  Driven particles in presence of crowded environment, obstacles or kinetic
constraints often exhibit negative differential mobility (NDM) due to their
decreased dynamical activity. We propose a new mechanism for complex
many-particle systems where slowing down of certain {\it non-driven} degrees of
freedom by the external field can give rise to NDM. This phenomenon, resulting
from inter-particle interactions, is illustrated in a pedagogical example of
two interacting random walkers, one of which is biased by an external field
while the same field only slows down the other keeping it unbiased. We also
introduce and solve exactly the steady state of several driven diffusive
systems, including a two species exclusion model, asymmetric misanthrope and
zero-range processes, to show explicitly that this mechanism indeed leads to
NDM.
