General no-go condition for stochastic pumping

The control of chemical dynamics requires understanding the effect of time-dependent transition rates between states of chemomechanical molecular configurations. Pumping refers to generating a net current, e.g., per period in the time dependence, through a cycle of consecutive states. The work of artificial machines or synthesized molecular motors depends on it. In this paper we give short and simple proofs of no-go theorems, some of which appeared before but here with essential extensions to non-Markovian dynamics, including the study of the diffusion limit. It allows to exclude certain protocols in the working of chemical motors where only the depth of the energy well is changed in time and not the barrier height between pairs of states. We also show how pre-existing steady state currents are, in general, modified with a multiplicative factor when this time dependence is turned on. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3446811]