  We have studied the dynamics of a generalized toric code based on qudits at
finite temperature by finding the master equation coupling the code's degrees
of freedom to a thermal bath. As a consequence, we find that for qutrits new
types of anyons and thermal processes appear that are forbidden for qubits.
These include creation, annihilation and diffusion throughout the system code.
It is possible to solve the master equation in a short-time regime and find
expressions for the decay rates as a function of the dimension $d$ of the
qudits. Although we provide an explicit proof that the system relax to the
Gibbs state for arbitrary qudits, we also prove that above a certain crossing
temperature, qutrits initial decay rate is smaller than the original case for
qubits. Surprisingly this behavior only happens with qutrits and not with other
qudits with $d>3$.
