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One of the fundamental open questions in plasma physics is the role of non-thermal particles distributions in poorly collisional plasma environments, a system that is 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 κ tends to be an uncorrelated time series, while the Maxwell–Boltzmann distribution shows a correlated stochastic processes behavior. Subsequently, we investigate the degree of temporary irreversibility of magnetic fluctuations that are 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 that is associated to the thermal equilibrium in the plasma, because the dissipative degree of the system increases as the value of κ parameter decreases and the distribution function departs from the Maxwell–Boltzmann equilibrium.

In this article, we address the reliance on probability density functions to obtain macroscopic properties in systems with multiple degrees of freedom as plasmas, and the limitations of expensive techniques for solving Equations such as Vlasov’s. We introduce the Ehrenfest procedure as an alternative tool that promises to address these challenges more efficiently. Based on the conjugate variable theorem and the well-known fluctuation-dissipation theorem, this procedure offers a less expensive way of deriving time evolution Equations for macroscopic properties in systems far from equilibrium. We investigate the application of the Ehrenfest procedure for the study of adiabatic invariants in magnetized plasmas. We consider charged particles trapped in a dipole magnetic field and apply the procedure to the study of adiabatic invariants in magnetized plasmas and derive Equations for the magnetic moment, longitudinal invariant, and magnetic flux. We validate our theoretical predictions using a test particle simulation, showing good agreement between theory and numerical results for these observables. Although we observed small differences due to time scales and simulation limitations, our research supports the utility of the Ehrenfest procedure for understanding and modeling the behavior of particles in magnetized plasmas. We conclude that this procedure provides a powerful tool for the study of dynamical systems and statistical mechanics out of equilibrium, and opens perspectives for applications in other systems with probabilistic continuity.

Kappa distributions (or κ -like distributions) represent a robust framework to characterize and understand complex phenomena with high degrees of freedom, as turbulent systems, using non-extensive statistical mechanics. Here we consider a coupled map lattice Langevin based model to analyze the relation of a turbulent flow, with its spatial scale dynamic, and κ -like distributions. We generate the steady-state velocity distribution of the fluid at each scale, and show that the generated distributions are well fitted by κ -like distributions. We observe a robust relation between the κ parameter, the scale, and the Reynolds number of the system, Re. In particular, our results show that there is a closed scaling relation between the level of turbulence and the κ parameter; namely κ ∼ Re k - 5 / 3 . We expect these results to be useful to characterize turbulence in different contexts, and our numerical predictions to be tested by observations and experimental setups.

Based on the extensive data accumulated during the COVID-19 pandemic, we put forward simple to implement indicators, that should alert authorities and provide early warnings of an impending sanitary crisis. In fact, Testing, Tracing, and Isolation (TTI) in conjunction with disciplined social distancing and vaccination were expected to achieve negligible COVID-19 contagion levels; however, they proved to be insufficient, and their implementation has led to controversial social, economic and ethical challenges. This paper focuses on the development of simple indicators, based on the experience gained by COVID-19 data, which provide a sort of yellow light as to when an epidemic might expand, despite some short term decrements. We show that if case growth is not stopped during the 7 to 14 days after onset, the growth risk increases considerably, and warrants immediate attention. Our model examines not only the COVID contagion propagation speed, but also how it accelerates as a function of time. We identify trends that emerge under the various policies that were applied, as well as their differences among countries. The data for all countries was obtained from ourworldindata.org . Our main conclusion is that if the reduction spread is lost during one, or at most two weeks, urgent measures should be implemented to avoid scenarios in which the epidemic gains strong impetus.

We focus on characterizing the high-energy emission mechanisms of blazars by analyzing the variability in the radio band of the light curves of more than a thousand sources. We are interested in assigning complexity parameters to these sources, modeling the time series of the light curves with the method of the Horizontal Visibility Graph (HVG), which allows us to obtain properties from degree distributions, such as a characteristic exponent to describe its stochasticity and the Kullback–Leibler Divergence (KLD), presenting a new perspective to the methods commonly used to study Active Galactic Nuclei (AGN). We contrast these parameters with the excess variance, which is an astronomical measurement of variability in light curves; at the same time, we use the spectral classification of the sources. While it is not possible to find significant correlations with the excess variance, the degree distributions extracted from the network are detecting differences related to the spectral classification of blazars. These differences suggest a chaotic behavior in the time series for the BL Lac sources and a correlated stochastic behavior in the time series for the FSRQ sources. Our results show that complex networks may be a valuable alternative tool to study AGNs according to the variability of their energy output.

Turbulence in space plasmas usually exhibits an energy cascade in which large-scale magnetic fluctuations are dominated by non-linear MHD wave–wave interactions following a Kolmogorov-like power-law spectrum. In addition, at scales at which kinetic effects take place, the magnetic spectrum follows a steeper power-law k−α shape given by a spectral index α>5/3. In a recent publication, a quasilinear model was used to study the evolution of ion temperatures in a collisionless plasma in which electromagnetic waves propagate along the background magnetic field, and it was found that the interaction between the plasma and a turbulent spectrum of ion-cyclotron waves may lead the plasma to states out of thermal equilibrium characterized by enhanced temperature anisotropies T⊥>T‖ and with a reduction in the parallel proton beta, which is consistent with space observations. Here, we complement such studies by analyzing the quasilinear interaction between plasma and a solar-wind-like turbulent spectrum of fast magnetosonic waves, and study the role of firehose instability (FHI) in the regulation of temperature anisotropy. Our results show that the presence of turbulence significantly modifies the FHI marginal stability threshold, as predicted from linear theory. Moreover, depending on the value of the plasma β, a turbulent magnetosonic spectrum may lead an initially thermally isotropic plasma to develop anisotropic states in which T⊥

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