The maximum speed of dynamical evolution

We discuss the problem of counting the maximum number of distinct states that an isolated physical system can pass through in a given period of time — its maximum speed of dynamical evolution. Previous analyses have given bounds in terms of ΔE, the standard deviation of the energy of the system; here we give a strict bound that depends only on E − E0, the system's average energy minus its ground state energy. We also discuss bounds on information processing rates implied by our bound on the speed of dynamical evolution. For example, adding 1 J of energy to a given computer can never increase its processing rate by more than about 3 × 1033 operations per second.