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: 17 May 2021.

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

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (10 papers)

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Review

Open AccessReview
The Entropy Universe
Entropy 2021, 23(2), 222; https://doi.org/10.3390/e23020222 - 11 Feb 2021
Cited by 2 | Viewed by 1039
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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Open AccessReview
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 1 | Viewed by 532
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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Open AccessReview
A Survey of Information Entropy Metrics for Complex Networks
Entropy 2020, 22(12), 1417; https://doi.org/10.3390/e22121417 - 15 Dec 2020
Viewed by 652
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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Open AccessReview
A Review of Fractional Order Entropies
Entropy 2020, 22(12), 1374; https://doi.org/10.3390/e22121374 - 05 Dec 2020
Cited by 1 | Viewed by 466
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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Open AccessReview
Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants
Entropy 2020, 22(11), 1241; https://doi.org/10.3390/e22111241 - 31 Oct 2020
Viewed by 416
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)
Open AccessReview
An Elementary Introduction to Information Geometry
Entropy 2020, 22(10), 1100; https://doi.org/10.3390/e22101100 - 29 Sep 2020
Cited by 5 | Viewed by 3915
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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Open AccessReview
Thermophoretic Micron-Scale Devices: Practical Approach and Review
Entropy 2020, 22(9), 950; https://doi.org/10.3390/e22090950 - 28 Aug 2020
Cited by 3 | Viewed by 869
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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Open AccessReview
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 2 | Viewed by 1957
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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Open AccessReview
How Incomputable Is Kolmogorov Complexity?
Entropy 2020, 22(4), 408; https://doi.org/10.3390/e22040408 - 03 Apr 2020
Cited by 2 | Viewed by 1031
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)
Open AccessEditor’s ChoiceReview
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
Viewed by 1367
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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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Name: Kostas Kleidis
Email:
[email protected]

Name: Shlomo Shamai(Shitz)
Email:
[email protected]

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