Before revision:  This raises the question of how they can arise in the real world. Here we investigate this question for the special case where the stochastic matrix being implemented is a (single-valued) function f. Examples range from logical gates in digital circuits to the (partial) function evaluated by an entire digital computer. As we show , any function f over a set of "visible" states X can be implemented--if the master equation implementing f has access to some additional "hidden" states not in X.
After revision:  This raises the question of how they arise in real-world systems like digital computers. We show that any deterministic map over some "visible" states X can be implemented--if the master equation implementing f has access to some additional "hidden" states not in X.