Special Issue "Entropies: Between Information Geometry and Kinetics"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 16 February 2020.

Special Issue Editors

Prof. Dr. Alexander N. Gorban
E-Mail Website
Guest Editor
Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
Interests: neural networks; physical, chemical, and biological kinetics; human adaptation to hard living conditions; artificial intelligence; methods and technologies of collective thinking
Special Issues and Collections in MDPI journals
Prof. Dr. Miroslav Grmela
E-Mail Website
Guest Editor
Ecole Polytechnique de Montreal, Montreal, QC H3C 3A7, Canada
Tel. +514 340-4711-4627
Interests: multiscale nonequilibrium thermodynamics; kinetic theory; mechanics of complex fluids; differential geometry
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

The history of entropy is a wonderful combination of physical, probabilistic, and geometrical ideas. Chemical and biological problems and modern data analysis further enrich this beautiful combination. This issue has an ambitious goal: To collect highly interdisciplinary papers that combine more than one subject and are related to geometric, statistical, and physical ideas of entropy. Geometric ideas in thermodynamics, statistical physics, and kinetics, geometry of data analytics in high dimensions, ideas of statistical physics in geometry, and mathematical backgrounds of all these approaches are very welcome. We are looking for new ideas and methods to support emerging and fast developing areas, like Artificial Intelligence and Smart Materials, and for solutions to classical problems such as efficient model reduction in kinetic systems. We also encourage authors to supplement articles with real-world applications whenever possible.

Prof. Dr. Alexander N. Gorban
Prof. Dr. Miroslav Grmela
Guest Editors

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 1600 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.

Keywords

  • entropy
  • thermodynamics
  • kinetics
  • geometry
  • information processing
  • measure concentration
  • high dimensionality
  • model reduction
  • data analysis

Published Papers (6 papers)

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Research

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Open AccessArticle
Learning the Macroscopic Flow Model of Short Fiber Suspensions from Fine-Scale Simulated Data
Entropy 2020, 22(1), 30; https://doi.org/10.3390/e22010030 - 24 Dec 2019
Abstract
Fiber–fiber interaction plays an important role in the evolution of fiber orientation in semi-concentrated suspensions. Flow induced orientation in short-fiber reinforced composites determines the anisotropic properties of manufactured parts and consequently their performances. In the case of dilute suspensions, the orientation evolution can [...] Read more.
Fiber–fiber interaction plays an important role in the evolution of fiber orientation in semi-concentrated suspensions. Flow induced orientation in short-fiber reinforced composites determines the anisotropic properties of manufactured parts and consequently their performances. In the case of dilute suspensions, the orientation evolution can be accurately described by using the Jeffery model; however, as soon as the fiber concentration increases, fiber–fiber interactions cannot be ignored anymore and the final orientation state strongly depends on the modeling of those interactions. First modeling frameworks described these interactions from a diffusion mechanism; however, it was necessary to consider richer descriptions (anisotropic diffusion, etc.) to address experimental observations. Even if different proposals were considered, none of them seem general and accurate enough. In this paper we do not address a new proposal of a fiber interaction model, but a data-driven methodology able to enrich existing models from data, that in our case comes from a direct numerical simulation of well resolved microscopic physics. Full article
(This article belongs to the Special Issue Entropies: Between Information Geometry and Kinetics)
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Open AccessArticle
Finite Amplitude Stability of Internal Steady Flows of the Giesekus Viscoelastic Rate-Type Fluid
Entropy 2019, 21(12), 1219; https://doi.org/10.3390/e21121219 - 13 Dec 2019
Cited by 1
Abstract
Using a Lyapunov type functional constructed on the basis of thermodynamical arguments, we investigate the finite amplitude stability of internal steady flows of viscoelastic fluids described by the Giesekus model. Using the functional, we derive bounds on the Reynolds and the Weissenberg number [...] Read more.
Using a Lyapunov type functional constructed on the basis of thermodynamical arguments, we investigate the finite amplitude stability of internal steady flows of viscoelastic fluids described by the Giesekus model. Using the functional, we derive bounds on the Reynolds and the Weissenberg number that guarantee the unconditional asymptotic stability of the corresponding steady internal flow, wherein the distance between the steady flow field and the perturbed flow field is measured with the help of the Bures–Wasserstein distance between positive definite matrices. The application of the theoretical results is documented in the finite amplitude stability analysis of Taylor–Couette flow. Full article
(This article belongs to the Special Issue Entropies: Between Information Geometry and Kinetics)
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Open AccessArticle
Data-Driven GENERIC Modeling of Poroviscoelastic Materials
Entropy 2019, 21(12), 1165; https://doi.org/10.3390/e21121165 - 28 Nov 2019
Abstract
Biphasic soft materials are challenging to model by nature. Ongoing efforts are targeting their effective modeling and simulation. This work uses experimental atomic force nanoindentation of thick hydrogels to identify the indentation forces are a function of the indentation depth. Later on, the [...] Read more.
Biphasic soft materials are challenging to model by nature. Ongoing efforts are targeting their effective modeling and simulation. This work uses experimental atomic force nanoindentation of thick hydrogels to identify the indentation forces are a function of the indentation depth. Later on, the atomic force microscopy results are used in a GENERIC general equation for non-equilibrium reversible–irreversible coupling (GENERIC) formalism to identify the best model conserving basic thermodynamic laws. The data-driven GENERIC analysis identifies the material behavior with high fidelity for both data fitting and prediction. Full article
(This article belongs to the Special Issue Entropies: Between Information Geometry and Kinetics)
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Open AccessFeature PaperArticle
Lifts of Symmetric Tensors: Fluids, Plasma, and Grad Hierarchy
Entropy 2019, 21(9), 907; https://doi.org/10.3390/e21090907 - 18 Sep 2019
Abstract
Geometrical and algebraic aspects of the Hamiltonian realizations of the Euler’s fluid and the Vlasov’s plasma are investigated. A purely geometric pathway (involving complete lifts and vertical representatives) is proposed, which establishes a link from particle motion to evolution of the field variables. [...] Read more.
Geometrical and algebraic aspects of the Hamiltonian realizations of the Euler’s fluid and the Vlasov’s plasma are investigated. A purely geometric pathway (involving complete lifts and vertical representatives) is proposed, which establishes a link from particle motion to evolution of the field variables. This pathway is free from Poisson brackets and Hamiltonian functionals. Momentum realizations (sections on T * T * Q ) of (both compressible and incompressible) Euler’s fluid and Vlasov’s plasma are derived. Poisson mappings relating the momentum realizations with the usual field equations are constructed as duals of injective Lie algebra homomorphisms. The geometric pathway is then used to construct the evolution equations for 10-moments kinetic theory. This way the entire Grad hierarchy (including entropic fields) can be constructed in a purely geometric way. This geometric way is an alternative to the usual Hamiltonian approach to mechanics based on Poisson brackets. Full article
(This article belongs to the Special Issue Entropies: Between Information Geometry and Kinetics)
Open AccessArticle
A Matrix Information-Geometric Method for Change-Point Detection of Rigid Body Motion
Entropy 2019, 21(5), 531; https://doi.org/10.3390/e21050531 - 25 May 2019
Abstract
A matrix information-geometric method was developed to detect the change-points of rigid body motions. Note that the set of all rigid body motions is the special Euclidean group SE(3), so the Riemannian mean based on the Lie group [...] Read more.
A matrix information-geometric method was developed to detect the change-points of rigid body motions. Note that the set of all rigid body motions is the special Euclidean group S E ( 3 ) , so the Riemannian mean based on the Lie group structures of S E ( 3 ) reflects the characteristics of change-points. Once a change-point occurs, the distance between the current point and the Riemannian mean of its neighbor points should be a local maximum. A gradient descent algorithm is proposed to calculate the Riemannian mean. Using the Baker–Campbell–Hausdorff formula, the first-order approximation of the Riemannian mean is taken as the initial value of the iterative procedure. The performance of our method was evaluated by numerical examples and manipulator experiments. Full article
(This article belongs to the Special Issue Entropies: Between Information Geometry and Kinetics)
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Review

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Open AccessReview
High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality
Entropy 2020, 22(1), 82; https://doi.org/10.3390/e22010082 - 09 Jan 2020
Abstract
High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the “curse of dimensionality” states: many problems become exponentially difficult in high dimensions. Recently, the other side of the [...] Read more.
High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the “curse of dimensionality” states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the “blessing of dimensionality”, has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience. Full article
(This article belongs to the Special Issue Entropies: Between Information Geometry and Kinetics)
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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.

Title: New Invariants in Chemical Kinetics
Authors: Gregory S. Yablonsky; Daniel Branco Pinto; Guy B Marin; Denis Constales
Affiliation: Parks College, Department of Chemistry, Saint Louis University

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