  From molecular machines to quantum dots, a wide range of mesoscopic systems
can be modeled by periodically driven Markov processes, or stochastic pumps.
Currents in the stochastic pumps are delimited by an exact no-go condition
called the no-pumping theorem (NPT). The letter presents a unified treatment of
all the adaptations of NPT known so far, and further extends it to systems with
many species of interacting particles.
