Entropy of an autoequivalence on Calabi-Yau manifolds

We prove that the categorical entropy of the autoequivalence $T_{mathcal{O}}circ(-otimesmathcal{O}(-1))$ on a Calabi-Yau manifold is the unique positive real number $lambda$ satisfying $$ sum_{kgeq 1}frac{chi(mathcal{O}(k))}{e^{klambda}}=e^{(d-1)t}. $$ We then use this result to construct the first counterexamples of a conjecture on categorical entropy by Kikuta and Takahashi.