  The Landau-Lifshitz-Gilbert (LLG) equation describes the dynamics of a damped
magnetization vector that can be understood as a generalization of Larmor spin
precession. The LLG equation cannot be deduced from the Hamiltonian framework,
by introducing a coupling to a usual bath, but requires the introduction of
additional constraints. It is shown that these constraints can be formulated
elegantly and consistently in the framework of dissipative Nambu mechanics.
This has many consequences for both the variational principle and for
topological aspects of hidden symmetries that control conserved quantities. We
particularly study how the damping terms of dissipative Nambu mechanics affect
the consistent interaction of magnetic systems with stochastic reservoirs and
derive a master equation for the magnetization. The proposals are supported by
numerical studies using symplectic integrators that preserve the topological
structure of Nambu equations. These results are compared to computations
performed by direct sampling of the stochastic equations and by using closure
assumptions for the moment equations, deduced from the master equation.
