Special Issue "20th Anniversary of Entropy—Review Papers Collection"

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

Deadline for manuscript submissions: closed (15 December 2018).

Special Issue Editor

Prof. Dr. Kevin H. Knuth
E-Mail Website
Guest Editor
Department of Physics, University at Albany, 1400 Washington Avenue, Albany, NY 12222, USA
Interests: entropy; probability theory; Bayesian; foundational issues; lattice theory; data analysis; maxent; machine learning; robotics; information theory; entropy-based experimental design
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

We are delighted to be celebrating the 20th anniversary of our journal Entropy in 2018. To date, the journal has published more than 3150 papers and the journal website attracts more than 160,000 monthly page-views. We thank our readers, innumerable authors, anonymous peer reviewers, editors, and all the people working in any way for the journal who have joined their efforts for years.

To celebrate this anniversary, we are launching this Special Issue, entitled “20th Anniversary of Entropy—Review Papers Collection”. We aim to collect a set of high-quality review papers that highlight the most recent advances in the fields of entropy and information theory. We kindly encourage all research groups covering relevant areas to contribute up-to-date, comprehensive reviews, highlighting the latest developments of entropy and information-theoretic concepts as well as their application in a broad variety of areas, including physics, engineering, economics, chemistry, biology, and others.

Prof. Dr. Kevin H. Knuth
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 (5 papers)

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Review

Open AccessReview
The Observable Representation
Entropy 2019, 21(3), 310; https://doi.org/10.3390/e21030310 - 21 Mar 2019
Viewed by 999
Abstract
The observable representation (OR) is an embedding of the space on which a stochastic dynamics is taking place into a low dimensional Euclidean space. The most significant feature of the OR is that it respects the dynamics. Examples are given in several areas: [...] Read more.
The observable representation (OR) is an embedding of the space on which a stochastic dynamics is taking place into a low dimensional Euclidean space. The most significant feature of the OR is that it respects the dynamics. Examples are given in several areas: the definition of a phase transition (including metastable phases), random walks in which the OR recovers the original space, complex systems, systems in which the number of extrema exceed convenient viewing capacity, and systems in which successful features are displayed, but without the support of known theorems. Full article
(This article belongs to the Special Issue 20th Anniversary of Entropy—Review Papers Collection)
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Open AccessReview
Entropic Effects in Polymer Nanocomposites
Entropy 2019, 21(2), 186; https://doi.org/10.3390/e21020186 - 15 Feb 2019
Cited by 8 | Viewed by 3126
Abstract
Polymer nanocomposite materials, consisting of a polymer matrix embedded with nanoscale fillers or additives that reinforce the inherent properties of the matrix polymer, play a key role in many industrial applications. Understanding of the relation between thermodynamic interactions and macroscopic morphologies of the [...] Read more.
Polymer nanocomposite materials, consisting of a polymer matrix embedded with nanoscale fillers or additives that reinforce the inherent properties of the matrix polymer, play a key role in many industrial applications. Understanding of the relation between thermodynamic interactions and macroscopic morphologies of the composites allow for the optimization of design and mechanical processing. This review article summarizes the recent advancement in various aspects of entropic effects in polymer nanocomposites, and highlights molecular methods used to perform numerical simulations, morphologies and phase behaviors of polymer matrices and fillers, and characteristic parameters that significantly correlate with entropic interactions in polymer nanocomposites. Experimental findings and insight obtained from theories and simulations are combined to understand how the entropic effects are turned into effective interparticle interactions that can be harnessed for tailoring nanostructures of polymer nanocomposites. Full article
(This article belongs to the Special Issue 20th Anniversary of Entropy—Review Papers Collection)
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Open AccessReview
Non-Equilibrium Liouville and Wigner Equations: Classical Statistical Mechanics and Chemical Reactions for Long Times
Entropy 2019, 21(2), 179; https://doi.org/10.3390/e21020179 - 14 Feb 2019
Cited by 1 | Viewed by 994
Abstract
We review and improve previous work on non-equilibrium classical and quantum statistical systems, subject to potentials, without ab initio dissipation. We treat classical closed three-dimensional many-particle interacting systems without any “heat bath” (hb), evolving through the Liouville equation for the [...] Read more.
We review and improve previous work on non-equilibrium classical and quantum statistical systems, subject to potentials, without ab initio dissipation. We treat classical closed three-dimensional many-particle interacting systems without any “heat bath” (h b), evolving through the Liouville equation for the non-equilibrium classical distribution W c, with initial states describing thermal equilibrium at large distances but non-equilibrium at finite distances. We use Boltzmann’s Gaussian classical equilibrium distribution W c , e q, as weight function to generate orthogonal polynomials (H n’s) in momenta. The moments of W c, implied by the H n’s, fulfill a non-equilibrium hierarchy. Under long-term approximations, the lowest moment dominates the evolution towards thermal equilibrium. A non-increasing Liapunov function characterizes the long-term evolution towards equilibrium. Non-equilibrium chemical reactions involving two and three particles in a h b are studied classically and quantum-mechanically (by using Wigner functions W). Difficulties related to the non-positivity of W are bypassed. Equilibrium Wigner functions W e q generate orthogonal polynomials, which yield non-equilibrium moments of W and hierarchies. In regimes typical of chemical reactions (short thermal wavelength and long times), non-equilibrium hierarchies yield approximate Smoluchowski-like equations displaying dissipation and quantum effects. The study of three-particle chemical reactions is new. Full article
(This article belongs to the Special Issue 20th Anniversary of Entropy—Review Papers Collection)
Open AccessReview
Approximation of Densities on Riemannian Manifolds
Entropy 2019, 21(1), 43; https://doi.org/10.3390/e21010043 - 09 Jan 2019
Cited by 1 | Viewed by 1400
Abstract
Finding an approximate probability distribution best representing a sample on a measure space is one of the most basic operations in statistics. Many procedures were designed for that purpose when the underlying space is a finite dimensional Euclidean space. In applications, however, such [...] Read more.
Finding an approximate probability distribution best representing a sample on a measure space is one of the most basic operations in statistics. Many procedures were designed for that purpose when the underlying space is a finite dimensional Euclidean space. In applications, however, such a simple setting may not be adapted and one has to consider data living on a Riemannian manifold. The lack of unique generalizations of the classical distributions, along with theoretical and numerical obstructions require several options to be considered. The present work surveys some possible extensions of well known families of densities to the Riemannian setting, both for parametric and non-parametric estimation. Full article
(This article belongs to the Special Issue 20th Anniversary of Entropy—Review Papers Collection)
Open AccessReview
A Brief Review of Generalized Entropies
Entropy 2018, 20(11), 813; https://doi.org/10.3390/e20110813 - 23 Oct 2018
Cited by 36 | Viewed by 2430
Abstract
Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review, we focus on the so-called generalized entropies, which [...] Read more.
Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review, we focus on the so-called generalized entropies, which from a mathematical point of view are nonnegative functions defined on probability distributions that satisfy the first three Shannon–Khinchin axioms: continuity, maximality and expansibility. While these three axioms are expected to be satisfied by all macroscopic physical systems, the fourth axiom (separability or strong additivity) is in general violated by non-ergodic systems with long range forces, this having been the main reason for exploring weaker axiomatic settings. Currently, non-additive generalized entropies are being used also to study new phenomena in complex dynamics (multifractality), quantum systems (entanglement), soft sciences, and more. Besides going through the axiomatic framework, we review the characterization of generalized entropies via two scaling exponents introduced by Hanel and Thurner. In turn, the first of these exponents is related to the diffusion scaling exponent of diffusion processes, as we also discuss. Applications are addressed as the description of the main generalized entropies advances. Full article
(This article belongs to the Special Issue 20th Anniversary of Entropy—Review Papers Collection)
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