  An optimal finite-time process drives a given initial distribution to a given
final one in a given time at the lowest cost as quantified by total entropy
production. We prove that for system with discrete states this optimal process
involves non-conservative driving, i.e., a genuine driving affinity, in
contrast to the case of system with continuous states. In a multicyclic
network, the optimal driving affinity is bounded by the number of states within
each cycle. If the driving affects forward and backwards rates
non-symmetrically, the bound additionally depends on a structural parameter
characterizing this asymmetry.
