A spatially extended model for a collective molecular motor is presented. T
he system is driven far from equilibrium by a quenched additive noise. As a
result, it exhibits anomalous transport properties, namely, negative resis
tance and a clockwise hysteresis cycle. The phase diagram and the region of
negative resistance are calculated using a Weiss mean field theory. Intuit
ive explanations of the anomalous transport properties as well as details o
f its energetics are given.