As the time span for a single trajectory and the evolution time for an ensemble increase, their resulting spatial distributions in the phase space converge to being identical. When these distributions become identical, the time average of any function is equal to its ensemble average.
Conditions: The system exhibits ergodicity.; The spatial distributions of the single trajectory and the ensemble are identical.
As the time span for a single trajectory and the evolution time for an ensemble increase, their resulting spatial distributions in the phase space converge to being identical. When these distributions become identical, the time average of any function is equal to its ensemble average.
Conditions: The system exhibits ergodicity.; The spatial distributions of the single trajectory and the ensemble are identical.