Entropy of shifts on higher-rank graph C*-algebras

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Let OLambda be a higher rank graph C*-algebra of rank r. For every tuple p of non-negative integers there is a canonical completely positive map Phiᵖ on OLambda and a subshift Tᵖ on the path space X of the graph. We show that ht(Phiᵖ)=h(Tᵖ), where ht is Voiculescu's approximation entropy and h the classical topological entropy. For a higher rank Cuntz-Krieger algebra Oₘ we obtain ht(Phiᵖ)= log r(M₁ᵖ¹M₂ᵖ²... Mᵣᵖʳ), r being the spectral radius. This generalises Boca and Goldstein's result for Cuntz-Krieger algebras.