  Given a categorical dynamical system, i.e. a triangulated category together
with an endofunctor, one can try to understand the complexity of the system by
computing the entropy of the endofunctor. Computing the entropy of the
composition of two endofunctors is hard, and in general the result doesn't have
to be related to the entropy of the single pieces. In this paper we compute the
entropy of the composition of two spherical twists around spherical objects,
showing that it depends on the dimension of the graded vector space of
morphisms between them. As a consequence of these computations we produce new
counterexamples to Kikuta-Takahashi's conjecture. In particular, we describe
the first counterexamples in odd dimension and examples for the $d$-Calabi-Yau
Ginzburg dg algebra associated to the $A_2$ quiver.
