  We defne the resource non-increasing (RNI) framework to study the dynamical
resource theory. With such a defnition, we propose several potential
quantifcation candidates under various free operation sets. For explicit
demonstrations, we quantify the quantum dynamical coherence in the scenarios
with and without post-selective measurements. Correspondingly, we show that
maximally incoherent operations (MIO) and incoherent operations (IO) in the
static coherence resource theory are free in the sense of dynamical coherence.
We also provide operational meanings for the measures by the quantum
discrimination tasks. Moreover, for the dynamical total coherence, we also
present convenient measures and give the analytic calculation for the amplitude
damping channel.
