Stochastic pumps of interacting particles

The design and synthesis of molecules that operate like microscopic machines is of fundamental importance. Such systems can be modelled theoretically by stochastic dynamics in which the system makes thermally activated transitions between a finite set of coarse-grained states. Artificial molecular machines can be driven away from thermal equilibrium in ways not found in biological molecular motors, in particular by time variation of external parameters.  Such systems are often termed stochastic pumps. We demonstrate that a seemingly natural protocol of driving such systems does not work.  We argue that this result holds also for systems of several particles with zero range interactions.