On the structural compatibility of a general formalism for nonequilibrium dynamics with special relativity

In the context of an imperfect fluid with heat flow we show that a recently developed formalism for nonequilibrium systems (GENERIC: general equation for the nonequilibrium reversible-irreversible coupling) is compatible with the structure of special relativity. An additional generalized thermal force variable, in a certain limit related to the heat flux, needs to be introduced. By doing so, common features of GENERIC and extended irreversible thermodynamics are revealed, and a new set of equations for relativistic imperfect fluids is formulated. These equations are compared to the classical first-order theory of Eckart, the second-order theory of Israel, and the equations derived by relativistic kinetic theory. The GENERIC generators of reversible and irreversible dynamics, energy and entropy, occur as the time components of the energy–momentum tensor and the entropy current four-vector, respectively