# Single-particle velocity distributions of collisionless, steady-state plasmas must follow Superstatistics

## TL;DR

This paper develops a statistical mechanical framework for collisionless, steady-state plasmas that derives velocity distributions without entropy, recovering superstatistics as a special case and introducing a microscopic inverse temperature definition.

## Contribution

It introduces a probability-based formalism for plasma velocity distributions, generalizing superstatistics and avoiding reliance on entropy concepts.

## Key findings

- Superstatistics is recovered as a limiting case.
- A microscopic definition of inverse temperature is provided.
- Non-extensivity arises from correlations, not assumed a priori.

## Abstract

The correct modelling of velocity distribution functions for particles in steady-state plasmas is a central element in the study of nuclear fusion and also in the description of space plasmas. In this work, a statistical mechanical formalism for the description of collisionless plasmas in a steady state is presented, based solely on the application of the rules of probability and not relying on the concept of entropy. Beck and Cohen's superstatistical framework is recovered as a limiting case, and a "microscopic" definition of inverse temperature $\beta$ is given. Non-extensivity is not invoked a priori but enters the picture only through the analysis of correlations between parts of the system.