  We study numerically the damping of quantum oscillations and the increase of
entropy with time in model spin systems decohered by a spin bath. In some
experimentally relevant cases, the oscillations of considerable amplitude can
persist long after the entropy has saturated near its maximum, i.e. when the
system has been decohered almost completely. Therefore, the pointer states of
the system demonstrate non-trivial dynamics. The oscillations exhibit slow
power-law decay, rather than exponential or Gaussian, and may be observable in
experiments.
