Formulation of the relativistic heat equation and the relativistic kinetic Fokker-Planck equation using GENERIC

TL;DR

This paper formulates relativistic heat and kinetic Fokker-Planck equations within the GENERIC framework, demonstrating their consistency as relativistic extensions of classical equations and identifying the relativistic Maxwellian as their stationary solution.

Contribution

It introduces a GENERIC-based formulation for relativistic heat and Fokker-Planck equations, providing a new theoretical foundation for these relativistic models.

Findings

Relativistic Maxwellian distribution is the stationary solution.

The equations are justified as meaningful relativistic generalizations.

The GENERIC framework is successfully applied to these equations.

Abstract

In this paper, we formulate the relativistic heat equation and the relativistic kinetic Fokker-Planck equations into the GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) framework. We also show that the relativistic Maxwellian distribution is the stationary solution of the latter. The GENERIC formulation provides an alternative justification that the two equations are meaningful relativistic generalizations of their nonrelativistic counterparts.