InterJournal Complex Systems, 59 Status: Accepted |
Manuscript Number: [59] Submission Date: 963011 |
The maximum speed of dynamical evolution |
Subject(s): CX.07
Category: Brief Article
Abstract:
Quantum mechanics tells us how to count the number of distinct states that an isolated physical system can be in, and thus allows us to quantify the maximum amount of information that can be encoded in this physical system. We discuss here the related problem of quantifying the maximum number of distinct states that such a system can pass through in a given period of time---the maximum speed of dynamical evolution. We will conclude that this rate is governed by the average energy E of the system. Previous analyses have given bounds in terms of the standard deviation dE, but dE can be arbitrarily large for a fixed value of E. We show here that, given a fixed Hamiltonian and a fixed average energy E, no state can evolve into an orthogonal state in a time less than h/4(E-E_0), where E_0 is the ground state energy of the system. We also discuss the maximum rate for long evolutions, and bounds on information processing rates implied by bounds 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.
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