  We present an example revealing that the sign of the "momentum" $P$ of the
Wigner "distribution" function $f(q, P)$ is not necessarily associated with the
direction of motion in the real world. This aspect, which is not related to the
well known limitation of the Wigner function that traces back to the
Heisenberg's uncertainty principle, is particularly relevant in transport
studies, wherein it is helpful to distinguish between electrons flowing from
electrodes into devices and vice versa.
