Applying the horizontal visibility graph method to study irreversibility of electromagnetic turbulence in non-thermal plasmas

TL;DR

This paper applies the Horizontal Visibility Graph method to analyze magnetic field fluctuations in plasma simulations, revealing how non-thermal particle distributions influence the irreversibility and entropy of plasma turbulence.

Contribution

It introduces a novel application of directed HVG to distinguish irreversibility in plasma turbulence based on particle distribution functions.

Findings

KLD can quantify the degree of irreversibility in plasma turbulence.

Kappa distributions tend to be uncorrelated, while Maxwell-Boltzmann shows correlated behavior.

Irreversibility increases as the plasma departs from thermal equilibrium.

Abstract

One of the fundamental open questions in plasma physics is the role of non-thermal particles distributions in poorly collisional plasma environments, a system commonly found throughout the Universe, e.g. the solar wind and the Earth's magnetosphere correspond to natural plasma physics laboratories in which turbulent phenomena can be studied. Our study perspective is born from the method of Horizontal Visibility Graph (HVG) that has been developed in the last years to analyze time series avoiding the tedium and the high computational cost that other methods offer. Here we build a complex network based on directed HVG technique applied to magnetic field fluctuations time series obtained from Particle In Cell (PIC) simulations of a magnetized collisionless plasma to distinguish the degree distributions and calculate the Kullback-Leibler Divergence (KLD) as a measure of relative entropy of data sets produced by processes that are not in equilibrium. First, we analyze the connectivity probability distribution for the undirected version of HVG finding how the Kappa distribution for low values of $\kappa$ tends to be an uncorrelated time series, while the Maxwell-Boltzmann distribution shows a correlated stochastic processes behavior. Then, we investigate the degree of temporary irreversibility of magnetic fluctuations self-generated by the plasma, comparing the case of a thermal plasma (described by a Maxwell-Botzmann velocity distribution function) with non-thermal Kappa distributions. We have shown that the KLD associated to the HVG is able to distinguish the level of reversibility associated to the thermal equilibrium in the plasma because the dissipative degree of the system increases as the value of $\kappa$ parameter decreases and the distribution function departs from the Maxwell-Boltzmann equilibrium.