  We study the GENERIC hydrodynamic theory for relativistic liquids formulated
by Ottinger and collaborators. We use the maximum entropy principle to derive
its conditions for linear stability (in an arbitrary reference frame) and for
relativistic causality. In addition, we show that, in the linear regime, its
field equations can be recast into a symmetric-hyperbolic form. Once rewritten
in this way, the linearised field equations turn out to be a particular
realization of the Israel-Stewart theory, where some of the Israel-Stewart free
parameters are constrained. This also allows us to reinterpret the GENERIC
framework in view of the principles of Extended Irreversible Thermodynamics
(EIT) and to discuss its physical relevance to model (possibly viscoelastic)
fluids.
