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The no-pumping theorem states that seemingly natural driving cycles ofstochastic machines fail to generate directed motion. Initially derived forsingle particle systems, the no-pumping theorem was recently extended tomany-particle systems with zero-range interactions. Interestingly, it is knownthat the theorem is violated by systems with exclusion interactions. These twoparadigmatic interactions differ by two qualitative aspects: the range ofinteractions, and the dependence of branching fractions on the state of thesystem. In this work two different models are studied in order to identify thequalitative property of the interaction that leads to breakdown of no-pumping.A model with finite-range interaction is shown analytically to satisfyno-pumping. In contrast, a model in which the interaction affects theprobabilities of reaching different sites, given that a particle is making atransition, is shown numerically to violate the no-pumping theorem. The resultssuggest that systems with interactions that lead to state-dependent branchingfractions do not satisfy the no-pumping theorem.

The validity of the no-pumping theorem in systems with finite-range interactions between particles