Long time asymptotic properties of a class of environmentally induced dynamical
semigroups on arbitrary von Neumann algebras are discussed. Such a semigroup
selects observables, called effective observables, which are immune to the process
of decoherence and so evolve in a reversible automorphic way. In particular, it is
shown that effective observables of the quantum system in the thermodynamic limit
may behave like simple classical dynamical systems.