  The control of chemical dynamics requires understanding the effect of
time-dependent transition rates between states of chemo-mechanical molecular
configurations. Pumping refers to generating a net current, e.g. per period in
the time-dependence, through a cycle of consecutive states. The working 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.
