  We compute rigorously the ground and equilibrium states for Kitaev's model in
2D, both the finite and infinite version, using an analogy with the 1D Ising
ferromagnet. Next, we investigate the structure of the reduced dynamics in the
presence of thermal baths in the Markovian regime. Special attention is paid to
the dynamics of the topological freedoms which have been proposed for storing
quantum information.
