  To an exact endofunctor of a triangulated category with a split-generator,
the notion of entropy is given by Dimitrov-Haiden-Katzarkov-Kontsevich, which
is a (possibly negative infinite) real-valued function of a real variable. In
this paper, we propose a conjecture which naturally generalizes the theorem by
Gromov-Yomdin, and show that the categorical entropy of a surjective
endomorphism of a smooth projective variety is equal to its topological
entropy. Moreover, we compute the entropy of autoequivalences of the derived
category in the case of the ample canonical or anti-canonical sheaf.
