  Let $ A $ be a finite connected graded cocommutative Hopf algebra over a
field $ k $. There is an endofunctor $ \mathsf{tw} $ on the stable module
category $ \mathrm{StMod}_A $ of $ A $ which twists the grading by $ 1 $. We
show the categorical entropy of $ \mathsf{tw} $ is zero. We provide a lower
bound for the categorical polynomial entropy of $ \mathsf{tw} $ in terms of the
Krull dimension of the cohomology of $ A $, and an upper bound in terms of the
existence of finite resolutions of $ A $-modules of a particular form. We
employ these tools to compute the categorical polynomial entropy of the twist
functor for examples of finite graded Hopf algebras over $ \mathbb{F}_2 $.
