# Ergodic theorem

**the suppl. deserts** - hypothesis of the statistic mechanics means that a temporal average value is equal to the ensemble average value.
Ergodisch is a dynamic system then only if the trajectory comes each point in the phase space (is compatible with the outside obligations) in finite time arbitrarily close.

One uses this term therefore also in the system theory for the classification of systems and/or. the signals produced by them. A ergodisches signal is both aperiodic and recurring a stochastic (the coincidence subjected) stationary signal is. This is z. B. the case, if the signal has a salient wave shape, without this repeats itself in firm intervals. Ergodi systems tend to produce an output signal which is only little dependent on the suggestion for initial.

In the case of spontaneous symmetry refraction the ergodic theorem is hurt. There are then disjunkte ergodische ranges in the phase space. This can happen with phase transitions, approximately with solidifying a liquid.