The maximum speed of dynamical evolution

TL;DR

The paper derives universal bounds on how fast a quantum system can evolve through mutually orthogonal states, grounding the limit in the system's average energy above its ground state. It establishes a short-time bound tau_perp >= h/(4E) and extends it to long sequences, showing that macroscopic systems can in principle pass through many orthogonal states at a rate nu_perp = 2E/h. It also connects energy to the maximal rate of computation-like state changes and develops the concept of an energy-time action volume Et that aggregates the accessible evolution over time. The results clarify how energy distribution, subsystem composition, and reference frames affect dynamical speed and have implications for fundamental limits on information processing.

Abstract

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 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 one Joule of energy to a given computer can never increase its processing rate by more than about 3x10^33 operations per second.