  We show that the the shift on the reduced C*--algebras of RD--groups,
including the free group on infinitely many generators, and the amalgamated
free product C*--algebras, enjoys the very strong ergodic property of the
convergence to the equilibrium. Namely, the free shift converges, pointwise in
the weak topology, to the conditional expectation onto the fixed--point
subalgebra. Provided the invariant state is unique, we also show that such an
ergodic property cannot be fulfilled by any classical dynamical system, unless
it is conjugate to the trivial one--point dynamical system.
