 In particular, we show that  having access to one extra binary degree of freedom (doubling the  number of states) is sufficient to carry out any P  . Our results provide a novel type of bound on the physical resources needed to perform information processing---the size of a system's  state space.
<meaning-changed>  In particular, we show that  having access to one extra binary degree of freedom (doubling the  number of states) is sufficient to carry out any P  . Our results provide a novel type of bound on the physical resources needed to perform information processing---the size of a system's  state space.
 In particular, we show that having access to one extra binary degree of freedom (doubling the number of states) is sufficient to carry out any P with zero entropy production . Our results provide a novel type of bound on the physical resources needed to perform information processing---the size of a system's state space.