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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, 799 KiB  
Article
The Influence of the Symmetry of Identical Particles on Flight Times
by Salvador Miret-Artés, Randall S. Dumont, Tom Rivlin and Eli Pollak
Entropy 2021, 23(12), 1675; https://doi.org/10.3390/e23121675 - 13 Dec 2021
Cited by 6 | Viewed by 2832
Abstract
In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ-barrier. For this goal, we [...] Read more.
In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ-barrier. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two sets of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a ‘screen’ is calculated in each case from the density and flux. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down the propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain, and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier and later than bosons when they are scattered by a δ-barrier. Although the particle symmetry does affect the mean tunneling flight time, in the limit of narrow in momentum initial Gaussian wave functions, the mean times are not affected by symmetry but tend to the phase time for distinguishable particles. Full article
(This article belongs to the Special Issue Quantum Mechanics and Its Foundations II)
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25 pages, 5936 KiB  
Article
Regularization, Bayesian Inference, and Machine Learning Methods for Inverse Problems
by Ali Mohammad-Djafari
Entropy 2021, 23(12), 1673; https://doi.org/10.3390/e23121673 - 13 Dec 2021
Cited by 25 | Viewed by 6295
Abstract
Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of [...] Read more.
Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of optimization algorithms have been proposed. When these two terms are distance or divergence measures, they can have a Bayesian Maximum A Posteriori (MAP) interpretation where these two terms correspond to the likelihood and prior-probability models, respectively. The Bayesian approach gives more flexibility in choosing these terms and, in particular, the prior term via hierarchical models and hidden variables. However, the Bayesian computations can become very heavy computationally. The machine learning (ML) methods such as classification, clustering, segmentation, and regression, based on neural networks (NN) and particularly convolutional NN, deep NN, physics-informed neural networks, etc. can become helpful to obtain approximate practical solutions to inverse problems. In this tutorial article, particular examples of image denoising, image restoration, and computed-tomography (CT) image reconstruction will illustrate this cooperation between ML and inversion. Full article
(This article belongs to the Special Issue MaxEnt 2020/2021—The 40th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering)
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11 pages, 2062 KiB  
Article
Stochastic Collisional Quantum Thermometry
by Eoin O’Connor, Bassano Vacchini and Steve Campbell
Entropy 2021, 23(12), 1634; https://doi.org/10.3390/e23121634 - 6 Dec 2021
Cited by 13 | Viewed by 3771
Abstract
We extend collisional quantum thermometry schemes to allow for stochasticity in the waiting time between successive collisions. We establish that introducing randomness through a suitable waiting time distribution, the Weibull distribution, allows us to significantly extend the parameter range for which an advantage [...] Read more.
We extend collisional quantum thermometry schemes to allow for stochasticity in the waiting time between successive collisions. We establish that introducing randomness through a suitable waiting time distribution, the Weibull distribution, allows us to significantly extend the parameter range for which an advantage over the thermal Fisher information is attained. These results are explicitly demonstrated for dephasing interactions and also hold for partial swap interactions. Furthermore, we show that the optimal measurements can be performed locally, thus implying that genuine quantum correlations do not play a role in achieving this advantage. We explicitly confirm this by examining the correlation properties for the deterministic collisional model. Full article
(This article belongs to the Special Issue Quantum Collision Models)
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12 pages, 3626 KiB  
Article
Generalizing Boltzmann Configurational Entropy to Surfaces, Point Patterns and Landscape Mosaics
by Samuel A. Cushman
Entropy 2021, 23(12), 1616; https://doi.org/10.3390/e23121616 - 1 Dec 2021
Cited by 10 | Viewed by 3138
Abstract
Several methods have been recently proposed to calculate configurational entropy, based on Boltzmann entropy. Some of these methods appear to be fully thermodynamically consistent in their application to landscape patch mosaics, but none have been shown to be fully generalizable to all kinds [...] Read more.
Several methods have been recently proposed to calculate configurational entropy, based on Boltzmann entropy. Some of these methods appear to be fully thermodynamically consistent in their application to landscape patch mosaics, but none have been shown to be fully generalizable to all kinds of landscape patterns, such as point patterns, surfaces, and patch mosaics. The goal of this paper is to evaluate if the direct application of the Boltzmann relation is fully generalizable to surfaces, point patterns, and landscape mosaics. I simulated surfaces and point patterns with a fractal neutral model to control their degree of aggregation. I used spatial permutation analysis to produce distributions of microstates and fit functions to predict the distributions of microstates and the shape of the entropy function. The results confirmed that the direct application of the Boltzmann relation is generalizable across surfaces, point patterns, and landscape mosaics, providing a useful general approach to calculating landscape entropy. Full article
(This article belongs to the Special Issue Entropy in Landscape Ecology II)
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36 pages, 1647 KiB  
Article
Real-World Data Difficulty Estimation with the Use of Entropy
by Przemysław Juszczuk, Jan Kozak, Grzegorz Dziczkowski, Szymon Głowania, Tomasz Jach and Barbara Probierz
Entropy 2021, 23(12), 1621; https://doi.org/10.3390/e23121621 - 1 Dec 2021
Cited by 16 | Viewed by 4950
Abstract
In the era of the Internet of Things and big data, we are faced with the management of a flood of information. The complexity and amount of data presented to the decision-maker are enormous, and existing methods often fail to derive nonredundant information [...] Read more.
In the era of the Internet of Things and big data, we are faced with the management of a flood of information. The complexity and amount of data presented to the decision-maker are enormous, and existing methods often fail to derive nonredundant information quickly. Thus, the selection of the most satisfactory set of solutions is often a struggle. This article investigates the possibilities of using the entropy measure as an indicator of data difficulty. To do so, we focus on real-world data covering various fields related to markets (the real estate market and financial markets), sports data, fake news data, and more. The problem is twofold: First, since we deal with unprocessed, inconsistent data, it is necessary to perform additional preprocessing. Therefore, the second step of our research is using the entropy-based measure to capture the nonredundant, noncorrelated core information from the data. Research is conducted using well-known algorithms from the classification domain to investigate the quality of solutions derived based on initial preprocessing and the information indicated by the entropy measure. Eventually, the best 25% (in the sense of entropy measure) attributes are selected to perform the whole classification procedure once again, and the results are compared. Full article
(This article belongs to the Special Issue Entropy in Real-World Datasets and Its Impact on Machine Learning)
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24 pages, 558 KiB  
Article
Quantum–Classical Correspondence Principle for Heat Distribution in Quantum Brownian Motion
by Jin-Fu Chen, Tian Qiu and Hai-Tao Quan
Entropy 2021, 23(12), 1602; https://doi.org/10.3390/e23121602 - 29 Nov 2021
Cited by 12 | Viewed by 2648
Abstract
Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of [...] Read more.
Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum–classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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26 pages, 6435 KiB  
Article
A Hybrid Multi-Criteria Decision-Making Approach Based on ANP-Entropy TOPSIS for Building Materials Supplier Selection
by Chun-Ho Chen
Entropy 2021, 23(12), 1597; https://doi.org/10.3390/e23121597 - 28 Nov 2021
Cited by 44 | Viewed by 6003
Abstract
This article will tell you how to combine “entropy” in the model to reduce the bias of multi-criteria evaluation. Subjective weights are usually determined by decision makers based on their professional background, experience and knowledge, and other factors. The objective weight is obtained [...] Read more.
This article will tell you how to combine “entropy” in the model to reduce the bias of multi-criteria evaluation. Subjective weights are usually determined by decision makers based on their professional background, experience and knowledge, and other factors. The objective weight is obtained by constructing an evaluation matrix of the information based on the actual information of the evaluation criteria of the scheme, and obtained through multi-step calculations. Different decision-making methods are based on different weight types. Considering only one of the two weights often leads to biased results. In addition, in order to establish an effective supply chain, buyers must find suitable merchants among suppliers that provide quality products and/or services. Based on the above factors, it is difficult to choose a suitable alternative. The main contribution of this paper is to combine analytic network process (ANP), entropy weight and the technique for order preference by similarity to an ideal solution (TOPSIS) to construct a suitable multi-criteria decision (MCDM) model. By means of ANP-entropy weights to extend the TOPSIS method, ANP-entropy weights are used to replace subjective weights. A supplier selection decision-making model based on ANP-entropy TOPSIS is proposed. At last, the sensitivity analysis shows that, taking the selection of building materials suppliers as an example, the hybrid ANP-entropy TOPSIS method can effectively select suitable suppliers. Full article
(This article belongs to the Special Issue Entropy Method for Decision Making)
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32 pages, 1035 KiB  
Review
Quantum Transport of Particles and Entropy
by Christoph Strunk
Entropy 2021, 23(12), 1573; https://doi.org/10.3390/e23121573 - 25 Nov 2021
Cited by 6 | Viewed by 3745
Abstract
A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric [...] Read more.
A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper, the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but elementary Fermi- or Bose-systems as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles but also of entropy can be derived in a concise way, and is illustrated both for ballistic quantum wires, and for diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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19 pages, 1081 KiB  
Article
Cooling Cycle Optimization for a Vuilleumier Refrigerator
by Raphael Paul, Abdellah Khodja, Andreas Fischer and Karl Heinz Hoffmann
Entropy 2021, 23(12), 1562; https://doi.org/10.3390/e23121562 - 24 Nov 2021
Cited by 7 | Viewed by 2028
Abstract
Vuilleumier refrigerators are a special type of heat-driven cooling machines. Essentially, they operate by using heat from a hot bath to pump heat from a cold bath to an environment at intermediate temperatures. In addition, some external energy in the form of electricity [...] Read more.
Vuilleumier refrigerators are a special type of heat-driven cooling machines. Essentially, they operate by using heat from a hot bath to pump heat from a cold bath to an environment at intermediate temperatures. In addition, some external energy in the form of electricity can be used as an auxiliary driving mechanism. Such refrigerators are, for example, advantageous in situations where waste heat is available and cooling power is needed. Here, the question of how the performance of Vuilleumier refrigerators can be improved is addressed with a particular focus on the piston motion and thus the thermodynamic cycle of the refrigerator. In order to obtain a quantitative estimate of the possible cooling power gain, a special class of piston movements (the AS motion class explained below) is used, which was already used successfully in the context of Stirling engines. We find improvements of the cooling power of more than 15%. Full article
(This article belongs to the Section Thermodynamics)
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23 pages, 379 KiB  
Article
On Epistemics in Expected Free Energy for Linear Gaussian State Space Models
by Magnus T. Koudahl, Wouter M. Kouw and Bert de Vries
Entropy 2021, 23(12), 1565; https://doi.org/10.3390/e23121565 - 24 Nov 2021
Cited by 7 | Viewed by 2851
Abstract
Active Inference (AIF) is a framework that can be used both to describe information processing in naturally intelligent systems, such as the human brain, and to design synthetic intelligent systems (agents). In this paper we show that Expected Free Energy (EFE) minimisation, a [...] Read more.
Active Inference (AIF) is a framework that can be used both to describe information processing in naturally intelligent systems, such as the human brain, and to design synthetic intelligent systems (agents). In this paper we show that Expected Free Energy (EFE) minimisation, a core feature of the framework, does not lead to purposeful explorative behaviour in linear Gaussian dynamical systems. We provide a simple proof that, due to the specific construction used for the EFE, the terms responsible for the exploratory (epistemic) drive become constant in the case of linear Gaussian systems. This renders AIF equivalent to KL control. From a theoretical point of view this is an interesting result since it is generally assumed that EFE minimisation will always introduce an exploratory drive in AIF agents. While the full EFE objective does not lead to exploration in linear Gaussian dynamical systems, the principles of its construction can still be used to design objectives that include an epistemic drive. We provide an in-depth analysis of the mechanics behind the epistemic drive of AIF agents and show how to design objectives for linear Gaussian dynamical systems that do include an epistemic drive. Concretely, we show that focusing solely on epistemics and dispensing with goal-directed terms leads to a form of maximum entropy exploration that is heavily dependent on the type of control signals driving the system. Additive controls do not permit such exploration. From a practical point of view this is an important result since linear Gaussian dynamical systems with additive controls are an extensively used model class, encompassing for instance Linear Quadratic Gaussian controllers. On the other hand, linear Gaussian dynamical systems driven by multiplicative controls such as switching transition matrices do permit an exploratory drive. Full article
(This article belongs to the Special Issue Emerging Methods in Active Inference)
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17 pages, 1446 KiB  
Article
A Quantum Blind Multi-Signature Method for the Industrial Blockchain
by Zhengying Cai, Shi Liu, Zhangyi Han, Rui Wang and Yuehua Huang
Entropy 2021, 23(11), 1520; https://doi.org/10.3390/e23111520 - 15 Nov 2021
Cited by 12 | Viewed by 3058
Abstract
Traditional anti-quantum methods and multi-signature technologies to secure the blockchain against quantum attacks will quickly reduce the efficiency and scalability of the industrial blockchain, where the computational resources will experience a polynomial rise with the increasing number of traders. Here, a quantum blind [...] Read more.
Traditional anti-quantum methods and multi-signature technologies to secure the blockchain against quantum attacks will quickly reduce the efficiency and scalability of the industrial blockchain, where the computational resources will experience a polynomial rise with the increasing number of traders. Here, a quantum blind multi-signature method is proposed for the multi-party transaction to provide anti-quantum security. First, the proposed multi-party transaction frame and quantum key distribution in the industrial blockchain are introduced. It integrates a novel quantum blind multi-signature algorithm that is based on the quantum entanglement mechanism, and it is absolutely secure in theory. Second, the anti-quantum multi-signature algorithm is illustrated, where there are four phases, i.e., initialization, signing, verification, and implementation. Third, the security and complexity of the proposed framework are analyzed and compared with related methods in references, and our proposed method is verified to be able to offer good computational performance and blockchain scalability for multi-party transaction. Last, the paper is summarized and future research directions are proposed. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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20 pages, 692 KiB  
Article
Thermality versus Objectivity: Can They Peacefully Coexist?
by Thao P. Le, Andreas Winter and Gerardo Adesso
Entropy 2021, 23(11), 1506; https://doi.org/10.3390/e23111506 - 13 Nov 2021
Cited by 9 | Viewed by 3049
Abstract
Under the influence of external environments, quantum systems can undergo various different processes, including decoherence and equilibration. We observe that macroscopic objects are both objective and thermal, thus leading to the expectation that both objectivity and thermalisation can peacefully coexist on the quantum [...] Read more.
Under the influence of external environments, quantum systems can undergo various different processes, including decoherence and equilibration. We observe that macroscopic objects are both objective and thermal, thus leading to the expectation that both objectivity and thermalisation can peacefully coexist on the quantum regime too. Crucially, however, objectivity relies on distributed classical information that could conflict with thermalisation. Here, we examine the overlap between thermal and objective states. We find that in general, one cannot exist when the other is present. However, there are certain regimes where thermality and objectivity are more likely to coexist: in the high temperature limit, at the non-degenerate low temperature limit, and when the environment is large. This is consistent with our experiences that everyday-sized objects can be both thermal and objective. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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13 pages, 1108 KiB  
Article
Environment-Assisted Shortcuts to Adiabaticity
by Akram Touil and Sebastian Deffner
Entropy 2021, 23(11), 1479; https://doi.org/10.3390/e23111479 - 9 Nov 2021
Cited by 7 | Viewed by 3138
Abstract
Envariance is a symmetry exhibited by correlated quantum systems. Inspired by this “quantum fact of life,” we propose a novel method for shortcuts to adiabaticity, which enables the system to evolve through the adiabatic manifold at all times, solely by controlling the environment. [...] Read more.
Envariance is a symmetry exhibited by correlated quantum systems. Inspired by this “quantum fact of life,” we propose a novel method for shortcuts to adiabaticity, which enables the system to evolve through the adiabatic manifold at all times, solely by controlling the environment. As the main results, we construct the unique form of the driving on the environment that enables such dynamics, for a family of composite states of arbitrary dimension. We compare the cost of this environment-assisted technique with that of counterdiabatic driving, and we illustrate our results for a two-qubit model. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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33 pages, 1495 KiB  
Article
Algorithmic Approaches for Assessing Irreversibility in Time Series: Review and Comparison
by Massimiliano Zanin and David Papo
Entropy 2021, 23(11), 1474; https://doi.org/10.3390/e23111474 - 8 Nov 2021
Cited by 26 | Viewed by 4298
Abstract
The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, [...] Read more.
The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, with alterations being connected to, for instance, pathologies in the human brain, heart and gait, or to inefficiencies in financial markets. Assessing irreversibility in time series is not an easy task, due to its many aetiologies and to the different ways it manifests in data. It is thus not surprising that several numerical methods have been proposed in the last decades, based on different principles and with different applications in mind. In this contribution we review the most important algorithmic solutions that have been proposed to test the irreversibility of time series, their underlying hypotheses, computational and practical limitations, and their comparative performance. We further provide an open-source software library that includes all tests here considered. As a final point, we show that “one size does not fit all”, as tests yield complementary, and sometimes conflicting views to the problem; and discuss some future research avenues. Full article
(This article belongs to the Special Issue Entropy and Irreversibility in Biological Systems)
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37 pages, 2536 KiB  
Article
Taming the Chaos in Neural Network Time Series Predictions
by Sebastian Raubitzek and Thomas Neubauer
Entropy 2021, 23(11), 1424; https://doi.org/10.3390/e23111424 - 28 Oct 2021
Cited by 8 | Viewed by 3373
Abstract
Machine learning methods, such as Long Short-Term Memory (LSTM) neural networks can predict real-life time series data. Here, we present a new approach to predict time series data combining interpolation techniques, randomly parameterized LSTM neural networks and measures of signal complexity, which we [...] Read more.
Machine learning methods, such as Long Short-Term Memory (LSTM) neural networks can predict real-life time series data. Here, we present a new approach to predict time series data combining interpolation techniques, randomly parameterized LSTM neural networks and measures of signal complexity, which we will refer to as complexity measures throughout this research. First, we interpolate the time series data under study. Next, we predict the time series data using an ensemble of randomly parameterized LSTM neural networks. Finally, we filter the ensemble prediction based on the original data complexity to improve the predictability, i.e., we keep only predictions with a complexity close to that of the training data. We test the proposed approach on five different univariate time series data. We use linear and fractal interpolation to increase the amount of data. We tested five different complexity measures for the ensemble filters for time series data, i.e., the Hurst exponent, Shannon’s entropy, Fisher’s information, SVD entropy, and the spectrum of Lyapunov exponents. Our results show that the interpolated predictions consistently outperformed the non-interpolated ones. The best ensemble predictions always beat a baseline prediction based on a neural network with only a single hidden LSTM, gated recurrent unit (GRU) or simple recurrent neural network (RNN) layer. The complexity filters can reduce the error of a random ensemble prediction by a factor of 10. Further, because we use randomly parameterized neural networks, no hyperparameter tuning is required. We prove this method useful for real-time time series prediction because the optimization of hyperparameters, which is usually very costly and time-intensive, can be circumvented with the presented approach. Full article
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13 pages, 1199 KiB  
Article
Engineering Classical Capacity of Generalized Pauli Channels with Admissible Memory Kernels
by Katarzyna Siudzińska, Arpan Das and Anindita Bera
Entropy 2021, 23(11), 1382; https://doi.org/10.3390/e23111382 - 21 Oct 2021
Cited by 5 | Viewed by 2045
Abstract
In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian [...] Read more.
In this paper, we analyze the classical capacity of the generalized Pauli channels generated via memory kernel master equations. For suitable engineering of the kernel parameters, evolution with non-local noise effects can produce dynamical maps with a higher capacity than a purely Markovian evolution. We provide instructive examples for qubit and qutrit evolution. Interestingly, similar behavior is not observed when analyzing time-local master equations. Full article
(This article belongs to the Special Issue Quantum Information Concepts in Open Quantum Systems)
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30 pages, 9881 KiB  
Review
Recent Advances in Loop Heat Pipes with Flat Evaporator
by Pawel Szymanski, Richard Law, Ryan J. MᶜGlen and David A. Reay
Entropy 2021, 23(11), 1374; https://doi.org/10.3390/e23111374 - 20 Oct 2021
Cited by 12 | Viewed by 5338
Abstract
The focus of this review is to present the current advances in Loop Heat Pipes (LHP) with flat evaporators, which address the current challenges to the wide implementation of the technology. A recent advance in LHP is the design of flat-shaped evaporators, which [...] Read more.
The focus of this review is to present the current advances in Loop Heat Pipes (LHP) with flat evaporators, which address the current challenges to the wide implementation of the technology. A recent advance in LHP is the design of flat-shaped evaporators, which is better suited to the geometry of discretely mounted electronics components (microprocessors) and therefore negate the need for an additional transfer surface (saddle) between component and evaporator. However, various challenges exist in the implementation of flat-evaporator, including (1) deformation of the evaporator due to high internal pressure and uneven stress distribution in the non-circular casing; (2) heat leak from evaporator heating zone and sidewall into the compensation chamber; (3) poor performance at start-up; (4) reverse flow through the wick; or (5) difficulties in sealing, and hence frequent leakage. This paper presents and reviews state-of-the-art LHP technologies; this includes an (a) review of novel manufacturing methods; (b) LHP evaporator designs; (c) working fluids; and (d) construction materials. The work presents solutions that are used to develop or improve the LHP construction, overall thermal performance, heat transfer distance, start-up time (especially at low heat loads), manufacturing cost, weight, possibilities of miniaturization and how they affect the solution on the above-presented problems and challenges in flat shape LHP development to take advantage in the passive cooling systems for electronic devices in multiple applications. Full article
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13 pages, 11972 KiB  
Article
Quantum Probes for the Characterization of Nonlinear Media
by Alessandro Candeloro, Sholeh Razavian, Matteo Piccolini, Berihu Teklu, Stefano Olivares and Matteo G. A. Paris
Entropy 2021, 23(10), 1353; https://doi.org/10.3390/e23101353 - 16 Oct 2021
Cited by 24 | Viewed by 2782
Abstract
Active optical media leading to interaction Hamiltonians of the form H=λ˜(a+a†)ζ represent a crucial resource for quantum optical technology. In this paper, we address the characterization of those nonlinear media using quantum probes, [...] Read more.
Active optical media leading to interaction Hamiltonians of the form H=λ˜(a+a†)ζ represent a crucial resource for quantum optical technology. In this paper, we address the characterization of those nonlinear media using quantum probes, as opposed to semiclassical ones. In particular, we investigate how squeezed probes may improve individual and joint estimation of the nonlinear coupling λ˜ and of the nonlinearity order ζ. Upon using tools from quantum estimation, we show that: (i) the two parameters are compatible, i.e., the may be jointly estimated without additional quantum noise; (ii) the use of squeezed probes improves precision at fixed overall energy of the probe; (iii) for low energy probes, squeezed vacuum represent the most convenient choice, whereas for increasing energy an optimal squeezing fraction may be determined; (iv) using optimized quantum probes, the scaling of the corresponding precision with energy improves, both for individual and joint estimation of the two parameters, compared to semiclassical coherent probes. We conclude that quantum probes represent a resource to enhance precision in the characterization of nonlinear media, and foresee potential applications with current technology. Full article
(This article belongs to the Special Issue Quantum Communication)
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36 pages, 7298 KiB  
Review
A Unified Treatment of Tribo-Components Degradation Using Thermodynamics Framework: A Review on Adhesive Wear
by Lijesh Koottaparambil and M. M. Khonsari
Entropy 2021, 23(10), 1329; https://doi.org/10.3390/e23101329 - 12 Oct 2021
Cited by 5 | Viewed by 3276
Abstract
An extensive survey of open literature reveals the need for a unifying approach for characterizing the degradation of tribo-pairs. This paper focuses on recent efforts made towards developing unified relationships for adhesive-type wear under unlubricated conditions through a thermodynamic framework. It is shown [...] Read more.
An extensive survey of open literature reveals the need for a unifying approach for characterizing the degradation of tribo-pairs. This paper focuses on recent efforts made towards developing unified relationships for adhesive-type wear under unlubricated conditions through a thermodynamic framework. It is shown that this framework can properly characterize many complex scenarios, such as degradation problems involving unidirectional, bidirectional (oscillatory and reciprocating motions), transient operating conditions (e.g., during the running-in period), and variable loading/speed sequencing. Full article
(This article belongs to the Section Entropy Reviews)
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11 pages, 279 KiB  
Article
The Law of the Iterated Logarithm for Linear Processes Generated by a Sequence of Stationary Independent Random Variables under the Sub-Linear Expectation
by Wei Liu and Yong Zhang
Entropy 2021, 23(10), 1313; https://doi.org/10.3390/e23101313 - 7 Oct 2021
Cited by 13 | Viewed by 2060
Abstract
In this paper, we obtain the law of iterated logarithm for linear processes in sub-linear expectation space. It is established for strictly stationary independent random variable sequences with finite second-order moments in the sense of non-additive capacity. Full article
21 pages, 1221 KiB  
Article
Causal Algebras on Chain Event Graphs with Informed Missingness for System Failure
by Xuewen Yu and Jim Q. Smith
Entropy 2021, 23(10), 1308; https://doi.org/10.3390/e23101308 - 6 Oct 2021
Cited by 7 | Viewed by 2392
Abstract
Graph-based causal inference has recently been successfully applied to explore system reliability and to predict failures in order to improve systems. One popular causal analysis following Pearl and Spirtes et al. to study causal relationships embedded in a system is to use a [...] Read more.
Graph-based causal inference has recently been successfully applied to explore system reliability and to predict failures in order to improve systems. One popular causal analysis following Pearl and Spirtes et al. to study causal relationships embedded in a system is to use a Bayesian network (BN). However, certain causal constructions that are particularly pertinent to the study of reliability are difficult to express fully through a BN. Our recent work demonstrated the flexibility of using a Chain Event Graph (CEG) instead to capture causal reasoning embedded within engineers’ reports. We demonstrated that an event tree rather than a BN could provide an alternative framework that could capture most of the causal concepts needed within this domain. In particular, a causal calculus for a specific type of intervention, called a remedial intervention, was devised on this tree-like graph. In this paper, we extend the use of this framework to show that not only remedial maintenance interventions but also interventions associated with routine maintenance can be well-defined using this alternative class of graphical model. We also show that the complexity in making inference about the potential relationships between causes and failures in a missing data situation in the domain of system reliability can be elegantly addressed using this new methodology. Causal modelling using a CEG is illustrated through examples drawn from the study of reliability of an energy distribution network. Full article
(This article belongs to the Special Issue Causal Inference for Heterogeneous Data and Information Theory)
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19 pages, 22390 KiB  
Article
Optimal Heat Exchanger Area Distribution and Low-Temperature Heat Sink Temperature for Power Optimization of an Endoreversible Space Carnot Cycle
by Tan Wang, Yanlin Ge, Lingen Chen, Huijun Feng and Jiuyang Yu
Entropy 2021, 23(10), 1285; https://doi.org/10.3390/e23101285 - 30 Sep 2021
Cited by 11 | Viewed by 1829
Abstract
Using finite-time thermodynamics, a model of an endoreversible Carnot cycle for a space power plant is established in this paper. The expressions of the cycle power output and thermal efficiency are derived. Using numerical calculations and taking the cycle power output as the [...] Read more.
Using finite-time thermodynamics, a model of an endoreversible Carnot cycle for a space power plant is established in this paper. The expressions of the cycle power output and thermal efficiency are derived. Using numerical calculations and taking the cycle power output as the optimization objective, the surface area distributions of three heat exchangers are optimized, and the maximum power output is obtained when the total heat transfer area of the three heat exchangers of the whole plant is fixed. Furthermore, the double-maximum power output is obtained by optimizing the temperature of a low-temperature heat sink. Finally, the influences of fixed plant parameters on the maximum power output performance are analyzed. The results show that there is an optimal temperature of the low-temperature heat sink and a couple of optimal area distributions that allow one to obtain the double-maximum power output. The results obtained have some guidelines for the design and optimization of actual space power plants. Full article
(This article belongs to the Section Thermodynamics)
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22 pages, 930 KiB  
Article
Impact of Thermal Fluctuations on Logarithmic Corrected Massive Gravity Charged Black Hole
by Abdul Jawad, Shahid Chaudhary and Kazuharu Bamba
Entropy 2021, 23(10), 1269; https://doi.org/10.3390/e23101269 - 28 Sep 2021
Cited by 6 | Viewed by 2094
Abstract
We investigate the influence of the first-order correction of entropy caused by thermal quantum fluctuations on the thermodynamics of a logarithmic corrected charged black hole in massive gravity. For this black hole, we explore the thermodynamic quantities, such as entropy, Helmholtz free energy, [...] Read more.
We investigate the influence of the first-order correction of entropy caused by thermal quantum fluctuations on the thermodynamics of a logarithmic corrected charged black hole in massive gravity. For this black hole, we explore the thermodynamic quantities, such as entropy, Helmholtz free energy, internal energy, enthalpy, Gibbs free energy and specific heat. We discuss the influence of the topology of the event horizon, dimensions and nonlinearity parameter on the local and global stability of the black hole. As a result, it is found that the holographic dual parameter vanishes. This means that the thermal corrections have no significant role to disturb the holographic duality of the logarithmic charged black hole in massive gravity, although the thermal corrections have a substantial impact on the thermodynamic quantities in the high-energy limit and the stability conditions of black holes. Full article
(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology III)
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33 pages, 4557 KiB  
Article
Stochastic Chaos and Markov Blankets
by Karl Friston, Conor Heins, Kai Ueltzhöffer, Lancelot Da Costa and Thomas Parr
Entropy 2021, 23(9), 1220; https://doi.org/10.3390/e23091220 - 17 Sep 2021
Cited by 75 | Viewed by 8963
Abstract
In this treatment of random dynamical systems, we consider the existence—and identification—of conditional independencies at nonequilibrium steady-state. These independencies underwrite a particular partition of states, in which internal states are statistically secluded from external states by blanket states. The existence of such partitions [...] Read more.
In this treatment of random dynamical systems, we consider the existence—and identification—of conditional independencies at nonequilibrium steady-state. These independencies underwrite a particular partition of states, in which internal states are statistically secluded from external states by blanket states. The existence of such partitions has interesting implications for the information geometry of internal states. In brief, this geometry can be read as a physics of sentience, where internal states look as if they are inferring external states. However, the existence of such partitions—and the functional form of the underlying densities—have yet to be established. Here, using the Lorenz system as the basis of stochastic chaos, we leverage the Helmholtz decomposition—and polynomial expansions—to parameterise the steady-state density in terms of surprisal or self-information. We then show how Markov blankets can be identified—using the accompanying Hessian—to characterise the coupling between internal and external states in terms of a generalised synchrony or synchronisation of chaos. We conclude by suggesting that this kind of synchronisation may provide a mathematical basis for an elemental form of (autonomous or active) sentience in biology. Full article
(This article belongs to the Special Issue Entropies, Information Geometry and Fluctuations in Non-equilibrium Systems)
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14 pages, 881 KiB  
Article
Wigner’s Friend Scenarios and the Internal Consistency of Standard Quantum Mechanics
by Dmitri Sokolovski and Alexandre Matzkin
Entropy 2021, 23(9), 1186; https://doi.org/10.3390/e23091186 - 9 Sep 2021
Cited by 4 | Viewed by 2673
Abstract
Wigner’s friend scenarios involve an Observer, or Observers, measuring a Friend, or Friends, who themselves make quantum measurements. In recent discussions, it has been suggested that quantum mechanics may not always be able to provide a consistent account of a situation involving two [...] Read more.
Wigner’s friend scenarios involve an Observer, or Observers, measuring a Friend, or Friends, who themselves make quantum measurements. In recent discussions, it has been suggested that quantum mechanics may not always be able to provide a consistent account of a situation involving two Observers and two Friends. We investigate this problem by invoking the basic rules of quantum mechanics as outlined by Feynman in the well-known “Feynman Lectures on Physics”. We show here that these “Feynman rules” constrain the a priori assumptions which can be made in generalised Wigner’s friend scenarios, because the existence of the probabilities of interest ultimately depends on the availability of physical evidence (material records) of the system’s past. With these constraints obeyed, a non-ambiguous and consistent account of all measurement outcomes is obtained for all agents, taking part in various Wigner’s Friend scenarios. Full article
(This article belongs to the Special Issue Quantum Mechanics and Its Foundations II)
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18 pages, 1105 KiB  
Article
Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws
by Mariana Krasnytska, Bertrand Berche, Yurij Holovatch and Ralph Kenna
Entropy 2021, 23(9), 1175; https://doi.org/10.3390/e23091175 - 7 Sep 2021
Cited by 11 | Viewed by 5258
Abstract
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ [...] Read more.
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new universality classes. Full article
(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)
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30 pages, 6086 KiB  
Review
Interfacial Area Transport Equation for Bubble Coalescence and Breakup: Developments and Comparisons
by Huiting Chen, Shiyu Wei, Weitian Ding, Han Wei, Liang Li, Henrik Saxén, Hongming Long and Yaowei Yu
Entropy 2021, 23(9), 1106; https://doi.org/10.3390/e23091106 - 25 Aug 2021
Cited by 13 | Viewed by 4968
Abstract
Bubble coalescence and breakup play important roles in physical-chemical processes and bubbles are treated in two groups in the interfacial area transport equation (IATE). This paper presents a review of IATE for bubble coalescence and breakup to model five bubble interaction mechanisms: bubble [...] Read more.
Bubble coalescence and breakup play important roles in physical-chemical processes and bubbles are treated in two groups in the interfacial area transport equation (IATE). This paper presents a review of IATE for bubble coalescence and breakup to model five bubble interaction mechanisms: bubble coalescence due to random collision, bubble coalescence due to wake entrainment, bubble breakup due to turbulent impact, bubble breakup due to shearing-off, and bubble breakup due to surface instability. In bubble coalescence, bubble size, velocity and collision frequency are dominant. In bubble breakup, the influence of viscous shear, shearing-off, and surface instability are neglected, and their corresponding theory and modelling are rare in the literature. Furthermore, combining turbulent kinetic energy and inertial force together is the best choice for the bubble breakup criterion. The reviewed one-group constitutive models include the one developed by Wu et al., Ishii and Kim, Hibiki and Ishii, Yao and Morel, and Nguyen et al. To extend the IATE prediction capability beyond bubbly flow, two-group IATE is needed and its performance is strongly dependent on the channel size and geometry. Therefore, constitutive models for two-group IATE in a three-type channel (i.e., narrow confined channel, round pipe and relatively larger pipe) are summarized. Although great progress in extending the IATE beyond churn-turbulent flow to churn-annual flow was made, there are still some issues in their modelling and experiments due to the highly distorted interface measurement. Regarded as the challenges to be addressed in the further study, some limitations of IATE general applicability and the directions for future development are highlighted. Full article
(This article belongs to the Special Issue Entropy in Particle Systems)
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13 pages, 314 KiB  
Article
Quantum and Classical Ergotropy from Relative Entropies
by Akira Sone and Sebastian Deffner
Entropy 2021, 23(9), 1107; https://doi.org/10.3390/e23091107 - 25 Aug 2021
Cited by 19 | Viewed by 4414
Abstract
The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect [...] Read more.
The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quantum as well as classical scenarios is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem. Full article
(This article belongs to the Special Issue Thermodynamics of Quantum Information)
21 pages, 361 KiB  
Article
Generalized Ordinal Patterns and the KS-Entropy
by Tim Gutjahr and Karsten Keller
Entropy 2021, 23(8), 1097; https://doi.org/10.3390/e23081097 - 23 Aug 2021
Cited by 3 | Viewed by 2957
Abstract
Ordinal patterns classifying real vectors according to the order relations between their components are an interesting basic concept for determining the complexity of a measure-preserving dynamical system. In particular, as shown by C. Bandt, G. Keller and B. Pompe, the permutation entropy based [...] Read more.
Ordinal patterns classifying real vectors according to the order relations between their components are an interesting basic concept for determining the complexity of a measure-preserving dynamical system. In particular, as shown by C. Bandt, G. Keller and B. Pompe, the permutation entropy based on the probability distributions of such patterns is equal to Kolmogorov–Sinai entropy in simple one-dimensional systems. The general reason for this is that, roughly speaking, the system of ordinal patterns obtained for a real-valued “measuring arrangement” has high potential for separating orbits. Starting from a slightly different approach of A. Antoniouk, K. Keller and S. Maksymenko, we discuss the generalizations of ordinal patterns providing enough separation to determine the Kolmogorov–Sinai entropy. For defining these generalized ordinal patterns, the idea is to substitute the basic binary relation ≤ on the real numbers by another binary relation. Generalizing the former results of I. Stolz and K. Keller, we establish conditions that the binary relation and the dynamical system have to fulfill so that the obtained generalized ordinal patterns can be used for estimating the Kolmogorov–Sinai entropy. Full article
(This article belongs to the Special Issue Entropy Measures for Data Analysis II: Theory, Algorithms and Applications)
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18 pages, 1675 KiB  
Article
Some Interesting Observations on the Free Energy Principle
by Karl J. Friston, Lancelot Da Costa and Thomas Parr
Entropy 2021, 23(8), 1076; https://doi.org/10.3390/e23081076 - 19 Aug 2021
Cited by 51 | Viewed by 7170
Abstract
Biehl et al. (2021) present some interesting observations on an early formulation of the free energy principle. We use these observations to scaffold a discussion of the technical arguments that underwrite the free energy principle. This discussion focuses on solenoidal coupling between various [...] Read more.
Biehl et al. (2021) present some interesting observations on an early formulation of the free energy principle. We use these observations to scaffold a discussion of the technical arguments that underwrite the free energy principle. This discussion focuses on solenoidal coupling between various (subsets of) states in sparsely coupled systems that possess a Markov blanket—and the distinction between exact and approximate Bayesian inference, implied by the ensuing Bayesian mechanics. Full article
(This article belongs to the Section Entropy and Biology)
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15 pages, 2177 KiB  
Article
Frequency Domain Repercussions of Instantaneous Granger Causality
by Luiz A. Baccalá and Koichi Sameshima
Entropy 2021, 23(8), 1037; https://doi.org/10.3390/e23081037 - 12 Aug 2021
Cited by 7 | Viewed by 2371
Abstract
Using directed transfer function (DTF) and partial directed coherence (PDC) in the information version, this paper extends the theoretical framework to incorporate the instantaneous Granger causality (iGC) frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow [...] Read more.
Using directed transfer function (DTF) and partial directed coherence (PDC) in the information version, this paper extends the theoretical framework to incorporate the instantaneous Granger causality (iGC) frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC’s repercussions associated with Granger connectivity, where interactions mediated without delay between time series can be easily detected. Full article
(This article belongs to the Special Issue Brain Connectivity and Information Theory)
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19 pages, 4151 KiB  
Article
Multifractal Behaviors of Stock Indices and Their Ability to Improve Forecasting in a Volatility Clustering Period
by Shuwen Zhang and Wen Fang
Entropy 2021, 23(8), 1018; https://doi.org/10.3390/e23081018 - 6 Aug 2021
Cited by 22 | Viewed by 3806
Abstract
The financial market is a complex system, which has become more complicated due to the sudden impact of the COVID-19 pandemic in 2020. As a result there may be much higher degree of uncertainty and volatility clustering in stock markets. How does this [...] Read more.
The financial market is a complex system, which has become more complicated due to the sudden impact of the COVID-19 pandemic in 2020. As a result there may be much higher degree of uncertainty and volatility clustering in stock markets. How does this “black swan” event affect the fractal behaviors of the stock market? How to improve the forecasting accuracy after that? Here we study the multifractal behaviors of 5-min time series of CSI300 and S&P500, which represents the two stock markets of China and United States. Using the Overlapped Sliding Window-based Multifractal Detrended Fluctuation Analysis (OSW-MF-DFA) method, we found that the two markets always have multifractal characteristics, and the degree of fractal intensified during the first panic period of pandemic. Based on the long and short-term memory which are described by fractal test results, we use the Gated Recurrent Unit (GRU) neural network model to forecast these indices. We found that during the large volatility clustering period, the prediction accuracy of the time series can be significantly improved by adding the time-varying Hurst index to the GRU neural network. Full article
(This article belongs to the Special Issue Fractal and Multifractal Analysis of Complex Networks)
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13 pages, 959 KiB  
Article
Quantum Darwinism in a Composite System: Objectivity versus Classicality
by Barış Çakmak, Özgür E. Müstecaplıoğlu, Mauro Paternostro, Bassano Vacchini and Steve Campbell
Entropy 2021, 23(8), 995; https://doi.org/10.3390/e23080995 - 31 Jul 2021
Cited by 20 | Viewed by 3664
Abstract
We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an N-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an [...] Read more.
We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an N-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an analytical expression for the dynamics is obtained. It demonstrates that part of the system Hilbert space redundantly proliferates its information to the environment, while the remaining subspace is decoupled and preserves clear non-classical signatures. For measurements performed on the system, we establish that a non-zero quantum discord is shared between the composite system and the environment, thus violating the conditions of strong Darwinism. However, due to the asymmetry of quantum discord, the information shared with the environment is completely classical for measurements performed on the environment. Our results imply a dichotomy between objectivity and classicality that emerges when considering composite systems. Full article
(This article belongs to the Special Issue Quantum Darwinism and Friends)
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44 pages, 449 KiB  
Article
General Non-Markovian Quantum Dynamics
by Vasily E. Tarasov
Entropy 2021, 23(8), 1006; https://doi.org/10.3390/e23081006 - 31 Jul 2021
Cited by 36 | Viewed by 3625
Abstract
A general approach to the construction of non-Markovian quantum theory is proposed. Non-Markovian equations for quantum observables and states are suggested by using general fractional calculus. In the proposed approach, the non-locality in time is represented by operator kernels of the Sonin type. [...] Read more.
A general approach to the construction of non-Markovian quantum theory is proposed. Non-Markovian equations for quantum observables and states are suggested by using general fractional calculus. In the proposed approach, the non-locality in time is represented by operator kernels of the Sonin type. A wide class of the exactly solvable models of non-Markovian quantum dynamics is suggested. These models describe open (non-Hamiltonian) quantum systems with general form of nonlocality in time. To describe these systems, the Lindblad equations for quantum observable and states are generalized by taking into account a general form of nonlocality. The non-Markovian quantum dynamics is described by using integro-differential equations with general fractional derivatives and integrals with respect to time. The exact solutions of these equations are derived by using the operational calculus that is proposed by Yu. Luchko for general fractional differential equations. Properties of bi-positivity, complete positivity, dissipativity, and generalized dissipativity in general non-Markovian quantum dynamics are discussed. Examples of a quantum oscillator and two-level quantum system with a general form of nonlocality in time are suggested. Full article
(This article belongs to the Special Issue Non-Hamiltonian Dynamics, Open Systems and Entropy)
22 pages, 1936 KiB  
Article
Feature Selection for Recommender Systems with Quantum Computing
by Riccardo Nembrini, Maurizio Ferrari Dacrema and Paolo Cremonesi
Entropy 2021, 23(8), 970; https://doi.org/10.3390/e23080970 - 28 Jul 2021
Cited by 40 | Viewed by 6711
Abstract
The promise of quantum computing to open new unexplored possibilities in several scientific fields has been long discussed, but until recently the lack of a functional quantum computer has confined this discussion mostly to theoretical algorithmic papers. It was only in the last [...] Read more.
The promise of quantum computing to open new unexplored possibilities in several scientific fields has been long discussed, but until recently the lack of a functional quantum computer has confined this discussion mostly to theoretical algorithmic papers. It was only in the last few years that small but functional quantum computers have become available to the broader research community. One paradigm in particular, quantum annealing, can be used to sample optimal solutions for a number of NP-hard optimization problems represented with classical operations research tools, providing an easy access to the potential of this emerging technology. One of the tasks that most naturally fits in this mathematical formulation is feature selection. In this paper, we investigate how to design a hybrid feature selection algorithm for recommender systems that leverages the domain knowledge and behavior hidden in the user interactions data. We represent the feature selection as an optimization problem and solve it on a real quantum computer, provided by D-Wave. The results indicate that the proposed approach is effective in selecting a limited set of important features and that quantum computers are becoming powerful enough to enter the wider realm of applied science. Full article
(This article belongs to the Special Issue Representation Learning: Theory, Applications and Ethical Issues)
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17 pages, 348 KiB  
Article
The Violation of Bell-CHSH Inequalities Leads to Different Conclusions Depending on the Description Used
by Aldo F. G. Solis-Labastida, Melina Gastelum and Jorge G. Hirsch
Entropy 2021, 23(7), 872; https://doi.org/10.3390/e23070872 - 8 Jul 2021
Cited by 2 | Viewed by 3314
Abstract
Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. However, the hypothesis from which Bell’s inequalities are derived differ according to the probability space used to write [...] Read more.
Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. However, the hypothesis from which Bell’s inequalities are derived differ according to the probability space used to write them. The violation of Bell’s inequalities can, alternatively, be explained by assuming that the hidden variables do not exist at all, that they exist but their values cannot be simultaneously assigned, that the values can be assigned but joint probabilities cannot be properly defined, or that averages taken in different contexts cannot be combined. All of the above are valid options, selected by different communities to provide support to their particular research program. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness III)
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10 pages, 4394 KiB  
Article
Spatial Entanglement of Fermions in One-Dimensional Quantum Dots
by Ivan P. Christov
Entropy 2021, 23(7), 868; https://doi.org/10.3390/e23070868 - 7 Jul 2021
Cited by 5 | Viewed by 2503
Abstract
The time-dependent quantum Monte Carlo method for fermions is introduced and applied in the calculation of the entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by this method allow one [...] Read more.
The time-dependent quantum Monte Carlo method for fermions is introduced and applied in the calculation of the entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by this method allow one to build reduced density matrices for each electron, and to quantify the spatial entanglement using measures such as quantum entropy by treating the electrons as identical or distinguishable particles. Our results indicate that the spatial entanglement in parallel-spin configurations is rather small, and is determined mostly by the spatial quantum nonlocality introduced by the ground state. By contrast, in the spin-compensated case, the outermost opposite-spin electrons interact like bosons, which prevails their entanglement, while the inner-shell electrons remain largely at their Hartree–Fock geometry. Our findings are in close correspondence with the numerically exact results, wherever such comparison is possible. Full article
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16 pages, 2343 KiB  
Article
Influences of Different Architectures on the Thermodynamic Performance and Network Structure of Aircraft Environmental Control System
by Han Yang, Chunxin Yang, Xingjuan Zhang and Xiugan Yuan
Entropy 2021, 23(7), 855; https://doi.org/10.3390/e23070855 - 3 Jul 2021
Cited by 13 | Viewed by 3750
Abstract
The environmental control system (ECS) is one of the most important systems in the aircraft used to regulate the pressure, temperature and humidity of the air in the cabin. This study investigates the influences of different architectures on the thermal performance and network [...] Read more.
The environmental control system (ECS) is one of the most important systems in the aircraft used to regulate the pressure, temperature and humidity of the air in the cabin. This study investigates the influences of different architectures on the thermal performance and network structure of ECS. The refrigeration and pressurization performances of ECS with four different architectures are analyzed and compared by the endoreversible thermodynamic analysis method, and their external and internal responses have also been discussed. The results show that the connection modes of the heat exchanger have minor effects on the performance of ECSs, but the influence of the air cycle machine is obvious. This study attempts to abstract the ECS as a network structure based on the graph theory, and use entropy in information theory for quantitative evaluation. The results provide a theoretical basis for the design of ECS and facilitate engineers to make reliable decisions. Full article
(This article belongs to the Collection Feature Papers in Information Theory)
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42 pages, 5704 KiB  
Article
Geometric Variational Inference
by Philipp Frank, Reimar Leike and Torsten A. Enßlin
Entropy 2021, 23(7), 853; https://doi.org/10.3390/e23070853 - 2 Jul 2021
Cited by 32 | Viewed by 5211
Abstract
Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) techniques. While MCMC methods that utilize [...] Read more.
Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) techniques. While MCMC methods that utilize the geometric properties of continuous probability distributions to increase their efficiency have been proposed, VI methods rarely use the geometry. This work aims to fill this gap and proposes geometric Variational Inference (geoVI), a method based on Riemannian geometry and the Fisher information metric. It is used to construct a coordinate transformation that relates the Riemannian manifold associated with the metric to Euclidean space. The distribution, expressed in the coordinate system induced by the transformation, takes a particularly simple form that allows for an accurate variational approximation by a normal distribution. Furthermore, the algorithmic structure allows for an efficient implementation of geoVI which is demonstrated on multiple examples, ranging from low-dimensional illustrative ones to non-linear, hierarchical Bayesian inverse problems in thousands of dimensions. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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21 pages, 608 KiB  
Article
List Decoding of Arıkan’s PAC Codes
by Hanwen Yao, Arman Fazeli and Alexander Vardy
Entropy 2021, 23(7), 841; https://doi.org/10.3390/e23070841 - 30 Jun 2021
Cited by 34 | Viewed by 4378
Abstract
Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short blocklengths under standard successive cancellation decoding is far from optimal. A well-known [...] Read more.
Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short blocklengths under standard successive cancellation decoding is far from optimal. A well-known way to improve the performance of polar codes at short blocklengths is CRC precoding followed by successive-cancellation list decoding. This approach, along with various refinements thereof, has largely remained the state of the art in polar coding since it was introduced in 2011. Recently, Arıkan presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. At short blocklengths, such codes offer a dramatic improvement in performance as compared to CRC-aided list decoding of conventional polar codes. PAC codes are based primarily upon the following main ideas: replacing CRC codes with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. One of our primary goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size L is moderately large (say, L⩾128). List decoding has distinct advantages over sequential decoding in certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, and use these estimates to approximate the union bound on their performance. These results indicate that PAC codes are superior to both polar codes and Reed–Muller codes. We also consider random time-varying convolutional precoding for PAC codes, and observe that this scheme achieves the same superior performance with constraint length as low as ν=2. Full article
(This article belongs to the Special Issue Short Packet Communications for 5G and Beyond)
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11 pages, 1339 KiB  
Article
On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures
by Donya Ohadi, David S. Corti and Mark J. Uline
Entropy 2021, 23(7), 846; https://doi.org/10.3390/e23070846 - 30 Jun 2021
Cited by 3 | Viewed by 2977
Abstract
Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state [...] Read more.
Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state. Full article
(This article belongs to the Special Issue Entropic Control of Soft Materials)
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20 pages, 3620 KiB  
Article
Ground-State Properties and Phase Separation of Binary Mixtures in Mesoscopic Ring Lattices
by Vittorio Penna, Alessandra Contestabile and Andrea Richaud
Entropy 2021, 23(7), 821; https://doi.org/10.3390/e23070821 - 28 Jun 2021
Cited by 1 | Viewed by 3139
Abstract
We investigated the spatial phase separation of the two components forming a bosonic mixture distributed in a four-well lattice with a ring geometry. We studied the ground state of this system, described by means of a binary Bose–Hubbard Hamiltonian, by implementing a well-known [...] Read more.
We investigated the spatial phase separation of the two components forming a bosonic mixture distributed in a four-well lattice with a ring geometry. We studied the ground state of this system, described by means of a binary Bose–Hubbard Hamiltonian, by implementing a well-known coherent-state picture which allowed us to find the semi-classical equations determining the distribution of boson components in the ring lattice. Their fully analytic solutions, in the limit of large boson numbers, provide the boson populations at each well as a function of the interspecies interaction and of other significant model parameters, while allowing to reconstruct the non-trivial architecture of the ground-state four-well phase diagram. The comparison with the L-well (L=2,3) phase diagrams highlights how increasing the number of wells considerably modifies the phase diagram structure and the transition mechanism from the full-mixing to the full-demixing phase controlled by the interspecies interaction. Despite the fact that the phase diagrams for L=2,3,4 share various general properties, we show that, unlike attractive binary mixtures, repulsive mixtures do not feature a transition mechanism which can be extended to an arbitrary lattice of size L. Full article
(This article belongs to the Special Issue The Ubiquity of Entropy II)
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22 pages, 2611 KiB  
Article
Data-Driven Analysis of Nonlinear Heterogeneous Reactions through Sparse Modeling and Bayesian Statistical Approaches
by Masaki Ito, Tatsu Kuwatani, Ryosuke Oyanagi and Toshiaki Omori
Entropy 2021, 23(7), 824; https://doi.org/10.3390/e23070824 - 28 Jun 2021
Cited by 4 | Viewed by 3733
Abstract
Heterogeneous reactions are chemical reactions that occur at the interfaces of multiple phases, and often show a nonlinear dynamical behavior due to the effect of the time-variant surface area with complex reaction mechanisms. It is important to specify the kinetics of heterogeneous reactions [...] Read more.
Heterogeneous reactions are chemical reactions that occur at the interfaces of multiple phases, and often show a nonlinear dynamical behavior due to the effect of the time-variant surface area with complex reaction mechanisms. It is important to specify the kinetics of heterogeneous reactions in order to elucidate the microscopic elementary processes and predict the macroscopic future evolution of the system. In this study, we propose a data-driven method based on a sparse modeling algorithm and sequential Monte Carlo algorithm for simultaneously extracting substantial reaction terms and surface models from a number of candidates by using partial observation data. We introduce a sparse modeling approach with non-uniform sparsity levels in order to accurately estimate rate constants, and the sequential Monte Carlo algorithm is employed to estimate time courses of multi-dimensional hidden variables. The results estimated using the proposed method show that the rate constants of dissolution and precipitation reactions that are typical examples of surface heterogeneous reactions, necessary surface models, and reaction terms underlying observable data were successfully estimated from only observable temporal changes in the concentration of the dissolved intermediate products. Full article
(This article belongs to the Special Issue Information Theory, Data Assimilation and Stochastics for Multiscale Nonlinear Systems)
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13 pages, 328 KiB  
Article
A Semi-Deterministic Random Walk with Resetting
by Javier Villarroel, Miquel Montero and Juan Antonio Vega
Entropy 2021, 23(7), 825; https://doi.org/10.3390/e23070825 - 28 Jun 2021
Cited by 6 | Viewed by 2917
Abstract
We consider a discrete-time random walk (xt) which, at random times, is reset to the starting position and performs a deterministic motion between them. We show that the quantity [...] Read more.
We consider a discrete-time random walk (xt) which, at random times, is reset to the starting position and performs a deterministic motion between them. We show that the quantity Prxt+1=n+1|xt=n,n→∞ determines if the system is averse, neutral or inclined towards resetting. It also classifies the stationary distribution. Double barrier probabilities, first passage times and the distribution of the escape time from intervals are determined. Full article
(This article belongs to the Special Issue New Trends in Random Walks)
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22 pages, 880 KiB  
Review
Three-Factor Kinetic Equation of Catalyst Deactivation
by Zoë Gromotka, Gregory Yablonsky, Nickolay Ostrovskii and Denis Constales
Entropy 2021, 23(7), 818; https://doi.org/10.3390/e23070818 - 27 Jun 2021
Cited by 10 | Viewed by 4065
Abstract
The three-factor kinetic equation of catalyst deactivation was obtained in terms of apparent kinetic parameters. The three factors correspond to the main cycle with a linear, detailed mechanism regarding the catalytic intermediates, a cycle of reversible deactivation, and a stage of irreversible deactivation [...] Read more.
The three-factor kinetic equation of catalyst deactivation was obtained in terms of apparent kinetic parameters. The three factors correspond to the main cycle with a linear, detailed mechanism regarding the catalytic intermediates, a cycle of reversible deactivation, and a stage of irreversible deactivation (aging), respectively. The rate of the main cycle is obtained for the fresh catalyst under a quasi-steady-state assumption. The phenomena of reversible and irreversible deactivation are presented as special separate factors (hierarchical separation). In this case, the reversible deactivation factor is a function of the kinetic apparent parameters of the reversible deactivation and of those of the main cycle. The irreversible deactivation factor is a function of the apparent kinetic parameters of the main cycle, of the reversible deactivation, and of the irreversible deactivation. The conditions of such separability are found. The obtained equation is applied successfully to describe the literature data on the reversible catalyst deactivation processes in the dehydration of acetaldehyde over TiO2 anatase and in crotonaldehyde hydrogenation on supported metal catalysts. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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8 pages, 10751 KiB  
Article
Josephson Currents and Gap Enhancement in Graph Arrays of Superconductive Islands
by Massimiliano Lucci, Davide Cassi, Vittorio Merlo, Roberto Russo, Gaetano Salina and Matteo Cirillo
Entropy 2021, 23(7), 811; https://doi.org/10.3390/e23070811 - 25 Jun 2021
Cited by 5 | Viewed by 2284
Abstract
Evidence is reported that topological effects in graph-shaped arrays of superconducting islands can condition superconducting energy gap and transition temperature. The carriers giving rise to the new phase are couples of electrons (Cooper pairs) which, in the superconducting state, behave as predicted for [...] Read more.
Evidence is reported that topological effects in graph-shaped arrays of superconducting islands can condition superconducting energy gap and transition temperature. The carriers giving rise to the new phase are couples of electrons (Cooper pairs) which, in the superconducting state, behave as predicted for bosons in our structures. The presented results have been obtained both on star and double comb-shaped arrays and the coupling between the islands is provided by Josephson junctions whose potential can be tuned by external magnetic field or temperature. Our peculiar technique for probing distribution on the islands is such that the hopping of bosons between the different islands occurs because their thermal energy is of the same order of the Josephson coupling energy between the islands. Both for star and double comb graph topologies the results are in qualitative and quantitative agreement with theoretical predictions. Full article
(This article belongs to the Special Issue Thermodynamics and Superconducting Devices)
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24 pages, 4538 KiB  
Article
The Carnot Cycle, Reversibility and Entropy
by David Sands
Entropy 2021, 23(7), 810; https://doi.org/10.3390/e23070810 - 25 Jun 2021
Cited by 3 | Viewed by 5065
Abstract
The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current [...] Read more.
The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current at the time, that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be performed in a reversible process rather than the work that is actually performed in an irreversible process. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, reversibility and irreversibility are investigated by means of a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can be traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appropriately, the gas can be made to trace out a Carnot cycle in P-V space. The cycle is dynamic as opposed to quasi-static as the piston has kinetic energy equal in difference to the work performed internally and externally. Full article
(This article belongs to the Special Issue The Foundations of Thermodynamics)
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13 pages, 3297 KiB  
Article
Hybrid Nanofluids Flows Determined by a Permeable Power-Law Stretching/Shrinking Sheet Modulated by Orthogonal Surface Shear
by Natalia C. Roşca and Ioan Pop
Entropy 2021, 23(7), 813; https://doi.org/10.3390/e23070813 - 25 Jun 2021
Cited by 15 | Viewed by 2084
Abstract
The present paper studies the flow and heat transfer of the hybrid nanofluids flows induced by a permeable power-law stretching/shrinking surface modulated orthogonal surface shear. The governing partial differential equations were converted into non-linear ordinary differential equations by using proper similarity transformations. These [...] Read more.
The present paper studies the flow and heat transfer of the hybrid nanofluids flows induced by a permeable power-law stretching/shrinking surface modulated orthogonal surface shear. The governing partial differential equations were converted into non-linear ordinary differential equations by using proper similarity transformations. These equations were then solved applying a numerical technique, namely bvp4c solver in MATLAB. Results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that increasing mass flux parameter slows down the velocity and, hence, decreases the temperature. Furthermore, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases. We apply similarity transformation in order to transform the governing model into a system of ODEs (ordinary differential equations). Numerical solutions for particular values of involved parameters are in very good agreement with previous calculations. The most important and interesting result of this paper is that for both the cases of shrinking and stretching sheet flows exhibit dual solutions in some intervals of the shrinking and stretching parameter. In spite of numerous published papers on the flow and heat transfer over a permeable stretching/shrinking surface in nanofluids and hybrid nanofluids, none of the researchers studied the present problem. Therefore, we believe that the results of the present paper are new, and have many industrial applications. Full article
(This article belongs to the Special Issue Entropy Analysis in Nanofluids and Porous Media)
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18 pages, 1363 KiB  
Article
Accuracy-Risk Trade-Off Due to Social Learning in Crowd-Sourced Financial Predictions
by Dhaval Adjodah, Yan Leng, Shi Kai Chong, P. M. Krafft, Esteban Moro and Alex Pentland
Entropy 2021, 23(7), 801; https://doi.org/10.3390/e23070801 - 24 Jun 2021
Cited by 3 | Viewed by 6200
Abstract
A critical question relevant to the increasing importance of crowd-sourced-based finance is how to optimize collective information processing and decision-making. Here, we investigate an often under-studied aspect of the performance of online traders: beyond focusing on just accuracy, what gives rise to the [...] Read more.
A critical question relevant to the increasing importance of crowd-sourced-based finance is how to optimize collective information processing and decision-making. Here, we investigate an often under-studied aspect of the performance of online traders: beyond focusing on just accuracy, what gives rise to the trade-off between risk and accuracy at the collective level? Answers to this question will lead to designing and deploying more effective crowd-sourced financial platforms and to minimizing issues stemming from risk such as implied volatility. To investigate this trade-off, we conducted a large online Wisdom of the Crowd study where 2037 participants predicted the prices of real financial assets (S&P 500, WTI Oil and Gold prices). Using the data collected, we modeled the belief update process of participants using models inspired by Bayesian models of cognition. We show that subsets of predictions chosen based on their belief update strategies lie on a Pareto frontier between accuracy and risk, mediated by social learning. We also observe that social learning led to superior accuracy during one of our rounds that occurred during the high market uncertainty of the Brexit vote. Full article
(This article belongs to the Special Issue Swarms and Network Intelligence)
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19 pages, 2973 KiB  
Article
Psychomotor Predictive Processing
by Stephen Fox
Entropy 2021, 23(7), 806; https://doi.org/10.3390/e23070806 - 24 Jun 2021
Cited by 5 | Viewed by 5159
Abstract
Psychomotor experience can be based on what people predict they will experience, rather than on sensory inputs. It has been argued that disconnects between human experience and sensory inputs can be addressed better through further development of predictive processing theory. In this paper, [...] Read more.
Psychomotor experience can be based on what people predict they will experience, rather than on sensory inputs. It has been argued that disconnects between human experience and sensory inputs can be addressed better through further development of predictive processing theory. In this paper, the scope of predictive processing theory is extended through three developments. First, by going beyond previous studies that have encompassed embodied cognition but have not addressed some fundamental aspects of psychomotor functioning. Second, by proposing a scientific basis for explaining predictive processing that spans objective neuroscience and subjective experience. Third, by providing an explanation of predictive processing that can be incorporated into the planning and operation of systems involving robots and other new technologies. This is necessary because such systems are becoming increasingly common and move us farther away from the hunter-gatherer lifestyles within which our psychomotor functioning evolved. For example, beliefs that workplace robots are threatening can generate anxiety, while wearing hardware, such as augmented reality headsets and exoskeletons, can impede the natural functioning of psychomotor systems. The primary contribution of the paper is the introduction of a new formulation of hierarchical predictive processing that is focused on psychomotor functioning. Full article
(This article belongs to the Section Entropy and Biology)
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