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Entropy of categorical dynamics is defined byDmitrov-Haiden-Katzarkov-Kontsevich. Motivated by the fundamental theorem ofthe topological entropy due to Gromov-Yomdin, it is natural to ask an equalitybetween the entropy and the spectral radius of induced morphisms on thenumerical Grothendieck group. In this paper, we add two results on thisequality: the lower bound in a general setting and the equality for orbifoldprojective lines.

A note on entropy of auto-equivalences: lower bound and the case of orbifold projective lines