Before revision:  We also show that any master equation implementing a given map can be decomposed into a sequence of "hidden" timesteps, demarcated by changes in what transitions are allowed under the rate matrix. Often there is a real-world cost for each additional hidden state, and for each additional hidden timestep.
After revision:  We also show that any master equation implementing a given map can be decomposed into a sequence of "hidden" timesteps, demarcated by changes in what state-to-state transitions have nonzero probability. In many real-world situations there is a real-world cost for each additional hidden state, and for each additional hidden timestep.