The ergodic hypothesis due to Boltzmann represents a foundation of statistical mechanics. In spite of its importance, whether the hypothesis is really valid, or even to what extent it is valid, is still not established. To help make the ergodic hypothesis more amenable to physical tests, we need to develop a workable ergodic condition. If a system is Hermitian, it is possible to formulate an ergodic condition using a dynamical response function appearing in inelastic scattering processes. The ergodic condition is expressed in terms of the relaxation function. It describes when the hypoth-esis is valid and when it can break down. As an application we show that a system ceases to be ergodic when the critical temperature is approached.

PACS numbers: 05.30.--d, 05.20.--y