Special Issue "Review Papers for Entropy"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Entropy Reviews".

Deadline for manuscript submissions: closed (15 April 2022) | Viewed by 40030

Special Issue Editor

Prof. Dr. Miguel Rubi
E-Mail Website
Guest Editor
University of Barcelona, Department of Condensed Matter Physics, Diagonal 647, 08028 Barcelona, Spain
Interests: non-equilibrium thermodynamics; non-equilibrium statistical physics; thermodynamics of small systems; heat exchange at the nanoscale; Casimir forces; diffusion in confined systems; small biological systems; non-equilibrium self-assembly
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Special Issue Information

Dear Colleague,

The main objective of this section is to publish review articles on topics of great current interest in which the concept of entropy plays a central role, and thus create a space where readers can find their most innovative ideas and applications. The concept of entropy developed in thermodynamics, statistics mechanics, and information theory has made a great impact on disciplines such as physics and physico-chemistry, engineering, biology, complex systems, and computer sciences in recent years. We are interested in receiving manuscripts that review theoretical, experimental, and computational studies on the topics included in such research areas.

Prof. Dr. Miguel Rubi
Guest Editor

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Published Papers (22 papers)

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Review

Review
Kinetic Theory of Polydisperse Granular Mixtures: Influence of the Partial Temperatures on Transport Properties—A Review
Entropy 2022, 24(6), 826; https://doi.org/10.3390/e24060826 - 14 Jun 2022
Viewed by 351
Abstract
It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently [...] Read more.
It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently adapted to account for inelastic collisions. A surprising result (compared to its molecular gas counterpart) for granular mixtures is the failure of the energy equipartition, even in homogeneous states. This means that the partial temperatures Ti (measuring the mean kinetic energy of each species) are different to the (total) granular temperature T. The goal of this paper is to provide an overview on the effect of different partial temperatures on the transport properties of the mixture. Our analysis addresses first the impact of energy nonequipartition on transport which is only due to the inelastic character of collisions. This effect (which is absent for elastic collisions) is shown to be significant in important problems in granular mixtures such as thermal diffusion segregation. Then, an independent source of energy nonequipartition due to the existence of a divergence of the flow velocity is studied. This effect (which was already analyzed in several pioneering works on dense hard-sphere molecular mixtures) affects to the bulk viscosity coefficient. Analytical (approximate) results are compared against Monte Carlo and molecular dynamics simulations, showing the reliability of kinetic theory for describing granular flows. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
Metastability of Synchronous and Asynchronous Dynamics
Entropy 2022, 24(4), 450; https://doi.org/10.3390/e24040450 - 24 Mar 2022
Viewed by 513
Abstract
Metastability is a ubiquitous phenomenon in nature, which interests several fields of natural sciences. Since metastability is a genuine non-equilibrium phenomenon, its description in the framework of thermodynamics and statistical mechanics has progressed slowly for a long time. Since the publication of the [...] Read more.
Metastability is a ubiquitous phenomenon in nature, which interests several fields of natural sciences. Since metastability is a genuine non-equilibrium phenomenon, its description in the framework of thermodynamics and statistical mechanics has progressed slowly for a long time. Since the publication of the first seminal paper in which the metastable behavior of the mean field Curie–Weiss model was approached by means of stochastic techniques, this topic has been largely studied by the scientific community. Several papers and books have been published in which many different spin models were studied and different approaches were developed. In this review, we focus on the comparison between the metastable behavior of synchronous and asynchronous dynamics, namely, stochastic processes in discrete time in which, at each time, either all the spins or one single spin is updated. In particular, we discuss how two different stochastic implementations of the very same Hamiltonian give rise to different metastable behaviors. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
A Short Review on Minimum Description Length: An Application to Dimension Reduction in PCA
Entropy 2022, 24(2), 269; https://doi.org/10.3390/e24020269 - 13 Feb 2022
Cited by 1 | Viewed by 666
Abstract
The minimun description length (MDL) is a powerful criterion for model selection that is gaining increasing interest from both theorists and practicioners. It allows for automatic selection of the best model for representing data without having a priori information about them. It simply [...] Read more.
The minimun description length (MDL) is a powerful criterion for model selection that is gaining increasing interest from both theorists and practicioners. It allows for automatic selection of the best model for representing data without having a priori information about them. It simply uses both data and model complexity, selecting the model that provides the least coding length among a predefined set of models. In this paper, we briefly review the basic ideas underlying the MDL criterion and its applications in different fields, with particular reference to the dimension reduction problem. As an example, the role of MDL in the selection of the best principal components in the well known PCA is investigated. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
λ-Deformation: A Canonical Framework for Statistical Manifolds of Constant Curvature
Entropy 2022, 24(2), 193; https://doi.org/10.3390/e24020193 - 27 Jan 2022
Viewed by 653
Abstract
This paper systematically presents the λ-deformation as the canonical framework of deformation to the dually flat (Hessian) geometry, which has been well established in information geometry. We show that, based on deforming the Legendre duality, all objects in the Hessian case have [...] Read more.
This paper systematically presents the λ-deformation as the canonical framework of deformation to the dually flat (Hessian) geometry, which has been well established in information geometry. We show that, based on deforming the Legendre duality, all objects in the Hessian case have their correspondence in the λ-deformed case: λ-convexity, λ-conjugation, λ-biorthogonality, λ-logarithmic divergence, λ-exponential and λ-mixture families, etc. In particular, λ-deformation unifies Tsallis and Rényi deformations by relating them to two manifestations of an identical λ-exponential family, under subtractive or divisive probability normalization, respectively. Unlike the different Hessian geometries of the exponential and mixture families, the λ-exponential family, in turn, coincides with the λ-mixture family after a change of random variables. The resulting statistical manifolds, while still carrying a dualistic structure, replace the Hessian metric and a pair of dually flat conjugate affine connections with a conformal Hessian metric and a pair of projectively flat connections carrying constant (nonzero) curvature. Thus, λ-deformation is a canonical framework in generalizing the well-known dually flat Hessian structure of information geometry. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
A Review of Bayesian Hypothesis Testing and Its Practical Implementations
Entropy 2022, 24(2), 161; https://doi.org/10.3390/e24020161 - 21 Jan 2022
Viewed by 844
Abstract
We discuss hypothesis testing and compare different theories in light of observed or experimental data as fundamental endeavors in the sciences. Issues associated with the p-value approach and null hypothesis significance testing are reviewed, and the Bayesian alternative based on the Bayes [...] Read more.
We discuss hypothesis testing and compare different theories in light of observed or experimental data as fundamental endeavors in the sciences. Issues associated with the p-value approach and null hypothesis significance testing are reviewed, and the Bayesian alternative based on the Bayes factor is introduced, along with a review of computational methods and sensitivity related to prior distributions. We demonstrate how Bayesian testing can be practically implemented in several examples, such as the t-test, two-sample comparisons, linear mixed models, and Poisson mixed models by using existing software. Caveats and potential problems associated with Bayesian testing are also discussed. We aim to inform researchers in the many fields where Bayesian testing is not in common use of a well-developed alternative to null hypothesis significance testing and to demonstrate its standard implementation. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
Review
Design and Test of an Integrated Random Number Generator with All-Digital Entropy Source
Entropy 2022, 24(2), 139; https://doi.org/10.3390/e24020139 - 18 Jan 2022
Cited by 1 | Viewed by 572
Abstract
In the cybersecurity field, the generation of random numbers is extremely important because they are employed in different applications such as the generation/derivation of cryptographic keys, nonces, and initialization vectors. The more unpredictable the random sequence, the higher its quality and the lower [...] Read more.
In the cybersecurity field, the generation of random numbers is extremely important because they are employed in different applications such as the generation/derivation of cryptographic keys, nonces, and initialization vectors. The more unpredictable the random sequence, the higher its quality and the lower the probability of recovering the value of those random numbers for an adversary. Cryptographically Secure Pseudo-Random Number Generators (CSPRNGs) are random number generators (RNGs) with specific properties and whose output sequence has such a degree of randomness that it cannot be distinguished from an ideal random sequence. In this work, we designed an all-digital RNG, which includes a Deterministic Random Bit Generator (DRBG) that meets the security requirements for cryptographic applications as CSPRNG, plus an entropy source that showed high portability and a high level of entropy. The proposed design has been intensively tested against both NIST and BSI suites to assess its entropy and randomness, and it is ready to be integrated into the European Processor Initiative (EPI) chip. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
Combining Measures of Signal Complexity and Machine Learning for Time Series Analyis: A Review
Entropy 2021, 23(12), 1672; https://doi.org/10.3390/e23121672 - 13 Dec 2021
Cited by 1 | Viewed by 888
Abstract
Measures of signal complexity, such as the Hurst exponent, the fractal dimension, and the Spectrum of Lyapunov exponents, are used in time series analysis to give estimates on persistency, anti-persistency, fluctuations and predictability of the data under study. They have [...] Read more.
Measures of signal complexity, such as the Hurst exponent, the fractal dimension, and the Spectrum of Lyapunov exponents, are used in time series analysis to give estimates on persistency, anti-persistency, fluctuations and predictability of the data under study. They have proven beneficial when doing time series prediction using machine and deep learning and tell what features may be relevant for predicting time-series and establishing complexity features. Further, the performance of machine learning approaches can be improved, taking into account the complexity of the data under study, e.g., adapting the employed algorithm to the inherent long-term memory of the data. In this article, we provide a review of complexity and entropy measures in combination with machine learning approaches. We give a comprehensive review of relevant publications, suggesting the use of fractal or complexity-measure concepts to improve existing machine or deep learning approaches. Additionally, we evaluate applications of these concepts and examine if they can be helpful in predicting and analyzing time series using machine and deep learning. Finally, we give a list of a total of six ways to combine machine learning and measures of signal complexity as found in the literature. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
Review
A Multi-Method Survey on the Use of Sentiment Analysis in Multivariate Financial Time Series Forecasting
Entropy 2021, 23(12), 1603; https://doi.org/10.3390/e23121603 - 29 Nov 2021
Cited by 1 | Viewed by 736
Abstract
In practice, time series forecasting involves the creation of models that generalize data from past values and produce future predictions. Moreover, regarding financial time series forecasting, it can be assumed that the procedure involves phenomena partly shaped by the social environment. Thus, the [...] Read more.
In practice, time series forecasting involves the creation of models that generalize data from past values and produce future predictions. Moreover, regarding financial time series forecasting, it can be assumed that the procedure involves phenomena partly shaped by the social environment. Thus, the present work is concerned with the study of the use of sentiment analysis methods in data extracted from social networks and their utilization in multivariate prediction architectures that involve financial data. Through an extensive experimental process, 22 different input setups using such extracted information were tested, over a total of 16 different datasets, under the schemes of 27 different algorithms. The comparisons were structured under two case studies. The first concerns possible improvements in the performance of the forecasts in light of the use of sentiment analysis systems in time series forecasting. The second, having as a framework all the possible versions of the above configuration, concerns the selection of the methods that perform best. The results, as presented by various illustrations, indicate, on the one hand, the conditional improvement of predictability after the use of specific sentiment setups in long-term forecasts and, on the other, a universal predominance of long short-term memory architectures. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
A Review of the System-Intrinsic Nonequilibrium Thermodynamics in Extended Space (MNEQT) with Applications
Entropy 2021, 23(12), 1584; https://doi.org/10.3390/e23121584 - 26 Nov 2021
Cited by 1 | Viewed by 601
Abstract
The review deals with a novel approach (MNEQT) to nonequilibrium thermodynamics (NEQT) that is based on the concept of internal equilibrium (IEQ) in an enlarged state space SZ involving internal variables as additional state variables. The IEQ macrostates are unique in [...] Read more.
The review deals with a novel approach (MNEQT) to nonequilibrium thermodynamics (NEQT) that is based on the concept of internal equilibrium (IEQ) in an enlarged state space SZ involving internal variables as additional state variables. The IEQ macrostates are unique in SZ and have no memory just as EQ macrostates are in the EQ state space SXSZ. The approach provides a clear strategy to identify the internal variables for any model through several examples. The MNEQT deals directly with system-intrinsic quantities, which are very useful as they fully describe irreversibility. Because of this, MNEQT solves a long-standing problem in NEQT of identifying a unique global temperature T of a system, thus fulfilling Planck’s dream of a global temperature for any system, even if it is not uniform such as when it is driven between two heat baths; T has the conventional interpretation of satisfying the Clausius statement that the exchange macroheatdeQflows from hot to cold, and other sensible criteria expected of a temperature. The concept of the generalized macroheat dQ=deQ+diQ converts the Clausius inequality dSdeQ/T0 for a system in a medium at temperature T0 into the Clausius equalitydSdQ/T, which also covers macrostates with memory, and follows from the extensivity property. The equality also holds for a NEQ isolated system. The novel approach is extremely useful as it also works when no internal state variables are used to study nonunique macrostates in the EQ state space SX at the expense of explicit time dependence in the entropy that gives rise to memory effects. To show the usefulness of the novel approach, we give several examples such as irreversible Carnot cycle, friction and Brownian motion, the free expansion, etc. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems
Entropy 2021, 23(11), 1393; https://doi.org/10.3390/e23111393 - 24 Oct 2021
Cited by 2 | Viewed by 636
Abstract
Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance [...] Read more.
Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance by quantifying how information unfolds over time as a probability density function (PDF) evolves in time. Here, we discuss some recent developments in information geometric theory focusing on time-dependent dynamic aspects of non-equilibrium processes (e.g., time-varying mean value, time-varying variance, or temperature, etc.) and their thermodynamic and physical/biological implications. We compare different distances between two given PDFs and highlight the importance of a path-dependent distance for a time-dependent PDF. We then discuss the role of the information rate Γ=dLdt and relative entropy in non-equilibrium thermodynamic relations (entropy production rate, heat flux, dissipated work, non-equilibrium free energy, etc.), and various inequalities among them. Here, L is the information length representing the total number of statistically distinguishable states a PDF evolves through over time. We explore the implications of a geodesic solution in information geometry for self-organization and control. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
Information Entropy in Chemistry: An Overview
Entropy 2021, 23(10), 1240; https://doi.org/10.3390/e23101240 - 23 Sep 2021
Cited by 4 | Viewed by 1330
Abstract
Basic applications of the information entropy concept to chemical objects are reviewed. These applications deal with quantifying chemical and electronic structures of molecules, signal processing, structural studies on crystals, and molecular ensembles. Recent advances in the mentioned areas make information entropy a central [...] Read more.
Basic applications of the information entropy concept to chemical objects are reviewed. These applications deal with quantifying chemical and electronic structures of molecules, signal processing, structural studies on crystals, and molecular ensembles. Recent advances in the mentioned areas make information entropy a central concept in interdisciplinary studies on digitalizing chemical reactions, chemico-information synthesis, crystal engineering, as well as digitally rethinking basic notions of structural chemistry in terms of informatics. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
Three-Factor Kinetic Equation of Catalyst Deactivation
Entropy 2021, 23(7), 818; https://doi.org/10.3390/e23070818 - 27 Jun 2021
Viewed by 768
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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Review
The Entropy Universe
Entropy 2021, 23(2), 222; https://doi.org/10.3390/e23020222 - 11 Feb 2021
Cited by 14 | Viewed by 2631
Abstract
About 160 years ago, the concept of entropy was introduced in thermodynamics by Rudolf Clausius. Since then, it has been continually extended, interpreted, and applied by researchers in many scientific fields, such as general physics, information theory, chaos theory, data mining, and mathematical [...] Read more.
About 160 years ago, the concept of entropy was introduced in thermodynamics by Rudolf Clausius. Since then, it has been continually extended, interpreted, and applied by researchers in many scientific fields, such as general physics, information theory, chaos theory, data mining, and mathematical linguistics. This paper presents The Entropy Universe, which aims to review the many variants of entropies applied to time-series. The purpose is to answer research questions such as: How did each entropy emerge? What is the mathematical definition of each variant of entropy? How are entropies related to each other? What are the most applied scientific fields for each entropy? We describe in-depth the relationship between the most applied entropies in time-series for different scientific fields, establishing bases for researchers to properly choose the variant of entropy most suitable for their data. The number of citations over the past sixteen years of each paper proposing a new entropy was also accessed. The Shannon/differential, the Tsallis, the sample, the permutation, and the approximate entropies were the most cited ones. Based on the ten research areas with the most significant number of records obtained in the Web of Science and Scopus, the areas in which the entropies are more applied are computer science, physics, mathematics, and engineering. The universe of entropies is growing each day, either due to the introducing new variants either due to novel applications. Knowing each entropy’s strengths and of limitations is essential to ensure the proper improvement of this research field. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
An Optimality Summary: Secret Key Agreement with Physical Unclonable Functions
Entropy 2021, 23(1), 16; https://doi.org/10.3390/e23010016 - 24 Dec 2020
Cited by 4 | Viewed by 1135
Abstract
We address security and privacy problems for digital devices and biometrics from an information-theoretic optimality perspective to conduct authentication, message encryption/decryption, identification or secure and private computations by using a secret key. A physical unclonable function (PUF) provides local security to digital devices [...] Read more.
We address security and privacy problems for digital devices and biometrics from an information-theoretic optimality perspective to conduct authentication, message encryption/decryption, identification or secure and private computations by using a secret key. A physical unclonable function (PUF) provides local security to digital devices and this review gives the most relevant summary for information theorists, coding theorists, and signal processing community members who are interested in optimal PUF constructions. Low-complexity signal processing methods are applied to simplify information-theoretic analyses. The best trade-offs between the privacy-leakage, secret-key, and storage rates are discussed. Proposed optimal constructions that jointly design the vector quantizer and error-correction code parameters are listed. These constructions include modern and algebraic codes such as polar codes and convolutional codes, both of which can achieve small block-error probabilities at short block lengths, corresponding to a small number of PUF circuits. Open problems in the PUF literature from signal processing, information theory, coding theory, and hardware complexity perspectives and their combinations are listed to stimulate further advancements in the research on local privacy and security. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
A Survey of Information Entropy Metrics for Complex Networks
Entropy 2020, 22(12), 1417; https://doi.org/10.3390/e22121417 - 15 Dec 2020
Cited by 8 | Viewed by 1395
Abstract
Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it difficult to identify available metrics and understand the context in which they [...] Read more.
Information entropy metrics have been applied to a wide range of problems that were abstracted as complex networks. This growing body of research is scattered in multiple disciplines, which makes it difficult to identify available metrics and understand the context in which they are applicable. In this work, a narrative literature review of information entropy metrics for complex networks is conducted following the PRISMA guidelines. Existing entropy metrics are classified according to three different criteria: whether the metric provides a property of the graph or a graph component (such as the nodes), the chosen probability distribution, and the types of complex networks to which the metrics are applicable. Consequently, this work identifies the areas in need for further development aiming to guide future research efforts. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
A Review of Fractional Order Entropies
Entropy 2020, 22(12), 1374; https://doi.org/10.3390/e22121374 - 05 Dec 2020
Cited by 10 | Viewed by 832
Abstract
Fractional calculus (FC) is the area of calculus that generalizes the operations of differentiation and integration. FC operators are non-local and capture the history of dynamical effects present in many natural and artificial phenomena. Entropy is a measure of uncertainty, diversity and randomness [...] Read more.
Fractional calculus (FC) is the area of calculus that generalizes the operations of differentiation and integration. FC operators are non-local and capture the history of dynamical effects present in many natural and artificial phenomena. Entropy is a measure of uncertainty, diversity and randomness often adopted for characterizing complex dynamical systems. Stemming from the synergies between the two areas, this paper reviews the concept of entropy in the framework of FC. Several new entropy definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. However, FC is not yet well disseminated in the community of entropy. Therefore, new definitions based on FC can generalize both concepts in the theoretical and applied points of view. The time to come will prove to what extend the new formulations will be useful. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants
Entropy 2020, 22(11), 1241; https://doi.org/10.3390/e22111241 - 31 Oct 2020
Cited by 1 | Viewed by 667
Abstract
We review a modern differential geometric description of fluid isentropic motion and features of it including diffeomorphism group structure, modelling the related dynamics, as well as its compatibility with the quasi-stationary thermodynamical constraints. We analyze the adiabatic liquid dynamics, within which, following the [...] Read more.
We review a modern differential geometric description of fluid isentropic motion and features of it including diffeomorphism group structure, modelling the related dynamics, as well as its compatibility with the quasi-stationary thermodynamical constraints. We analyze the adiabatic liquid dynamics, within which, following the general approach, the nature of the related Poissonian structure on the fluid motion phase space as a semidirect Banach groups product, and a natural reduction of the canonical symplectic structure on its cotangent space to the classical Lie-Poisson bracket on the adjoint space to the corresponding semidirect Lie algebras product are explained in detail. We also present a modification of the Hamiltonian analysis in case of a flow governed by isothermal liquid dynamics. We study the differential-geometric structure of isentropic magneto-hydrodynamic superfluid phase space and its related motion within the Hamiltonian analysis and related invariant theory. In particular, we construct an infinite hierarchy of different kinds of integral magneto-hydrodynamic invariants, generalizing those previously constructed in the literature, and analyzing their differential-geometric origins. A charged liquid dynamics on the phase space invariant with respect to an abelian gauge group transformation is also investigated, and some generalizations of the canonical Lie-Poisson type bracket is presented. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
Review
An Elementary Introduction to Information Geometry
Entropy 2020, 22(10), 1100; https://doi.org/10.3390/e22101100 - 29 Sep 2020
Cited by 26 | Viewed by 13129
Abstract
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential [...] Read more.
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential geometry. Proofs are omitted for brevity. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
Thermophoretic Micron-Scale Devices: Practical Approach and Review
Entropy 2020, 22(9), 950; https://doi.org/10.3390/e22090950 - 28 Aug 2020
Cited by 9 | Viewed by 1451
Abstract
In recent years, there has been increasing interest in the development of micron-scale devices utilizing thermal gradients to manipulate molecules and colloids, and to measure their thermophoretic properties quantitatively. Various devices have been realized, such as on-chip implements, micro-thermogravitational columns and other micron-scale [...] Read more.
In recent years, there has been increasing interest in the development of micron-scale devices utilizing thermal gradients to manipulate molecules and colloids, and to measure their thermophoretic properties quantitatively. Various devices have been realized, such as on-chip implements, micro-thermogravitational columns and other micron-scale thermophoretic cells. The advantage of the miniaturized devices lies in the reduced sample volume. Often, a direct observation of particles using various microscopic techniques is possible. On the other hand, the small dimensions lead to some technical problems, such as a precise temperature measurement on small length scale with high spatial resolution. In this review, we will focus on the “state of the art” thermophoretic micron-scale devices, covering various aspects such as generating temperature gradients, temperature measurement, and the analysis of the current micron-scale devices. We want to give researchers an orientation for their development of thermophoretic micron-scale devices for biological, chemical, analytical, and medical applications. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
Stock Market Volatility and Return Analysis: A Systematic Literature Review
Entropy 2020, 22(5), 522; https://doi.org/10.3390/e22050522 - 04 May 2020
Cited by 11 | Viewed by 4084
Abstract
In the field of business research method, a literature review is more relevant than ever. Even though there has been lack of integrity and inflexibility in traditional literature reviews with questions being raised about the quality and trustworthiness of these types of reviews. [...] Read more.
In the field of business research method, a literature review is more relevant than ever. Even though there has been lack of integrity and inflexibility in traditional literature reviews with questions being raised about the quality and trustworthiness of these types of reviews. This research provides a literature review using a systematic database to examine and cross-reference snowballing. In this paper, previous studies featuring a generalized autoregressive conditional heteroskedastic (GARCH) family-based model stock market return and volatility have also been reviewed. The stock market plays a pivotal role in today’s world economic activities, named a “barometer” and “alarm” for economic and financial activities in a country or region. In order to prevent uncertainty and risk in the stock market, it is particularly important to measure effectively the volatility of stock index returns. However, the main purpose of this review is to examine effective GARCH models recommended for performing market returns and volatilities analysis. The secondary purpose of this review study is to conduct a content analysis of return and volatility literature reviews over a period of 12 years (2008–2019) and in 50 different papers. The study found that there has been a significant change in research work within the past 10 years and most of researchers have worked for developing stock markets. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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Review
How Incomputable Is Kolmogorov Complexity?
Entropy 2020, 22(4), 408; https://doi.org/10.3390/e22040408 - 03 Apr 2020
Cited by 8 | Viewed by 1491
Abstract
Kolmogorov complexity is the length of the ultimately compressed version of a file (i.e., anything which can be put in a computer). Formally, it is the length of a shortest program from which the file can be reconstructed. We discuss the incomputability of [...] Read more.
Kolmogorov complexity is the length of the ultimately compressed version of a file (i.e., anything which can be put in a computer). Formally, it is the length of a shortest program from which the file can be reconstructed. We discuss the incomputability of Kolmogorov complexity, which formal loopholes this leaves us with, recent approaches to compute or approximate Kolmogorov complexity, which approaches are problematic, and which approaches are viable. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
Review
On the Evidence of Thermodynamic Self-Organization during Fatigue: A Review
Entropy 2020, 22(3), 372; https://doi.org/10.3390/e22030372 - 24 Mar 2020
Cited by 3 | Viewed by 2045
Abstract
In this review paper, the evidence and application of thermodynamic self-organization are reviewed for metals typically with single crystals subjected to cyclic loading. The theory of self-organization in thermodynamic processes far from equilibrium is a cutting-edge theme for the development of a new [...] Read more.
In this review paper, the evidence and application of thermodynamic self-organization are reviewed for metals typically with single crystals subjected to cyclic loading. The theory of self-organization in thermodynamic processes far from equilibrium is a cutting-edge theme for the development of a new generation of materials. It could be interpreted as the formation of globally coherent patterns, configurations and orderliness through local interactivities by “cascade evolution of dissipative structures”. Non-equilibrium thermodynamics, entropy, and dissipative structures connected to self-organization phenomenon (patterning, orderliness) are briefly discussed. Some example evidences are reviewed in detail to show how thermodynamics self-organization can emerge from a non-equilibrium process; fatigue. Evidences including dislocation density evolution, stored energy, temperature, and acoustic signals can be considered as the signature of self-organization. Most of the attention is given to relate an analogy between persistent slip bands (PSBs) and self-organization in metals with single crystals. Some aspects of the stability of dislocations during fatigue of single crystals are discussed using the formulation of excess entropy generation. Full article
(This article belongs to the Special Issue Review Papers for Entropy)
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