  General equations for conservative yet dissipative (entropy producing)
extended magnetohydrodynamics are derived from two-fluid theory. Keeping all
terms generates unusual cross-effects, such as thermophoresis and a current
viscosity that mixes with the usual velocity viscosity. While the Poisson
bracket of the ideal version of this model have already been discovered, we
determine its metriplectic counterpart that describes the dissipation. This is
done using a new and general thermodynamic point of view for deriving
dissipative brackets, a means of derivation that is natural for understanding
and creating dissipative brackets. Finally the formalism is used to study
dissipation in the Lagrangian variable picture where, in the context of
extended magnetohydrodynamics, nonlocal dissipative brackets naturally emerge.
