A proof by graphical construction of the no-pumping theorem of stochastic pumps

A stochastic pump is a Markov model of a mesoscopic system evolving under the control of externally varied parameters. In the model, the system makes random transitions among a network of states. For such models, a 'no-pumping theorem' has been obtained, which identifies minimal conditions for generating directed motion or currents. We provide a derivation of this result using a simple graphical construction on the network of states.

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