  Using free probability constructions involving Cuntz-Pimsner C*-algebras we
show that the topological entropy of the free product of two automorphisms is
equal to the maximum of the individual entropies. As applications we show that
general free shifts have entropy zero. We show that any nuclear C*-dynamical
system admits an entropy preserving covariant embedding into the Cuntz algebra
on infinitely many generators. It follows that any simple nuclear purely
infinite C*-algebra admits an automorphism with any given value of entropy. As
a final application we show that if two automorphisms satisfy a CNT-variational
principle then so does their free product.
