  We show that a reversible pumping mechanism operating between two states of a
kinetic network can give rise to Poisson transitions between these two states.
An external observer, for whom the pumping mechanism is not accessible, will
observe a Markov chain satisfying local detailed balance with an emerging
effective force induced by the hidden pump. Due to the reversibility of the
pump, the actual entropy production turns out to be lower than the coarse
grained entropy production estimated from the flows and affinities of the
resulting Markov chain. Moreover, in presence of a large time scale separation
between the fast pumping dynamics and the slow network dynamics, a finite
current with zero dissipation may be produced. We make use of these general
results to build a synthetase-like kinetic scheme able to reversibly produce
high free energy molecules at a finite rate and a rotatory motor achieving
100\% efficiency at finite speed.
