Stochastic pumping of particles with zero-range interactions

We consider a model of a stochastic pump in which many particles jump between sites along a ring. The particles interact with each other via zero-range interactions. We argue that for slow driving the dynamics can be approximated by a nonlinear diffusion equation. This nonlinear equation is then used to derive a current decomposition formula, expressing the current as a sum of two contributions. The first is from the momentary steady state while the second arises due to the variation of the density with time, and is identified as the pumped current. The dynamics is found to satisfy the no-pumping theorem for cyclic processes, in agreement with recent results in discrete systems.