Ergodic hypothesis
In physics and thermodynamics, the ergodic hypothesis says that, over long periods of time, the time spent by a system in some region of the phase space of microstates with the same energy is proportional to the volume of this region; i.e., that over long periods of time all accessible microstates are equiprobable. Liouville's theorem states that, for a Hamiltonian system, the local density of microstates following a particle path through phase space is constant as viewed by an observer moving with the ensemble—i.e., the convective time derivative is zero.