Before revision:  Here we show that any conditional distribution P can however be implemented if the master equation dynamics has access to additional "hidden" states , not in X . We investigate how the minimal number of such hidden states needed to implement some P in a thermodynamically reversible manner depends on P.
After revision:  Here we show that any conditional distribution P can however be implemented if the master equation dynamics has access to additional "hidden" states , not in X are available. Moreover, we show that it is always possible to implement P in a thermodynamically reversible manner. We then investigate a novel cost of the physical resources needed to implement a given distribution P: the minimal number of such hidden states needed to implement some P in a thermodynamically reversible manner depends on P.