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 in fact be implemented---if 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.