No-pumping theorem for many particle stochastic pumps

Stochastic pumps are models of artificial molecular machines which are driven by periodic time variation of parameters, such as site and barrier energies. The no-pumping theorem states that no directed motion is generated by variation of only site or barrier energies [S. Rahav, J. Horowitz, and C. Jarzynski, Phys. Rev. Lett., 101, 140602 (2008)]. We study stochastic pumps of several interacting particles and demonstrate that the net current of particles satisfy an additional no- pumping theorem.