  We consider the topological entropy of state space and quasi-state space
homeomorphisms induced from C*-algebra automorphisms. Our main result asserts
that, for automorphisms of separable exact C*-algebras, zero Voiculescu-Brown
entropy implies zero topological entropy on the quasi-state space (and also
more generally on the entire unit ball of the dual). As an application we
obtain a simple description of the topological Pinsker algebra in terms of
local Voiculescu-Brown entropy.
