  We study the relationship between the categorical entropy of the twist and
cotwist functors along a spherical functor. In particular, we prove the
categorical entropy of the twist functor coincides with that of the cotwist
functor if the essential image of the right adjoint functor of the spherical
functor contains a split-generator. We also see our results generalize the
computations of the categorical entropy of spherical twists and
$\mathbb{P}$-twists by Ouchi and Fan. As an application, we apply our results
to the Gromov--Yomdin type conjecture by Kikuta--Takahashi.
