  From the perspective of Markovian piecewise deterministic processes (PDPs),
we investigate the derivation of a kinetic uncertainty relation (KUR), which
was originally proposed in Markovian open quantum systems. First, stationary
distributions of classical PDPs are explicitly constructed. Then, a tilting
method is used to derive a rate functional of large deviations. Finally, based
on an improved approximation scheme, we recover the KUR. These classical
results are directly extended to the open quantum systems. We use a driven
two-level quantum system to exemplify the quantum results.
