# On the Statistical Foundations of Kaluza's Magnetohydrodynamics

## TL;DR

This paper develops a statistical framework for magnetohydrodynamics using a 5D relativistic approach, deriving transport equations for charged fluids with electromagnetic fields based on kinetic theory.

## Contribution

It introduces a novel 5D relativistic kinetic theory framework to derive MHD transport equations, connecting Kaluza's approach with statistical physics.

## Key findings

- Derived transport equations for dilute charged fluids in electromagnetic fields.
- Evaluated the 5D stress-energy tensor using relativistic Jüttner functions.
- Outlined the potential of Kaluza-type models for magnetohydrodynamics.

## Abstract

The introduction of electromagnetic fields into the Boltzmann equation following a 5D general relativistic approach is considered in order to establish the transport equations for dilute charged fluids in the presence of a weak electromagnetic field. The conserved 5D stress-energy tensor is evaluated using the J\"uttner function for non-degenerate relativistic gases in local equilibrium, and the evolution equations for the local thermodynamic variables are established by means of relativistic kinetic theory. An outline of the possibilities offered by the Kaluza-type approach to MHD is also included.