, the ergodic hypothesis
says that, over long periods of time, the time spent in some region of the phase space
of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over long period of time. Equivalently, it says that time average and average over the statistical ensemble
are the same.
Ergodic theory is a branch of mathematics which deals with dynamical systems which satisfy this hypothesis.