  It is well known in the realm of quantum mechanics and information theory
that the entropy is non-decreasing for the class of unital physical processes.
However, in general, the entropy does not exhibit monotonic behavior. This has
restricted the use of entropy change in characterizing evolution processes.
Recently, a lower bound on the entropy change was provided in the work of
Buscemi, Das, and Wilde~[Phys.~Rev.~A~93(6),~062314~(2016)]. We explore the
limit that this bound places on the physical evolution of a quantum system and
discuss how these limits can be used as witnesses to characterize quantum
dynamics. In particular, we derive a lower limit on the rate of entropy change
for memoryless quantum dynamics, and we argue that it provides a witness of
non-unitality. This limit on the rate of entropy change leads to definitions of
several witnesses for testing memory effects in quantum dynamics. Furthermore,
from the aforementioned lower bound on entropy change, we obtain a measure of
non-unitarity for unital evolutions.
