  The thermalization process of the 2D Kitaev model is studied within the
Markovian weak coupling approximation. It is shown that its largest relaxation
time is bounded from above by a constant independent of the system size and
proportional to $\exp(2\Delta/kT)$ where $\Delta$ is an energy gap over the
4-fold degenerate ground state. This means that the 2D Kitaev model is not an
example of a memory, neither quantum nor classical.
