On entropy of $\mathbb{P}$-twists

Abstract

We show that the $\mathbb{P}$-twist associated to any $\mathbb{P}$-object of a smooth project variety is not conjugate to a standard autoequivalence. This result is obtained by computing the categorical entropy functions of $\mathbb{P}$-twists. We also determine the categorical polynomial entropy of spherical twists and $\mathbb{P}$-twists, under an additional assumption.