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 $exp(2Delta/kT)$ 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.
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