzegorz Baron
Entropy 2024, 26(5), 404; https://doi.org/10.3390/e26050404 - 6 May 2024
Abstract
►▼
Show Figures
The nature of the input features is one of the key factors indicating what kind of tools, methods, or approaches can be used in a knowledge discovery process. Depending on the characteristics of the available attributes, some techniques could lead to unsatisfactory performance
[...] Read more.
The nature of the input features is one of the key factors indicating what kind of tools, methods, or approaches can be used in a knowledge discovery process. Depending on the characteristics of the available attributes, some techniques could lead to unsatisfactory performance or even may not proceed at all without additional preprocessing steps. The types of variables and their domains affect performance. Any changes to their form can influence it as well, or even enable some learners. On the other hand, the relevance of features for a task constitutes another element with a noticeable impact on data exploration. The importance of attributes can be estimated through the application of mechanisms belonging to the feature selection and reduction area, such as rankings. In the described research framework, the data form was conditioned on relevance by the proposed procedure of gradual discretisation controlled by a ranking of attributes. Supervised and unsupervised discretisation methods were employed to the datasets from the stylometric domain and the task of binary authorship attribution. For the selected classifiers, extensive tests were performed and they indicated many cases of enhanced prediction for partially discretised datasets.
Full article
Figure 1
Open AccessArticle
A Novel Classification Method: Neighborhood-Based Positive Unlabeled Learning Using Decision Tree (NPULUD)
by
Bita Ghasemkhani, Kadriye Filiz Balbal, Kokten Ulas Birant and Derya Birant
Entropy 2024, 26(5), 403; https://doi.org/10.3390/e26050403 - 4 May 2024
Abstract
In a standard binary supervised classification task, the existence of both negative and positive samples in the training dataset are required to construct a classification model. However, this condition is not met in certain applications where only one class of samples is obtainable.
[...] Read more.
In a standard binary supervised classification task, the existence of both negative and positive samples in the training dataset are required to construct a classification model. However, this condition is not met in certain applications where only one class of samples is obtainable. To overcome this problem, a different classification method, which learns from positive and unlabeled (PU) data, must be incorporated. In this study, a novel method is presented: neighborhood-based positive unlabeled learning using decision tree (NPULUD). First, NPULUD uses the nearest neighborhood approach for the PU strategy and then employs a decision tree algorithm for the classification task by utilizing the entropy measure. Entropy played a pivotal role in assessing the level of uncertainty in the training dataset, as a decision tree was developed with the purpose of classification. Through experiments, we validated our method over 24 real-world datasets. The proposed method attained an average accuracy of 87.24%, while the traditional supervised learning approach obtained an average accuracy of 83.99% on the datasets. Additionally, it is also demonstrated that our method obtained a statistically notable enhancement (7.74%), with respect to state-of-the-art peers, on average.
Full article
(This article belongs to the Special Issue Entropy in Real-World Datasets and Its Impact on Machine Learning II)
►▼
Show Figures
Figure 1
Open AccessArticle
Detracking Autoencoding Conditional Generative Adversarial Network: Improved Generative Adversarial Network Method for Tabular Missing Value Imputation
by
Jingrui Liu, Zixin Duan, Xinkai Hu, Jingxuan Zhong and Yunfei Yin
Entropy 2024, 26(5), 402; https://doi.org/10.3390/e26050402 - 4 May 2024
Abstract
►▼
Show Figures
Due to various reasons, such as limitations in data collection and interruptions in network transmission, gathered data often contain missing values. Existing state-of-the-art generative adversarial imputation methods face three main issues: limited applicability, neglect of latent categorical information that could reflect relationships among
[...] Read more.
Due to various reasons, such as limitations in data collection and interruptions in network transmission, gathered data often contain missing values. Existing state-of-the-art generative adversarial imputation methods face three main issues: limited applicability, neglect of latent categorical information that could reflect relationships among samples, and an inability to balance local and global information. We propose a novel generative adversarial model named DTAE-CGAN that incorporates detracking autoencoding and conditional labels to address these issues. This enhances the network’s ability to learn inter-sample correlations and makes full use of all data information in incomplete datasets, rather than learning random noise. We conducted experiments on six real datasets of varying sizes, comparing our method with four classic imputation baselines. The results demonstrate that our proposed model consistently exhibited superior imputation accuracy.
Full article
Figure 1
Open AccessReview
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
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)
►▼
Show Figures
Figure 1
Open AccessArticle
Dynamic Weighting Translation Transfer Learning for Imbalanced Medical Image Classification
by
Chenglin Yu and Hailong Pei
Entropy 2024, 26(5), 400; https://doi.org/10.3390/e26050400 - 1 May 2024
Abstract
Medical image diagnosis using deep learning has shown significant promise in clinical medicine. However, it often encounters two major difficulties in real-world applications: (1) domain shift, which invalidates the trained model on new datasets, and (2) class imbalance problems leading to model biases
[...] Read more.
Medical image diagnosis using deep learning has shown significant promise in clinical medicine. However, it often encounters two major difficulties in real-world applications: (1) domain shift, which invalidates the trained model on new datasets, and (2) class imbalance problems leading to model biases towards majority classes. To address these challenges, this paper proposes a transfer learning solution, named Dynamic Weighting Translation Transfer Learning (DTTL), for imbalanced medical image classification. The approach is grounded in information and entropy theory and comprises three modules: Cross-domain Discriminability Adaptation (CDA), Dynamic Domain Translation (DDT), and Balanced Target Learning (BTL). CDA connects discriminative feature learning between source and target domains using a synthetic discriminability loss and a domain-invariant feature learning loss. The DDT unit develops a dynamic translation process for imbalanced classes between two domains, utilizing a confidence-based selection approach to select the most useful synthesized images to create a pseudo-labeled balanced target domain. Finally, the BTL unit performs supervised learning on the reassembled target set to obtain the final diagnostic model. This paper delves into maximizing the entropy of class distributions, while simultaneously minimizing the cross-entropy between the source and target domains to reduce domain discrepancies. By incorporating entropy concepts into our framework, our method not only significantly enhances medical image classification in practical settings but also innovates the application of entropy and information theory within deep learning and medical image processing realms. Extensive experiments demonstrate that DTTL achieves the best performance compared to existing state-of-the-art methods for imbalanced medical image classification tasks.
Full article
(This article belongs to the Section Signal and Data Analysis)
►▼
Show Figures
Figure 1
Open AccessReview
Hamiltonian Computational Chemistry: Geometrical Structures in Chemical Dynamics and Kinetics
by
Stavros C. Farantos
Entropy 2024, 26(5), 399; https://doi.org/10.3390/e26050399 - 30 Apr 2024
Abstract
The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show
[...] Read more.
The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space. Observable quantities are calculated by properly transforming the extended phase space onto a reduced space, and trajectories are integrated by solving Hamilton’s equations of motion. After defining a Riemannian metric, we can also estimate the length between two states. Local constants of motion are investigated by integrating Jacobi fields and solving the variational linear equations. Diagonalizing the symplectic fundamental matrix, eigenvalues equal to one reveal the number of constants of motion. For conservative systems, geometrical quantum mechanics has proved that solving the Schrödinger equation in extended Hilbert space, which incorporates the quantum phase, is equivalent to solving Hamilton’s equations in the projective Hilbert space. In classical thermodynamics, we take entropy and energy as canonical variables to construct the extended phase space and to represent the Lagrangian submanifold. Hamilton’s and variational equations are written and solved in the same fashion as in classical mechanics. Solvers based on high-order finite differences for numerically solving Hamilton’s, variational, and Schrödinger equations are described. Employing the Hénon–Heiles two-dimensional nonlinear model, representative results for time-dependent, quantum, and dissipative macroscopic systems are shown to illustrate concepts and methods. High-order finite-difference algorithms, despite their accuracy in low-dimensional systems, require substantial computer resources when they are applied to systems with many degrees of freedom, such as polyatomic molecules. We discuss recent research progress in employing Hamiltonian neural networks for solving Hamilton’s equations. It turns out that Hamiltonian geometry, shared with all physical theories, yields the necessary and sufficient conditions for the mutual assistance of humans and machines in deep-learning processes.
Full article
(This article belongs to the Special Issue Kinetic Models of Chemical Reactions)
►▼
Show Figures
Figure 1
Open AccessArticle
On an Aggregated Estimate for Human Mobility Regularities through Movement Trends and Population Density
by
Fabio Vanni and David Lambert
Entropy 2024, 26(5), 398; https://doi.org/10.3390/e26050398 - 30 Apr 2024
Abstract
This article introduces an analytical framework that interprets individual measures of entropy-based mobility derived from mobile phone data. We explore and analyze two widely recognized entropy metrics: random entropy and uncorrelated Shannon entropy. These metrics are estimated through collective variables of human mobility,
[...] Read more.
This article introduces an analytical framework that interprets individual measures of entropy-based mobility derived from mobile phone data. We explore and analyze two widely recognized entropy metrics: random entropy and uncorrelated Shannon entropy. These metrics are estimated through collective variables of human mobility, including movement trends and population density. By employing a collisional model, we establish statistical relationships between entropy measures and mobility variables. Furthermore, our research addresses three primary objectives: firstly, validating the model; secondly, exploring correlations between aggregated mobility and entropy measures in comparison to five economic indicators; and finally, demonstrating the utility of entropy measures. Specifically, we provide an effective population density estimate that offers a more realistic understanding of social interactions. This estimation takes into account both movement regularities and intensity, utilizing real-time data analysis conducted during the peak period of the COVID-19 pandemic.
Full article
(This article belongs to the Special Issue Modeling and Control of Epidemic Spreading in Complex Societies)
►▼
Show Figures
Figure 1
Open AccessArticle
QUBO Problem Formulation of Fragment-Based Protein–Ligand Flexible Docking
by
Keisuke Yanagisawa, Takuya Fujie, Kazuki Takabatake and Yutaka Akiyama
Entropy 2024, 26(5), 397; https://doi.org/10.3390/e26050397 - 30 Apr 2024
Abstract
Protein–ligand docking plays a significant role in structure-based drug discovery. This methodology aims to estimate the binding mode and binding free energy between the drug-targeted protein and candidate chemical compounds, utilizing protein tertiary structure information. Reformulation of this docking as a quadratic unconstrained
[...] Read more.
Protein–ligand docking plays a significant role in structure-based drug discovery. This methodology aims to estimate the binding mode and binding free energy between the drug-targeted protein and candidate chemical compounds, utilizing protein tertiary structure information. Reformulation of this docking as a quadratic unconstrained binary optimization (QUBO) problem to obtain solutions via quantum annealing has been attempted. However, previous studies did not consider the internal degrees of freedom of the compound that is mandatory and essential. In this study, we formulated fragment-based protein–ligand flexible docking, considering the internal degrees of freedom of the compound by focusing on fragments (rigid chemical substructures of compounds) as a QUBO problem. We introduced four factors essential for fragment–based docking in the Hamiltonian: (1) interaction energy between the target protein and each fragment, (2) clashes between fragments, (3) covalent bonds between fragments, and (4) the constraint that each fragment of the compound is selected for a single placement. We also implemented a proof-of-concept system and conducted redocking for the protein–compound complex structure of Aldose reductase (a drug target protein) using SQBM+, which is a simulated quantum annealer. The predicted binding pose reconstructed from the best solution was near-native (RMSD = 1.26 Å), which can be further improved (RMSD = 0.27 Å) using conventional energy minimization. The results indicate the validity of our QUBO problem formulation.
Full article
(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications II)
►▼
Show Figures
Figure 1
Open AccessArticle
Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks
by
Siyuan Xing and Efstathios G. Charalampidis
Entropy 2024, 26(5), 396; https://doi.org/10.3390/e26050396 - 30 Apr 2024
Abstract
In this paper, we apply a machine learning approach to learning traveling solitary waves across various physical systems that are described by families of partial differential equations (PDEs). Our approach integrates a novel interpretable neural network (NN) architecture called the Separable Gaussian Neural
[...] Read more.
In this paper, we apply a machine learning approach to learning traveling solitary waves across various physical systems that are described by families of partial differential equations (PDEs). Our approach integrates a novel interpretable neural network (NN) architecture called the Separable Gaussian Neural Network (SGNN) into the framework of Physics-Informed Neural Networks (PINNs). Unlike the traditional PINNs, which treat spatial and temporal data as independent inputs, the present method leverages wave characteristics to transform data into what is called the co-traveling wave frame. This adaptation effectively addresses the issue of propagation failure in PINNs when applied to large computational domains. Here, the SGNN architecture demonstrates robust approximation capabilities for single-peakon, multi-peakon, and stationary solutions (known as “leftons”) within the (1 + 1)-dimensional b-family of PDEs. In addition, we expand our investigation and explore not only peakon solutions in the -family but also compacton solutions in the (2 + 1)-dimensional Rosenau–Hyman family of PDEs. A comparative analysis with a multi-layer perceptron (MLP) reveals that the SGNN achieves comparable accuracy with fewer than a tenth of the neurons, underscoring its efficiency and potential for broader applications in solving complex nonlinear PDEs.
Full article
(This article belongs to the Special Issue Recent Advances in the Theory of Nonlinear Lattices)
Open AccessArticle
A Spectral Investigation of Criticality and Crossover Effects in Two and Three Dimensions: Short Timescales with Small Systems in Minute Random Matrices
by
Eliseu Venites Filho, Roberto da Silva and José Roberto Drugowich de Felício
Entropy 2024, 26(5), 395; https://doi.org/10.3390/e26050395 - 30 Apr 2024
Abstract
Random matrix theory, particularly using matrices akin to the Wishart ensemble, has proven successful in elucidating the thermodynamic characteristics of critical behavior in spin systems across varying interaction ranges. This paper explores the applicability of such methods in investigating critical phenomena and the
[...] Read more.
Random matrix theory, particularly using matrices akin to the Wishart ensemble, has proven successful in elucidating the thermodynamic characteristics of critical behavior in spin systems across varying interaction ranges. This paper explores the applicability of such methods in investigating critical phenomena and the crossover to tricritical points within the Blume–Capel model. Through an analysis of eigenvalue mean, dispersion, and extrema statistics, we demonstrate the efficacy of these spectral techniques in characterizing critical points in both two and three dimensions. Crucially, we propose a significant modification to this spectral approach, which emerges as a versatile tool for studying critical phenomena. Unlike traditional methods that eschew diagonalization, our method excels in handling short timescales and small system sizes, widening the scope of inquiry into critical behavior.
Full article
(This article belongs to the Special Issue Random Matrix Theory and Its Innovative Applications)
►▼
Show Figures
Figure 1
Open AccessFeature PaperArticle
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
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)
►▼
Show Figures
Figure 1
Journal Menu
► ▼ Journal Menu-
- Entropy Home
- Aims & Scope
- Editorial Board
- Reviewer Board
- Topical Advisory Panel
- Video Exhibition
- Instructions for Authors
- Special Issues
- Topics
- Sections & Collections
- Article Processing Charge
- Indexing & Archiving
- Editor’s Choice Articles
- Most Cited & Viewed
- Journal Statistics
- Journal History
- Journal Awards
- Society Collaborations
- Conferences
- Editorial Office
Journal Browser
► ▼ Journal Browser-
arrow_forward_ios
Forthcoming issue
arrow_forward_ios Current issue - Vol. 26 (2024)
- Vol. 25 (2023)
- Vol. 24 (2022)
- Vol. 23 (2021)
- Vol. 22 (2020)
- Vol. 21 (2019)
- Vol. 20 (2018)
- Vol. 19 (2017)
- Vol. 18 (2016)
- Vol. 17 (2015)
- Vol. 16 (2014)
- Vol. 15 (2013)
- Vol. 14 (2012)
- Vol. 13 (2011)
- Vol. 12 (2010)
- Vol. 11 (2009)
- Vol. 10 (2008)
- Vol. 9 (2007)
- Vol. 8 (2006)
- Vol. 7 (2005)
- Vol. 6 (2004)
- Vol. 5 (2003)
- Vol. 4 (2002)
- Vol. 3 (2001)
- Vol. 2 (2000)
- Vol. 1 (1999)
Highly Accessed Articles
Latest Books
E-Mail Alert
News
Topics
Topic in
Algorithms, Computation, Entropy, Fractal Fract, MCA
Analytical and Numerical Methods for Stochastic Biological Systems
Topic Editors: Mehmet Yavuz, Necati Ozdemir, Mouhcine Tilioua, Yassine SabbarDeadline: 10 May 2024
Topic in
Algorithms, Diagnostics, Entropy, Information, J. Imaging
Application of Machine Learning in Molecular Imaging
Topic Editors: Allegra Conti, Nicola Toschi, Marianna Inglese, Andrea Duggento, Matthew Grech-Sollars, Serena Monti, Giancarlo Sportelli, Pietro CarraDeadline: 31 May 2024
Topic in
Education Sciences, Entropy, JAL, Societies, Sustainability
Sustainability in Aging and Depopulation Societies
Topic Editors: Shiro Horiuchi, Gregor Wolbring, Takeshi MatsudaDeadline: 15 June 2024
Topic in
Buildings, Energies, Entropy, Resources, Sustainability
Advances in Solar Heating and Cooling
Topic Editors: Salvatore Vasta, Sotirios Karellas, Marina Bonomolo, Alessio Sapienza, Uli JakobDeadline: 30 June 2024
Conferences
22–26 November 2024
2024 International Conference on Science and Engineering of Electronics (ICSEE'2024) Wuhan, China
28–31 May 2024
XXII Conference on Non-equilibrium Statistical Mechanics and Nonlinear Physics—MEDYFINOL 2024
Special Issues
Special Issue in
Entropy
Information Theory for Interpretable Machine Learning
Guest Editors: Marco Piangerelli, Sotiris KotsiantisDeadline: 15 May 2024
Special Issue in
Entropy
Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications
Guest Editors: Brian Dennis, Mark L. Taper, Jose Miguel PoncianoDeadline: 31 May 2024
Special Issue in
Entropy
Nonlinear Dynamics in Cardiovascular Signals
Guest Editor: Claudia LermaDeadline: 15 June 2024
Special Issue in
Entropy
Non-equilibrium Thermodynamics
Guest Editors: Duc Nguyen-Manh, Abraham MarmurDeadline: 30 June 2024
Topical Collections
Topical Collection in
Entropy
Algorithmic Information Dynamics: A Computational Approach to Causality from Cells to Networks
Collection Editors: Hector Zenil, Felipe Abrahão
Topical Collection in
Entropy
Wavelets, Fractals and Information Theory
Collection Editor: Carlo Cattani
Topical Collection in
Entropy
Entropy in Image Analysis
Collection Editor: Amelia Carolina Sparavigna