Motivated by non-equilibrium phenomena in nature, we study dynamical systems
whose time-evolution is determined by non-stationary compositions of chaotic
maps. The constituent maps are topologically transitive Anosov diffeomorphisms
on a 2-dimensional compact Riemannian manifold, which are allowed to change
with time - slowly, but in a rather arbitrary fashion. In particular, such
systems admit no invariant measure. By constructing a coupling, we prove that
any two sufficiently regular distributions of the initial state converge
exponentially with time.