  Let $\omega$ be a factor state on the quasi-local algebra $\cal{A}$ of
observables generated by a relativistic quantum field, which in addition
satisfies certain regularity conditions (satisfied by ground states and the
recently constructed thermal states of the $P(\phi)_2$ theory). We prove that
there exist space and time translation invariant states, some of which are
arbitrarily close to $\omega$ in the weak* topology, for which the time
evolution is weakly asymptotically abelian.
