  Negative differential mobility is the phenomenon in which the velocity of a
particle decreases when the force driving it increases. We study this
phenomenon in Markov jump models where a particle moves in the presence of
walls that act as traps. We consider transition rates that obey local detailed
balance but differ in normalisation, the inclusion of a rate to cross a wall
and a load factor. We illustrate the full counting statistics for different
choices of the jumping rates. We also show examples of thermodynamic
uncertainty relations. The variety of behaviours we encounter highlights that
negative differential mobility depends crucially on the chosen rates and points
out the necessity that such choices should be based on proper coarse-graining
studies of a more microscopic description.
