Special Issue "Theoretical Aspects of Kappa Distributions"

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

Deadline for manuscript submissions: 30 September 2019.

Special Issue Editor

Guest Editor
Dr. George Livadiotis Website E-Mail
Space Science and Engineering, Southwest Research Institute, San Antonio, TX 78238, USA
Interests: statistical physics & thermodynamics; mathematical physics; plasma & space physics; nonlinear dynamics & complexity

Special Issue Information

Dear Colleagues,

Classical particle systems reside at thermal equilibrium with their velocity distribution function, stabilized into a Maxwell distribution. On the other hand, collisionless and correlated particle systems, such as space plasmas, are characterized by a non-Maxwellian behavior, typically described by the so-called kappa distributions. Empirical kappa distributions have become increasingly widespread across space and plasma physics. However, a breakthrough in the field came with the connection of kappa distributions with the solid background of non-extensive statistical mechanics. Understanding the statistical background and origin of kappa distributions was a cornerstone of further theoretical developments, for example, among many others: the physical meaning of thermal parameters, e.g., temperature and kappa index; the N-particle description of kappa distributions; the generalization to phase-space kappa distribution of a Hamiltonian with non-zero potential; the entropy associated with kappa distributions.

In this Special Issue, we welcome papers reporting on the progress of the theory of kappa distributions. The subjects may include, but are not limited to, the following three broad areas:

A.    Statistical background:

-    Connection of kappa distributions with Non-extensive statistical mechanics;
-    Superstatistics and formulation of kappa distributions;
-    Superposition on kappa indices.

B.    Formulation:

-     Multi-particle distributions;
-     Distributions in the presence of potential energy;
-     Anisotropy of velocity space;
-     Relativistic distributions;
-     Further generalization in Lp norms;
-     Discrete formalism.

C.    Properties:

-     Concept of temperature for stationary states out of thermal equilibrium;
-     Physical meaning of kappa and its connection to particle correlations;
-     Higher statistical moments;
-     Parameter estimation methods;
-     Rankine–Hugoniot conditions for shocks in particle systems described by kappa distributions;
-     Polytropic relations and connection with the theory of kappa distributions;
-     Entropic formulations associated with kappa distributions;
-     Information measures and kappa distributions.

Dr. George  Livadiotis
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 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.

Published Papers (3 papers)

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Research

Open AccessArticle
Non-Extensive Statistical Analysis of Energetic Particle Flux Enhancements Caused by the Interplanetary Coronal Mass Ejection-Heliospheric Current Sheet Interaction
Entropy 2019, 21(7), 648; https://doi.org/10.3390/e21070648 - 30 Jun 2019
Abstract
In this study we use theoretical concepts and computational-diagnostic tools of Tsallis non-extensive statistical theory (Tsallis q-triplet: q s e n ,   q r e l ,   q s t a t ), complemented by other known tools of nonlinear dynamics [...] Read more.
In this study we use theoretical concepts and computational-diagnostic tools of Tsallis non-extensive statistical theory (Tsallis q-triplet: q s e n ,   q r e l ,   q s t a t ), complemented by other known tools of nonlinear dynamics such as Correlation Dimension and surrogate data, Hurst exponent, Flatness coefficient, and p-modeling of multifractality, in order to describe and understand Small-scale Magnetic Islands (SMIs) structures observed in Solar Wind (SW) with a typical size of ~0.01–0.001 AU at 1 AU. Specifically, we analyze ~0.5 MeV energetic ion time-intensity and magnetic field profiles observed by the STEREO A spacecraft during a rare, widely discussed event. Our analysis clearly reveals the non-extensive character of SW space plasmas during the periods of SMIs events, as well as significant physical complex phenomena in accordance with nonlinear dynamics and complexity theory. As our analysis also shows, a non-equilibrium phase transition parallel with self-organization processes, including the reduction of dimensionality and development of long-range correlations in connection with anomalous diffusion and fractional acceleration processes can be observed during SMIs events. Full article
(This article belongs to the Special Issue Theoretical Aspects of Kappa Distributions)
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Open AccessArticle
Tsallis Entropy Index q and the Complexity Measure of Seismicity in Natural Time under Time Reversal before the M9 Tohoku Earthquake in 2011
Entropy 2018, 20(10), 757; https://doi.org/10.3390/e20100757 - 02 Oct 2018
Cited by 5
Abstract
The observed earthquake scaling laws indicate the existence of phenomena closely associated with the proximity of the system to a critical point. Taking this view that earthquakes are critical phenomena (dynamic phase transitions), here we investigate whether in this case the Lifshitz–Slyozov–Wagner (LSW) [...] Read more.
The observed earthquake scaling laws indicate the existence of phenomena closely associated with the proximity of the system to a critical point. Taking this view that earthquakes are critical phenomena (dynamic phase transitions), here we investigate whether in this case the Lifshitz–Slyozov–Wagner (LSW) theory for phase transitions showing that the characteristic size of the minority phase droplets grows with time as t 1 / 3 is applicable. To achieve this goal, we analyzed the Japanese seismic data in a new time domain termed natural time and find that an LSW behavior is actually obeyed by a precursory change of seismicity and in particular by the fluctuations of the entropy change of seismicity under time reversal before the Tohoku earthquake of magnitude 9.0 that occurred on 11 March 2011 in Japan. Furthermore, the Tsallis entropic index q is found to exhibit a precursory increase. Full article
(This article belongs to the Special Issue Theoretical Aspects of Kappa Distributions)
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Open AccessArticle
High Density Nodes in the Chaotic Region of 1D Discrete Maps
Entropy 2018, 20(1), 24; https://doi.org/10.3390/e20010024 - 04 Jan 2018
Cited by 1
Abstract
We report on the definition and characteristics of nodes in the chaotic region of bifurcation diagrams in the case of 1D mono-parametrical and S-unimodal maps, using as guiding example the logistic map. We examine the arrangement of critical curves, the identification and arrangement [...] Read more.
We report on the definition and characteristics of nodes in the chaotic region of bifurcation diagrams in the case of 1D mono-parametrical and S-unimodal maps, using as guiding example the logistic map. We examine the arrangement of critical curves, the identification and arrangement of nodes, and the connection between the periodic windows and nodes in the chaotic zone. We finally present several characteristic features of nodes, which involve their convergence and entropy. Full article
(This article belongs to the Special Issue Theoretical Aspects of Kappa Distributions)
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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.

In this Special Issue, we welcome papers reporting on the progress of the theory of kappa distributions. The subjects may include, but are not limited to, the following three broad areas:

A.    Statistical background:

-    Connection of kappa distributions with Non-extensive statistical mechanics;
-    Superstatistics and formulation of kappa distributions;
-    Superposition on kappa indices.

B.    Formulation:

-     Multi-particle distributions;
-     Distributions in the presence of potential energy;
-     Anisotropy of velocity space;
-     Relativistic distributions;
-     Further generalization in Lp norms;
-     Discrete formalism.

C.    Properties:

-     Concept of temperature for stationary states out of thermal equilibrium;
-     Physical meaning of kappa and its connection to particle correlations;
-     Higher statistical moments;
-     Parameter estimation methods;
-     Rankine–Hugoniot conditions for shocks in particle systems described by kappa distributions;
-     Polytropic relations and connection with the theory of kappa distributions;
-     Entropic formulations associated with kappa distributions;
-     Information measures and kappa distributions.

Dr. George  Livadiotis
Guest Editor

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