Before revision: We consider the problem of constructing a physical system whose evolution implements some specified stochastic matrix. We restrict attention to physical systemswhose dynamics can be modeled with a time-inhomogeneous master equation over a finite state space, which includes many of the systems considered in stochastic thermodynamics. It is known that many stochastic matrices cannot be implemented by any master equation, even approximately.
After revision: Master equations are commonly used to model the dynamics of physical systems. Surprisingly, many deterministic maps x \rightarrow f(x) cannot be implemented by any master equation, even approximately.