  In the pioneer work by Dimitrov-Haiden-Katzarkov-Kontsevich, they introduced
various categorical analogies from classical theory of dynamical systems. In
particular, they defined the entropy of an endofunctor on a triangulated
category with a split generator. In the connection between categorical theory
and classical theory, a stability condition on a triangulated category plays
the role of a measured foliation so that one can measure the "volume" of
objects, called the mass, via the stability condition. The aim of this paper is
to establish fundamental properties of the growth rate of mass of objects under
the mapping by the endofunctor and to clarify the relationship between the
entropy and that. We also show that they coincide under a certain condition.
