  The metriplectic framework, which permits to formulate an algebraic structure
for dissipative systems, is applied to visco-resistive Magneto-Hydrodynamics
(MHD), adapting what had already been done for non-ideal Hydrodynamics (HD).
The result is obtained by extending the HD symmetric bracket and free energy to
include magnetic field dynamics and resistive dissipation. The correct
equations of motion are obtained once one of the Casimirs of the Poisson
bracket for ideal MHD is identified with the total thermodynamical entropy of
the plasma. The metriplectic framework of MHD is shown to be invariant under
the Galileo Group. The metriplectic structure also permits to obtain the
asymptotic equilibria toward which the dynamics of the system evolves. This
scheme is finally adapted to the two-dimensional incompressible resistive MHD,
that is of major use in many applications.
