  Dissipation can be represented in Hamiltonian mechanics in an extended phase
space as a symplectic process. The method uses an auxiliary variable which
represents the excitation of unresolved dynamics and a Hamiltonian for the
interaction between the resolved dynamics and the auxiliary variable. This
method is applied to viscous dissipation (including hyper-viscosity) in a
two-dimensional fluid, for which the dynamics is non-canonical. We derive a
metriplectic representation and suggest a measure for the entropy of the
system.
