  In most cases, a small system weakly interacting with a thermal bath will
finally reach the thermal state with the temperature of the bath. We show that
this intuitive picture is not always true by a spin star model where non-Markov
effect predominates in the whole dynamical process. The spin star system
consists a central spin homogeneously interacting with an ensemble of identical
noninteracting spins. We find that the correlation time of the bath is
infinite, which implies that the bath has a perfect memory, and that the
dynamical evolution of the central spin must be non- Markovian. A direct
consequence is that the final state of the central spin is not the thermal
state equilibrium with the bath, but a steady state which depends on its
initial state.
