Entropy

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Dear Colleagues,

Entropy plays a key role in plasma theory and modeling. Firstly, entropy provides an important point-of-view of the equilibrium state. Secondly, analysis of entropy cascades, entropy flux, and entropy transfer in general brings important information about plasma dynamics and about the range of validity of a numerical approach, especially in strongly nonlinear plasma settings. This is true for fluid and kinetic plasma models. Accurate treatment of entropy is even more crucial in a turbulent setting since energy or enstrophy (depending on the dimensionality of the system) flows toward very small scales. Thirdly, collisions play a crucial role in dissipating or diffusing small scales, and their impact on entropy balance must be accounted for. In collisionless plasmas, the formation of small-scale structures in the phase-space of particle trajectories, and filamentation of the distribution function, are also very sensitive to the treatment of entropy and loss of information—this is also linked to phase-mixing, and phasestrophy cascades. In this Special Issue, we aim at gathering reviews, recent advances, and research papers on the various roles of entropy in plasma theory and modeling, mainly but not only in a turbulent setting. We welcome contributions relating to a wide range of plasmas, from low to high-temperature plasmas, from closed to open systems, from local to global modeling, and from fixed-gradient to flux-driven conditions.

Dr. Maxime Lesur
Guest Editor

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Keywords

plasma
turbulence
Vlasov
fluid
MHD
filamentation
entropy cascade
entropy transfer

Published Papers (1 paper)

Research

16 pages, 747 KiB

Open AccessArticle

Chaos and Predictability in Ionospheric Time Series

by Massimo Materassi, Tommaso Alberti, Yenca Migoya-Orué, Sandro Maria Radicella and Giuseppe Consolini

Entropy 2023, 25(2), 368; https://doi.org/10.3390/e25020368 - 17 Feb 2023

Cited by 3 | Viewed by 1401

Abstract

Modelling the Earth’s ionosphere is a big challenge, due to the complexity of the system. Different first principle models have been developed over the last 50 years, based on ionospheric physics and chemistry, mostly controlled by Space Weather conditions. However, it is not understood in depth if the residual or mismodelled component of the ionosphere’s behaviour is predictable in principle as a simple dynamical system, or is conversely so chaotic to be practically stochastic. Working on an ionospheric quantity very popular in aeronomy, we here suggest data analysis techniques to deal with the question of how chaotic and how predictable the local ionosphere’s behaviour is. In particular, we calculate the correlation dimension

D_{2}

and the Kolmogorov entropy rate

K_{2}

for two one-year long time series of data of vertical total electron content (vTEC), collected on the top of the mid-latitude GNSS station of Matera (Italy), one for the year of Solar Maximum 2001 and one for the year of Solar Minimum 2008. The quantity

D_{2}

is a proxy of the degree of chaos and dynamical complexity.

K_{2}

measures the speed of destruction of the time-shifted self-mutual information of the signal, so that

K_{2}^{- 1}

is a sort of maximum time horizon for predictability. The analysis of the

D_{2}

and

K_{2}

for the vTEC time series allows to give a measure of chaos and predictability of the Earth’s ionosphere, expected to limit any claim of prediction capacity of any model. The results reported here are preliminary, and must be intended only to demonstrate how the application of the analysis of these quantities to the ionospheric variability is feasible, and with a reasonable output. Full article

(This article belongs to the Special Issue Plasma Turbulence: Theory and Modelling)

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