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Special Issue "Entropy: From Physics to Information Sciences and Geometry"

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

Deadline for manuscript submissions: 30 June 2018

Special Issue Editors

Guest Editor
Prof. Dr. Ali Mohammad-Djafari

Laboratoire des Signaux et Systmes, UMR 8506 CNRS-SUPELEC-UNIV PARIS SUD, Gif-sur-Yvette, France
Website | E-Mail
Interests: inference, inverse problems, bayesian computation, information and maximum entropy, knowledge extraction
Guest Editor
Prof. Dr. Miguel Rubi

Secció de Física Estadística i Interdisciplinària - Departament de Física de la Matèria Condensada, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
Website | E-Mail
Phone: +34-934021162
Interests: statistical physics, thermodynamics, biophysic

Special Issue Information

Dear Colleagues,

One of the most frequently used scientific words, is the word “Entropy”. The reason is that it is related to two main scientific domains: physics and information theory. Its origin goes back to the start of physics (thermodynamics), but since Shannon, it has become related to information theory.

The main topics of the special issue include:

  • Physics: classical thermodynamics and quantum
  • Statistical physics and Bayesian computation
  • Geometrical science of information, topology and metrics
  • Maximum entropy principle and inference
  • Kullback and Bayes or information theory and Bayesian inference
  • Entropy in action (applications)

The inter-disciplinary nature of contributions from both theoretical and applied perspectives are very welcome, including papers addressing conceptual and methodological developments, as well as new applications of entropy and information theory.

This special issue will publish the extended version of papers presented at Entropy 2018 conference but not limited to that.  This issue is open to any other contrinutions related to the subjects of Entropy 2018 conference.

Prof. Dr. Ali Mohammad-Djafari
Prof. Dr. Miguel Rubi
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 1500 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 (3 papers)

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Research

Open AccessArticle Relating Vertex and Global Graph Entropy in Randomly Generated Graphs
Entropy 2018, 20(7), 481; https://doi.org/10.3390/e20070481 (registering DOI)
Received: 22 May 2018 / Revised: 14 June 2018 / Accepted: 17 June 2018 / Published: 21 June 2018
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Abstract
Combinatoric measures of entropy capture the complexity of a graph but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an
[...] Read more.
Combinatoric measures of entropy capture the complexity of a graph but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of vertex level measures that do not suffer from this pathological computational complexity, but that can be shown to be effective at quantifying graph complexity. In this paper, we consider whether these local measures are fundamentally equivalent to global entropy measures. Specifically, we investigate the existence of a correlation between vertex level and global measures of entropy for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate strong correlation for this subset of graphs and outline how this may arise theoretically. Full article
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
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Open AccessArticle Quantum Statistical Manifolds
Entropy 2018, 20(6), 472; https://doi.org/10.3390/e20060472
Received: 26 May 2018 / Revised: 15 June 2018 / Accepted: 15 June 2018 / Published: 17 June 2018
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Abstract
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose, the emphasis is shifted from a manifold
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Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose, the emphasis is shifted from a manifold of strictly positive density matrices to a manifold of faithful quantum states on the C*-algebra of bounded linear operators. In addition, ideas from the parameter-free approach to information geometry are adopted. The underlying Hilbert space is assumed to be finite-dimensional. In this way, technicalities are avoided so that strong results are obtained, which one can hope to prove later on in a more general context. Two different atlases are introduced, one in which it is straightforward to show that the quantum states form a Banach manifold, the other which is compatible with the inner product of Bogoliubov and which yields affine coordinates for the exponential connection. Full article
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
Open AccessArticle Divergence from, and Convergence to, Uniformity of Probability Density Quantiles
Entropy 2018, 20(5), 317; https://doi.org/10.3390/e20050317
Received: 7 March 2018 / Revised: 10 April 2018 / Accepted: 19 April 2018 / Published: 25 April 2018
PDF Full-text (995 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
We demonstrate that questions of convergence and divergence regarding shapes of distributions can be carried out in a location- and scale-free environment. This environment is the class of probability density quantiles (pdQs), obtained by normalizing the composition of the density with the associated
[...] Read more.
We demonstrate that questions of convergence and divergence regarding shapes of distributions can be carried out in a location- and scale-free environment. This environment is the class of probability density quantiles (pdQs), obtained by normalizing the composition of the density with the associated quantile function. It has earlier been shown that the pdQ is representative of a location-scale family and carries essential information regarding shape and tail behavior of the family. The class of pdQs are densities of continuous distributions with common domain, the unit interval, facilitating metric and semi-metric comparisons. The Kullback–Leibler divergences from uniformity of these pdQs are mapped to illustrate their relative positions with respect to uniformity. To gain more insight into the information that is conserved under the pdQ mapping, we repeatedly apply the pdQ mapping and find that further applications of it are quite generally entropy increasing so convergence to the uniform distribution is investigated. New fixed point theorems are established with elementary probabilistic arguments and illustrated by examples. Full article
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
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