# Ergodic hypothesis

In

physics and

thermodynamics, 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.