Abstract

Let {S_i}_i=1ⁿ be generators of the Cuntz algebra O_n and let Φ be the *-endomorphism of O_n defined by Φ(x) = ∑ _i=1ⁿS_ixS_i^*. Then both of Connes–Narnhofer–Thirring’s entropy h_φ(Φ) and Voiculescu’s topological entropy ht(Φ) are log n, where φ is the unique log n-KMS state of O_n. Also Longo’s canonical endomorphism for N ⊂ M have the same entropy log n, where the inclusion N ⊂ M comes from O_n .

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