Kappa distributions in the framework of superstatistics

Abstract

The kappa distribution of velocities appears routinely in the study of collisionless plasmas present in Earth's magnetosphere, the solar wind among other contexts where particles are unable to reach thermal equilibrium. Originally justified through the use of Tsallis' non-extensive statistics, nowadays there are alternative frameworks that provide insight into these distributions, such as superstatistics. In this work we review the derivation of the multi-particle and single-particle kappa distributions for collisionless plasmas within the framework of superstatistics, as an alternative to the use of non-extensive statistics. We also show the utility of the superstatistical framework in the computation of expectation values under kappa distributions. Some consequences of the superstatistical formalism regarding correlations, temperature and entropy of kappa-distributed plasmas are also discussed.

References in corpus (23)

• Superstatistics
• Kappa distributions: theory and applications in space plasmas
• Non Linear Kinetics underlying Generalized Statistics
• Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics
• Superstatistics: Theory and Applications
• A critique of non-extensive q-entropy for thermal statistics
• Maximum Entropy Principle in statistical inference: case for non-Shannonian entropies
• Nonadditive Entropies Yield Probability Distributions with Biases not Warranted by the Data
• Bayesian approach to superstatistics
• Superstatistics approach to path integral for a relativistic particle
• Single-particle velocity distributions of collisionless, steady-state plasmas must follow Superstatistics
• Universality of market superstatistics
• Superstatistics and the effective QCD phase diagram
• Entropy, Information, and the Updating of Probabilities
• Physical correlations lead to kappa distributions
• On the Relation between Kappa Distribution Functions and the Plasma Beta Parameter in the Earth Magnetosphere: THEMIS observations
• A maximum entropy thermodynamics of small systems
• Temperature is not an observable in superstatistics
• Conceptual Inadequacy of the Shore and Johnson Axioms for Wide Classes of Complex Systems
• Fluctuating temperature outside superstatistics: thermodynamics of small systems
• Fokker-Planck Theory of Nonequilibrium Systems Governed by Hierarchical Dynamics
• Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas
• A superstatistical measure of distance from canonical equilibrium