# Maximum-Entropy States for Magnetized Ion Transport

## TL;DR

This paper derives maximum-entropy states for magnetized ion transport in plasmas, revealing that under certain constraints, the equilibrium distribution aligns with the impurity pinch relation, independent of collision details.

## Contribution

It introduces a maximum-entropy derivation for ion transport states that relies solely on conservation laws, not collision specifics.

## Key findings

- Maximum-entropy states correspond to impurity pinch relations.
- Derivation is independent of collision operator details.
- Provides a unified framework for ion transport equilibrium.

## Abstract

For a plasma with fixed total energy, number of particles, and momentum, the distribution function that maximizes entropy is a Boltzmann distribution. If, in addition, the rearrangement of charge is constrained, as happens on ion-ion collisional timescales for cross-field multiple-species transport, the maximum-entropy state is instead given by the classic impurity pinch relation. The maximum-entropy derivation, unlike previous approaches, does not rely on the details of the collision operator, only on the presence of certain conservation properties.