Before revision:  We demonstrate a fundamental tradeoff between the number of hidden states and the number of hidden timesteps needed to implement any given f using master equation dynamics. These tradeoffs are analogous to space / time tradeoffs in theoretical computer science. They can also be viewed as a type of resource theory, applying to master equation models of physical systems rather than quantum computation .
After revision:  We demonstrate a fundamental tradeoff between the number of hidden states and the number of hidden timesteps needed to implement any given f (x) .