  We consider a class of quantum dissipative semigroup on a von-Neumann algebra
which admits a normal invariant state. We investigate asymptotic behavior of
the dissipative dynamics and their relation to that of the canonical Markov
shift. In case the normal invariant state is also faithful, we also extend the
notion of `quantum detailed balance' introduced by Frigerio-Gorini and prove
that forward weak Markov process and backward weak Markov process are
equivalent by an anti-unitary operator.
