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Special Issue "Nonadditive Entropies and Complex Systems"

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

Deadline for manuscript submissions: 30 November 2018

Special Issue Editors

Guest Editor
Prof. Dr. Andrea Rapisarda

1. Dipartimento di Fisica e Astronomia and INFN sezione di Catania, Via S.Sofia 64, 95123 Catania, Italy
2. Complexity Science Hub Vienna, Josefstädter Straße 39, 1080 Vienna, Austria; http://csh.ac.at/
Website | E-Mail
Interests: complex systems; statistical mechanics; agent-based models; complex networks; econophysics; chaos and nonlinear dynamics
Guest Editor
Prof. Dr. Stefan Thurner

1 Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria
2 Complexity Science Hub Vienna, Josefstädter Straße 39, 1080 Vienna, Austria; http://csh.ac.at/
Website | E-Mail
Interests: statistical mechanics of complex systems; theory of evolutionary processes; entropy formulations; network theory; scaling theory; anomalous diffusion
Guest Editor
Prof. Dr. Constantino Tsallis

1 Department of Theoretical Physics, Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil
2 Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
3 Complexity Science Hub Vienna, Josefstädter Straße 39, 1080 Vienna, Austria; http://csh.ac.at/
Website | E-Mail
Fax: +55 21 2141 7190
Interests: nonextensive statistical mechanics; foundations and applications of statistical mechanics; complex systems

Special Issue Information

Dear Colleagues,

Complexity and complex systems emerge in natural, artificial, and social contexts, and have attracted strong and enthusiastic scientific attention all over the world during the last decades. The study of these fascinating systems focuses on concepts of emergent behavior, living organisms, languages, earthquakes, economics, ecology, social networks, and other fundamental problems of contemporary science and societies. Most of these systems are out-of-equilibrium and present weak chaos, long-range correlations, nonergodic behavior, multifractal hierarchical structures, for which standard equilibrium Boltzmann-Gibbs statistical mechanics is not applicable. In the last few decades, a large variety of complex systems, in various fields, has been successfully described using nonextensive generalized formalisms of statistical mechanics.

The aim of the present Special Issue is to solicit original and interdisciplinary contributions which cover new developments and original applications of generalized statistical mechanics to complex systems of various natures.

Prof. Dr. Andrea Rapisarda
Prof. Dr. Stefan Thurner
Prof. Dr. Constantino Tsallis
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.

Keywords

  • nonadditive entropies
  • nonextensive statistical mechanics
  • complex systems
  • complex networks
  • thermodynamics
  • applications

Published Papers (4 papers)

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Research

Open AccessArticle Analytic Study of Complex Fractional Tsallis’ Entropy with Applications in CNNs
Entropy 2018, 20(10), 722; https://doi.org/10.3390/e20100722
Received: 29 July 2018 / Revised: 5 September 2018 / Accepted: 10 September 2018 / Published: 20 September 2018
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Abstract
In this paper, we study Tsallis’ fractional entropy (TFE) in a complex domain by applying the definition of the complex probability functions. We study the upper and lower bounds of TFE based on some special functions. Moreover, applications in complex neural networks (CNNs)
[...] Read more.
In this paper, we study Tsallis’ fractional entropy (TFE) in a complex domain by applying the definition of the complex probability functions. We study the upper and lower bounds of TFE based on some special functions. Moreover, applications in complex neural networks (CNNs) are illustrated to recognize the accuracy of CNNs. Full article
(This article belongs to the Special Issue Nonadditive Entropies and Complex Systems)
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Open AccessArticle Hedging for the Regime-Switching Price Model Based on Non-Extensive Statistical Mechanics
Entropy 2018, 20(4), 248; https://doi.org/10.3390/e20040248
Received: 13 March 2018 / Revised: 1 April 2018 / Accepted: 3 April 2018 / Published: 3 April 2018
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Abstract
To describe the movement of asset prices accurately, we employ the non-extensive statistical mechanics and the semi-Markov process to establish an asset price model. The model can depict the peak and fat tail characteristics of returns and the regime-switching phenomenon of macroeconomic system.
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To describe the movement of asset prices accurately, we employ the non-extensive statistical mechanics and the semi-Markov process to establish an asset price model. The model can depict the peak and fat tail characteristics of returns and the regime-switching phenomenon of macroeconomic system. Moreover, we use the risk-minimizing method to study the hedging problem of contingent claims and obtain the explicit solutions of the optimal hedging strategies. Full article
(This article belongs to the Special Issue Nonadditive Entropies and Complex Systems)
Open AccessArticle Generalized Pesin-Like Identity and Scaling Relations at the Chaos Threshold of the Rössler System
Entropy 2018, 20(4), 216; https://doi.org/10.3390/e20040216
Received: 16 February 2018 / Revised: 15 March 2018 / Accepted: 20 March 2018 / Published: 23 March 2018
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Abstract
In this paper, using the Poincaré section of the flow we numerically verify a generalization of a Pesin-like identity at the chaos threshold of the Rössler system, which is one of the most popular three-dimensional continuous systems. As Poincaré section points of the
[...] Read more.
In this paper, using the Poincaré section of the flow we numerically verify a generalization of a Pesin-like identity at the chaos threshold of the Rössler system, which is one of the most popular three-dimensional continuous systems. As Poincaré section points of the flow show similar behavior to that of the logistic map, for the Rössler system we also investigate the relationships with respect to important properties of nonlinear dynamics, such as correlation length, fractal dimension, and the Lyapunov exponent in the vicinity of the chaos threshold. Full article
(This article belongs to the Special Issue Nonadditive Entropies and Complex Systems)
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Open AccessArticle Non-Gaussian Closed Form Solutions for Geometric Average Asian Options in the Framework of Non-Extensive Statistical Mechanics
Entropy 2018, 20(1), 71; https://doi.org/10.3390/e20010071
Received: 17 November 2017 / Revised: 30 December 2017 / Accepted: 16 January 2018 / Published: 18 January 2018
Cited by 1 | PDF Full-text (266 KB) | HTML Full-text | XML Full-text
Abstract
In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics
[...] Read more.
In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics of returns. Thus, the description of underlying asset price and the pricing of options are more accurate. Moreover, using the martingale method, we obtain closed form solutions for geometric average Asian options. Furthermore, the numerical analysis shows that the model can avoid underestimating risks relative to the Black-Scholes model. Full article
(This article belongs to the Special Issue Nonadditive Entropies and Complex Systems)
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