Before revision:  Our results also imply that for certain P that can be implemented without hidden states, having additional states available permits an implementation that generates less heat . These results can be seen as uncovering and investigating a novel type of cost of the physical resources needed to perform information processing---the size of a system's hidden state space .
After revision:  Our results also imply that for certain P that can be implemented without hidden states, having additional states available permits an implementation that generates less heat .