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

Abstract

h i g h l i g h t s • 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. a b s t r a c tIn this paper, we formulate the relativistic heat equation and the relativistic kinetic FokkerPlanck equations into the GENERIC (General Equation for Non-Equilibrium ReversibleIrreversible 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.

A minimizing-movements approach to GENERIC systems

“…In the last years, GENERIC has attracted increasing attention and has been applied to a number of situations ranging from complex fluids [18], to dissipative quantum mechanics [32], to thermomechanics [5,[21][22][23]31], to electromagnetism [24], to shape-memory alloys [3], to the Vlasov-Fokker-Planck [13,14,20] and the Boltzmann equation [35], and to large-deviation limits of reversible stochastic processes [26,27].…”