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

•GENERIC formulation of the relativistic heat equation.•GENERIC formulation of the relativistic kinetic Fokker–Planck equations.•Alternative computations of the stationary solution of the relativistic kinetic FP equations.

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 non-relativistic counterparts.