  In this paper, we study a dynamical property of an exact endofunctor $\Phi :
\mathcal{D} \to \mathcal{D}$ of a triangulated category $\mathcal{D}$. In
particular, we are interested in the following question: Given full
triangulated subcategories $\mathcal{A},\mathcal{B} \subset \mathcal{D}$ such
that $\Phi(\mathcal{A}) \subset \mathcal{A}$ and $\Phi(\mathcal{B}) \subset
\mathcal{B}$, how the categorical entropies of $\Phi|_\mathcal{A}$ and
$\Phi|_\mathcal{B}$ are related? To answer this question, we introduce new
entropy-type invariants using bounded (co-)t-structures with finite (co-)hearts
and prove their basic properties. We then apply these results to answer our
question for the situation where $\mathcal{A}$ has a bounded t-structure and
$\mathcal{B}$ has a bounded co-t-structure which are, in some sense, dual to
each other.
