  Increasing the crowding in an environment does not necessarily trigger
negative differential mobility of strongly pushed particles. Moreover, the
choice of the model, in particular the kind of microscopic jump rates, may be
very relevant in determining the mobility. We support these points via simple
examples and we therefore address recent claims saying that crowding in an
environment is likely to promote negative differential mobility. Trapping of
tagged particles enhanced by increasing the force remains the mechanism
determining a drift velocity not monotonous in the driving force.

Statistical Mechanics;Soft Condensed Matter