  We investigate the dynamics of an N -level quantum system weakly coupled to a
thermal reservoir. For any fixed temperature of the bath there exists a natural
reference state: the equilibrium state of the system. Among all quantum
operations on the system one distinguishes Davies maps, they pre- serve the
equilibrium state, satisfy the detailed balance condition and belong to a
semi-group. A complete characterization of the three dimensional set of qubit
Davies maps is given. We analyze these maps and find their mini- mum output
entropy. A characterization of Davies maps for qutrits is also provided.
