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Entropy MDPI

Entropy (ISSN 1099-4300) is an open access, peer reviewed journal on entropy and information sciences

02/12/2024

🔥 Entropy MDPI Hot Picks
📹 Quantum Annealing in the NISQ Era: Railway Conflict Management
✍️ Krzysztof Domino, Mátyás Koniorczyk, Krzysztof Krawiec, Konrad Jałowiecki, Sebastian Deffner and Bartłomiej Gardas
🔗 https://bit.ly/3ZeE482
🕹 We are in the noisy intermediate-scale quantum (NISQ) devices’ era, in which quantum hardware has become available for application in real-world problems. However, demonstrations of the usefulness of such NISQ devices are still rare. In this work, we consider a practical railway dispatching problem: delay and conflict management on single-track railway lines. We examine the train dispatching consequences of the arrival of an already delayed train to a given network segment. This problem is computationally hard and needs to be solved almost in real time. We introduce a quadratic unconstrained binary optimization (QUBO) model of this problem, which is compatible with the emerging quantum annealing technology. The model’s instances can be executed on present-day quantum annealers. As a proof-of-concept, we solve selected real-life problems from the Polish railway network using D-Wave quantum annealers. As a reference, we also provide solutions calculated with classical methods, including the conventional solution of a linear integer version of the model as well as the solution of the QUBO model using a tensor network-based algorithm. Our preliminary results illustrate the degree of difficulty of real-life railway instances for the current quantum annealing technology. Moreover, our analysis shows that the new generation of quantum annealers (the advantage system) does not perform well on those instances, either.

26/11/2024

🔥Entropy MDPI Hot Picks
📹 Entanglement Witness for the Weak Equivalence Principle
✍️ Sougato Bose, Anupam Mazumdar, Martine Schut and Marko Toroš
🔗 https://bit.ly/4fHJyPr
🕹 The Einstein equivalence principle is based on the equality of gravitational and inertial mass, which has led to the universality of a free-fall concept. The principle has been extremely well tested so far and has been tested with a great precision. However, all these tests and the corresponding arguments are based on a classical setup where the notion of position and velocity of the mass is associated with a classical value as opposed to the quantum entities.Here, we provide a simple quantum protocol based on creating large spatial superposition states in a laboratory to test the quantum regime of the equivalence principle where both matter and gravity are treated at par as a quantum entity. The two gravitational masses of the two spatial superpositions source the gravitational potential for each other. We argue that such a quantum protocol is unique with regard to testing especially the generalisation of the weak equivalence principle by constraining the equality of gravitational and inertial mass via witnessing quantum entanglement.

21/11/2024

💽Special Issue: Advances in Quantum Computing

👤Guest Editors: Dr. Brian R. La Cour (The University of Texas at Austin) and Prof. Giuliano Benenti (University of Insubria)

There were 25 articles published including one Editorial with this Entropy MDPI Special Issue. Read the articles in detail: https://bit.ly/3YRmqXy

🕹This Special Issue focuses on the recent advances, and challenges, in developing large-scale, fault-tolerant quantum computers capable of solving tomorrow’s growing computational needs. Original unpublished papers and review articles are invited on the following topics: (1) advances in quantum computing hardware, (2) novel quantum and hybrid algorithms, (3) applications to real-world problems using noisy, intermediate-scale quantum devices, (4) quantum networks and distributed quantum computing, (5) classical challenges to demonstrations of quantum advantage, and (6) investigations into the scalability of different quantum hardware architectures.

19/11/2024

🔥Entropy MDPI Hot Picks
📹 Water Quality Prediction Based on Machine Learning and Comprehensive Weighting Methods
✍️ Xianhe Wang, Ying Li, Qian Qiao, Adriano Tavares and Yanchun Liang
🔗 https://bit.ly/4fTg3dd
🕹 In the context of escalating global environmental concerns, the importance of preserving water resources and upholding ecological equilibrium has become increasingly apparent. As a result, the monitoring and prediction of water quality have emerged as vital tasks in achieving these objectives. However, ensuring the accuracy and dependability of water quality prediction has proven to be a challenging endeavor. To address this issue, this study proposes a comprehensive weight-based approach that combines entropy weighting with the Pearson correlation coefficient to select crucial features in water quality prediction. This approach effectively considers both feature correlation and information content, avoiding excessive reliance on a single criterion for feature selection. Through the utilization of this comprehensive approach, a comprehensive evaluation of the contribution and importance of the features was achieved, thereby minimizing subjective bias and uncertainty. By striking a balance among various factors, features with stronger correlation and greater information content can be selected, leading to improved accuracy and robustness in the feature-selection process. Furthermore, this study explored several machine learning models for water quality prediction, including Support Vector Machines (SVMs), Multilayer Perceptron (MLP), Random Forest (RF), XGBoost, and Long Short-Term Memory (LSTM). SVM exhibited commendable performance in predicting Dissolved Oxygen (DO), showcasing excellent generalization capabilities and high prediction accuracy. MLP demonstrated its strength in nonlinear modeling and performed well in predicting multiple water quality parameters. Conversely, the RF and XGBoost models exhibited relatively inferior performance in water quality prediction. In contrast, the LSTM model, a recurrent neural network specialized in processing time series data, demonstrated exceptional abilities in water quality prediction. It effectively captured the dynamic patterns present in time series data, offering stable and accurate predictions for various water quality parameters.

14/11/2024

🌟Entropy MDPI New Paper
📹Understanding Higher-Order Interactions in Information Space
✍️Herbert Edelsbrunner, Katharina Ölsböck and Hubert Wagner
🔗 https://bit.ly/4fPll9T
🕹 Methods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. One such setting is a finite collection of discrete probability distributions embedded in the probability simplex measured with the relative entropy (Kullback–Leibler divergence). More generally, one can work with a Bregman divergence parameterized by a different notion of entropy. While theoretical algorithms exist for this setup, there is a paucity of implementations for exploring and comparing geometric-topological properties of various information spaces. The interest of this work is therefore twofold. First, we propose the first robust algorithms and software for geometric and topological data analysis in information space. Perhaps surprisingly, despite working with Bregman divergences, our design reuses robust libraries for the Euclidean case. Second, using the new software, we take the first steps towards understanding the geometric-topological structure of these spaces. In particular, we compare them with the more familiar spaces equipped with the Euclidean and Fisher metrics.

13/11/2024

🔥Entropy MDPI Hot Picks
📹 A Survey of Deep Learning-Based Multimodal Emotion Recognition: Speech, Text, and Face
✍️ Hailun Lian, Cheng Lu, Sunan Li, Yan Zhao, Chuangao Tang and Yuan Zong
🔗 https://bit.ly/3URgWLh
🕹 Multimodal emotion recognition (MER) refers to the identification and understanding of human emotional states by combining different signals, including—but not limited to—text, speech, and face cues. MER plays a crucial role in the human–computer interaction (HCI) domain. With the recent progression of deep learning technologies and the increasing availability of multimodal datasets, the MER domain has witnessed considerable development, resulting in numerous significant research breakthroughs. However, a conspicuous absence of thorough and focused reviews on these deep learning-based MER achievements is observed. This survey aims to bridge this gap by providing a comprehensive overview of the recent advancements in MER based on deep learning. For an orderly exposition, this paper first outlines a meticulous analysis of the current multimodal datasets, emphasizing their advantages and constraints. Subsequently, we thoroughly scrutinize diverse methods for multimodal emotional feature extraction, highlighting the merits and demerits of each method. Moreover, we perform an exhaustive analysis of various MER algorithms, with particular focus on the model-agnostic fusion methods (including early fusion, late fusion, and hybrid fusion) and fusion based on intermediate layers of deep models (encompassing simple concatenation fusion, utterance-level interaction fusion, and fine-grained interaction fusion). We assess the strengths and weaknesses of these fusion strategies, providing guidance to researchers to help them select the most suitable techniques for their studies. In summary, this survey aims to provide a thorough and insightful review of the field of deep learning-based MER. It is intended as a valuable guide to aid researchers in furthering the evolution of this dynamic and impactful field.

12/11/2024

🌟Entropy MDPI Issue Cover Paper
📹How Much Is Enough? A Study on Diffusion Times in Score-Based Generative Models
✍️Giulio Franzese, Simone Rossi, Lixuan Yang, Alessandro Finamore, Dario Rossi, Maurizio Filippone and Pietro Michiardi
🔗 https://bit.ly/4fmYuT8
🕹 Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, a detailed understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive with regard to the state of the art, according to standard sample quality metrics and log-likelihood.

11/11/2024

🔥Entropy MDPI Hot Picks
📹Precision Machine Learning
✍️Eric J. Michaud, Ziming Liu and Max Tegmark
🔗 https://bit.ly/4hTu4ts
🕹 We explore unique considerations involved in fitting machine learning (ML) models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with increasing parameters and data. We find that neural networks (NNs) can often outperform classical approximation methods on high-dimensional examples, by (we hypothesize) auto-discovering and exploiting modular structures therein. However, neural networks trained with common optimizers are less powerful for low-dimensional cases, which motivates us to study the unique properties of neural network loss landscapes and the corresponding optimization challenges that arise in the high precision regime. To address the optimization issue in low dimensions, we develop training tricks which enable us to train neural networks to extremely low loss, close to the limits allowed by numerical precision.

07/11/2024

🌟Entropy MDPI Issue Cover Paper
📹Elementary Observations: Building Blocks of Physical Information Gain
✍️J. Gerhard Müller
🔗 https://bit.ly/4fgg4bc
🕹 In this paper, we are concerned with the process of experimental information gain. Building on previous work, we show that this is a discontinuous process in which the initiating quantum-mechanical matter–instrument interactions are being turned into macroscopically observable events (EOs). In the course of time, such EOs evolve into spatio-temporal patterns of EOs, which allow conceivable alternatives of physical explanation to be distinguished. Focusing on the specific case of photon detection, we show that during their lifetimes, EOs proceed through the four phases of initiation, detection, erasure and reset. Once generated, the observational value of EOs can be measured in units of the Planck quantum of physical action ℎ=4.136×10−15eVs. Once terminated, each unit of entropy of size 𝑘𝐵=8.617×10−5eV/K, which had been created in the instrument during the observational phase, needs to be removed from the instrument to ready it for a new round of photon detection. This withdrawal of entropy takes place at an energetic cost of at least two units of the Landauer minimum energy bound of 𝐸𝐿𝑎=ln(2)𝑘𝐵𝑇𝐷 for each unit of entropy of size 𝑘𝐵.

06/11/2024

🌟Entropy MDPI Issue Cover Paper
📹On the Accurate Estimation of Information-Theoretic Quantities from Multi-Dimensional Sample Data
✍️Manuel Álvarez Chaves, Hoshin V. Gupta, Uwe Ehret and Anneli Guthke
🔗 https://bit.ly/3Cs2zGQ
🕹 Using information-theoretic quantities in practical applications with continuous data is often hindered by the fact that probability density functions need to be estimated in higher dimensions, which can become unreliable or even computationally unfeasible. To make these useful quantities more accessible, alternative approaches such as binned frequencies using histograms and k-nearest neighbors (k-NN) have been proposed. However, a systematic comparison of the applicability of these methods has been lacking. We wish to fill this gap by comparing kernel-density-based estimation (KDE) with these two alternatives in carefully designed synthetic test cases. Specifically, we wish to estimate the information-theoretic quantities: entropy, Kullback–Leibler divergence, and mutual information, from sample data. As a reference, the results are compared to closed-form solutions or numerical integrals. We generate samples from distributions of various shapes in dimensions ranging from one to ten. We evaluate the estimators’ performance as a function of sample size, distribution characteristics, and chosen hyperparameters. We further compare the required computation time and specific implementation challenges. Notably, k-NN estimation tends to outperform other methods, considering algorithmic implementation, computational efficiency, and estimation accuracy, especially with sufficient data. This study provides valuable insights into the strengths and limitations of the different estimation methods for information-theoretic quantities. It also highlights the significance of considering the characteristics of the data, as well as the targeted information-theoretic quantity when selecting an appropriate estimation technique. These findings will assist scientists and practitioners in choosing the most suitable method, considering their specific application and available data. We have collected the compared estimation methods in a ready-to-use open-source Python 3 toolbox and, thereby, hope to promote the use of information-theoretic quantities by researchers and practitioners to evaluate the information in data and models in various disciplines.

05/11/2024

🌟Entropy MDPI Issue Cover Paper
📹Modeling the Arrows of Time with Causal Multibaker Maps
✍️Aram Ebtekar and Marcus Hutter
🔗 https://bit.ly/3YUxLYp
🕹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.

04/11/2024

📹An Entropy Generation Rate Model for Tropospheric Behavior That Includes Cloud Evolution
✍️Jainagesh A. Sekhar
🔗 https://bit.ly/3YwkKmq
🕹A postulate that relates global warming to higher entropy generation rate demand in the tropospheric is offered and tested. This article introduces a low-complexity model to calculate the entropy generation rate required in the troposphere. The entropy generation rate per unit volume is noted to be proportional to the square of the Earth’s average surface temperature for a given positive rate of surface warming. The main postulate is that the troposphere responds with mechanisms to provide for the entropy generation rate that involves specific cloud morphologies and wind behavior. A diffuse-interface model is used to calculate the entropy generation rates of clouds. Clouds with limited vertical development, like the high-altitude cirrus or mid-altitude stratus clouds, are close-to-equilibrium clouds that do not generate much entropy but contribute to warming. Clouds like the cumulonimbus permit rapid vertical cloud development and can rapidly generate new entropy. Several extreme weather events that the Earth is experiencing are related to entropy-generating clouds that discharge a high rate of rain, hail, or transfer energy in the form of lightning. The water discharge from a cloud can cool the surface below the cloud but also add to the demand for a higher entropy generation rate in the cloud and troposphere. The model proposed predicts the atmospheric conditions required for bifurcations to severe-weather clouds. The calculated vertical velocity of thunderclouds associated with high entropy generation rates matches the recorded observations. The scale of instabilities for an evolving diffuse interface is related to the entropy generation rate per unit volume. Significant similarities exist between the morphologies and the entropy generation rate correlations in vertical cloud evolution and directionally solidified grainy microstructures. Such similarities are also explored to explore a generalized framework of pattern evolution and establish the relationships with the corresponding entropy generation rate. A complex system like the troposphere can invoke multiple phenomena that dominate at different spatial scales to meet the demand for an entropy generation rate. A few such possibilities are presented in the context of rapid and slow changes in weather patterns.
🎯The original article was published with Entropy MDPI

01/11/2024

🌟Entropy MDPI Issue Cover - Volume 26, Issue 10
📹Bias in O-Information Estimation
✍️Johanna Gehlen, Jie Li, Cillian Hourican, Stavroula Tassi, Pashupati P. Mishra, Terho Lehtimäki, Mika Kähönen, Olli Raitakari, Jos A. Bosch and Rick Quax
🔗 https://bit.ly/4f1V9Zs
🕹Higher-order relationships are a central concept in the science of complex systems. A popular method of attempting to estimate the higher-order relationships of synergy and redundancy from data is through the O-information. It is an information–theoretic measure composed of Shannon entropy terms that quantifies the balance between redundancy and synergy in a system. However, bias is not yet taken into account in the estimation of the O-information of discrete variables. In this paper, we explain where this bias comes from and explore it for fully synergistic, fully redundant, and fully independent simulated systems of 𝑛=3 variables. Specifically, we explore how the sample size and number of bins affect the bias in the O-information estimation. The main finding is that the O-information of independent systems is severely biased towards synergy if the sample size is smaller than the number of jointly possible observations. This could mean that triplets identified as highly synergistic may in fact be close to independent. A bias approximation based on the Miller–Maddow method is derived for the O-information. We find that for systems of 𝑛=3 variables the bias approximation can partially correct for the bias. However, simulations of fully independent systems are still required as null models to provide a benchmark of the bias of the O-information.

31/10/2024

🌟Entropy MDPI Issue Cover Paper
📹Finite-Time Dynamics of an Entanglement Engine: Current, Fluctuations and Kinetic Uncertainty Relations
✍️Jeanne Bourgeois, Gianmichele Blasi, Shishir Khandelwal and Géraldine Haack
🔗 https://bit.ly/3YruAWz
🕹 Entanglement engines are autonomous quantum thermal machines designed to generate entanglement from the presence of a particle current flowing through the device. In this work, we investigate the functioning of a two-qubit entanglement engine beyond the steady-state regime. Within a master equation approach, we derive the time-dependent state, the particle current, as well as the associated current correlation functions. Our findings establish a direct connection between coherence and internal current, elucidating the existence of a critical current that serves as an indicator for entanglement in the steady state. We then apply our results to investigate kinetic uncertainty relations (KURs) at finite times. We demonstrate that there is more than one possible definition for KURs at finite times. Although the two definitions agree in the steady-state regime, they lead to different parameter ranges for violating KUR at finite times.

30/10/2024

🔥 Entropy MDPI Hot Picks
📹 Non-Hermitian Floquet Topological Matter—A Review
✍️ Longwen Zhou and Da-Jian Zhang
🔗 https://bit.ly/3CfQvZd
🕹 The past few years have witnessed a surge of interest in non-Hermitian Floquet topological matter due to its exotic properties resulting from the interplay between driving fields and non-Hermiticity. The present review sums up our studies on non-Hermitian Floquet topological matter in one and two spatial dimensions. We first give a bird’s-eye view of the literature for clarifying the physical significance of non-Hermitian Floquet systems. We then introduce, in a pedagogical manner, a number of useful tools tailored for the study of non-Hermitian Floquet systems and their topological properties. With the aid of these tools, we present typical examples of non-Hermitian Floquet topological insulators, superconductors, and quasicrystals, with a focus on their topological invariants, bulk-edge correspondences, non-Hermitian skin effects, dynamical properties, and localization transitions. We conclude this review by summarizing our main findings and presenting our vision of future directions.

29/10/2024

📹Fisher and Shannon Functionals for Hyperbolic Diffusion
✍️Manuel Osvaldo Caceres, Marco Nizama and Flavia Pennini
🔗https://bit.ly/3Af1DFi
🕹The complexity measure for the distribution in space-time of a finite-velocity diffusion process is calculated. Numerical results are presented for the calculation of Fisher’s information, Shannon’s entropy, and the Cramér–Rao inequality, all of which are associated with a positively normalized solution to the telegrapher’s equation. In the framework of hyperbolic diffusion, the non-local Fisher’s information with the x-parameter is related to the local Fisher’s information with the t-parameter. A perturbation theory is presented to calculate Shannon’s entropy of the telegrapher’s equation at long times, as well as a toy model to describe the system as an attenuated wave in the ballistic regime (short times).
📌The original article was published with Entropy MDPI

28/10/2024

🔥Entropy MDPI Hot Picks
📹Exploiting Dynamic Vector-Level Operations and a 2D-Enhanced Logistic Modular Map for Efficient Chaotic Image Encryption
✍️Hongmin Li, Shuqi Yu, Wei Feng, Yao Chen, Jing Zhang, Zhentao Qin, Zhengguo Zhu and Marcin Wozniak
🔗 https://bit.ly/48r3Tpm
🕹Over the past few years, chaotic image encryption has gained extensive attention. Nevertheless, the current studies on chaotic image encryption still possess certain constraints. To break these constraints, we initially created a two-dimensional enhanced logistic modular map (2D-ELMM) and subsequently devised a chaotic image encryption scheme based on vector-level operations and 2D-ELMM (CIES-DVEM). In contrast to some recent schemes, CIES-DVEM features remarkable advantages in several aspects. Firstly, 2D-ELMM is not only simpler in structure, but its chaotic performance is also significantly better than that of some newly reported chaotic maps. Secondly, the key stream generation process of CIES-DVEM is more practical, and there is no need to replace the secret key or recreate the chaotic sequence when handling different images. Thirdly, the encryption process of CIES-DVEM is dynamic and closely related to plaintext images, enabling it to withstand various attacks more effectively. Finally, CIES-DVEM incorporates lots of vector-level operations, resulting in a highly efficient encryption process. Numerous experiments and analyses indicate that CIES-DVEM not only boasts highly significant advantages in terms of encryption efficiency, but it also surpasses many recent encryption schemes in practicality and security.

25/10/2024

🔥Entropy MDPI Hot Picks
📹Natural Language Generation and Understanding of Big Code for AI-Assisted Programming: A Review
✍️Man Fai Wong, Shangxin Guo, Ching Nam Hang, Siu Wai Ho and Chee Wei Tan
🔗 https://bit.ly/3Upu1eF
🕹 This paper provides a comprehensive review of the literature concerning the utilization of Natural Language Processing (NLP) techniques, with a particular focus on transformer-based large language models (LLMs) trained using Big Code, within the domain of AI-assisted programming tasks. LLMs, augmented with software naturalness, have played a crucial role in facilitating AI-assisted programming applications, including code generation, code completion, code translation, code refinement, code summarization, defect detection, and clone detection. Notable examples of such applications include the GitHub Copilot powered by OpenAI’s Codex and DeepMind AlphaCode. This paper presents an overview of the major LLMs and their applications in downstream tasks related to AI-assisted programming. Furthermore, it explores the challenges and opportunities associated with incorporating NLP techniques with software naturalness in these applications, with a discussion on extending AI-assisted programming capabilities to Apple’s Xcode for mobile software development. This paper also presents the challenges of and opportunities for incorporating NLP techniques with software naturalness, empowering developers with advanced coding assistance and streamlining the software development process.

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📹An Entropy Generation Rate Model for Tropospheric Behavior That Includes Cloud Evolution ✍️Jainagesh A. Sekhar 🔗 https://bit.ly/3YwkKmq 🕹A postulate that relates global warming to higher entropy generation rate demand in the tropospheric is offered and tested. This article introduces a low-complexity model to calculate the entropy generation rate required in the troposphere. The entropy generation rate per unit volume is noted to be proportional to the square of the Earth’s average surface temperature for a given positive rate of surface warming. The main postulate is that the troposphere responds with mechanisms to provide for the entropy generation rate that involves specific cloud morphologies and wind behavior. A diffuse-interface model is used to calculate the entropy generation rates of clouds. Clouds with limited vertical development, like the high-altitude cirrus or mid-altitude stratus clouds, are close-to-equilibrium clouds that do not generate much entropy but contribute to warming. Clouds like the cumulonimbus permit rapid vertical cloud development and can rapidly generate new entropy. Several extreme weather events that the Earth is experiencing are related to entropy-generating clouds that discharge a high rate of rain, hail, or transfer energy in the form of lightning. The water discharge from a cloud can cool the surface below the cloud but also add to the demand for a higher entropy generation rate in the cloud and troposphere. The model proposed predicts the atmospheric conditions required for bifurcations to severe-weather clouds. The calculated vertical velocity of thunderclouds associated with high entropy generation rates matches the recorded observations. The scale of instabilities for an evolving diffuse interface is related to the entropy generation rate per unit volume. Significant similarities exist between the morphologies and the entropy generation rate correlations in vertical cloud evolution and directionally solidifie

📹Fisher and Shannon Functionals for Hyperbolic Diffusion ✍️Manuel Osvaldo Caceres, Marco Nizama and Flavia Pennini 🔗https://bit.ly/3Af1DFi 🕹The complexity measure for the distribution in space-time of a finite-velocity diffusion process is calculated. Numerical results are presented for the calculation of Fisher’s information, Shannon’s entropy, and the Cramér–Rao inequality, all of which are associated with a positively normalized solution to the telegrapher’s equation. In the framework of hyperbolic diffusion, the non-local Fisher’s information with the x-parameter is related to the local Fisher’s information with the t-parameter. A perturbation theory is presented to calculate Shannon’s entropy of the telegrapher’s equation at long times, as well as a toy model to describe the system as an attenuated wave in the ballistic regime (short times). 📌The original article was published with Entropy MDPI

📹On Magnetic Models in Wavefunction Ensembles 🕹In a wavefunction-only philosophy, thermodynamics must be recast in terms of an ensemble of wavefunctions. In this perspective we study how to construct Gibbs ensembles for magnetic quantum spin models. We show that with free boundary conditions and distinguishable “spins” there are no finite-temperature phase transitions because of high dimensionality of the phase space. Then we focus on the simplest case, namely the mean-field (Curie–Weiss) model, in order to discover whether phase transitions are even possible in this model class. This strategy at least diminishes the dimensionality of the problem. We found that, even assuming exchange symmetry in the wavefunctions, no finite-temperature phase transitions appear when the Hamiltonian is given by the usual energy expression of quantum mechanics (in this case the analytical argument is not totally satisfactory and we relied partly on a computer analysis). However, a variant model with additional “wavefunction energy” does have a phase transition to a magnetized state. (With respect to dynamics, which we do not consider here, wavefunction energy induces a non-linearity which nevertheless preserves norm and energy. This non-linearity becomes significant only at the macroscopic level.) The three results together suggest that magnetization in large wavefunction spin chains appears if and only if we consider indistinguishable particles and block macroscopic dispersion (i.e., macroscopic superpositions) by energy conservation. Our principle technique involves transforming the problem to one in probability theory, then applying results from large deviations, particularly the Gärtner–Ellis Theorem. Finally, we discuss Gibbs vs. Boltzmann/Einstein entropy in the choice of the quantum thermodynamic ensemble, as well as open problems. ✍️Leonardo De Carlo and William D. Wick 🔗https://bit.ly/3YpqVtz The original article was published with Entropy MDPI

📹A Joint Communication and Computation Design for Probabilistic Semantic Communications ✍️Zhouxiang Zhao, Zhaohui Yang, Mingzhe Chen, Zhaoyang Zhang and H. Vincent Poor 🔗https://bit.ly/3zYBNFs 🕹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. 📌The original article was published with Entropy MDPI

🔥Entropy MDPI Hot Picks 📹Quantum Advantage of Thermal Machines with Bose and Fermi Gases ✍️Saikat Sur and Arnab Ghosh 🔗bit.ly/3tz0RiW 🕹 The paper shows that a quantum gas, a collection of massive, non-interacting, indistinguishable quantum particles, can be realized as a thermodynamic machine as an artifact of energy quantization and, hence, bears no classical analog. Such a thermodynamic machine depends on the statistics of the particles, the chemical potential, and the spatial dimension of the system. Our detailed analysis demonstrates the fundamental features of quantum Stirling cycles, from the viewpoint of particle statistics and system dimensions, that helps us to realize desired quantum heat engines and refrigerators by exploiting the role of quantum statistical mechanics. In particular, a clear distinction between the behavior of a Fermi gas and a Bose gas is observed in one dimension, rather than in higher dimensions, solely due to the innate differences in their particle statistics indicating the conspicuous role of a quantum thermodynamic signature in lower dimensions.

📹The Law of Entropy Increase and the Meissner Effect ✍️Alexey Nikulov 🔗bit.ly/41N6erL 🕹 The law of entropy increase postulates the existence of irreversible processes in physics: the total entropy of an isolated system can increase, but cannot decrease. The annihilation of an electric current in normal metal with the generation of Joule heat because of a non-zero resistance is a well-known example of an irreversible process. The persistent current, an undamped electric current observed in a superconductor, annihilates after the transition into the normal state. Therefore, this transition was considered as an irreversible thermodynamic process before 1933. The original paper was published with Entropy MDPI