Weak ergodicity breaking induced by global memory effects.

Abstract

We study the phenomenon of weak ergodicity breaking for a class of globally correlated random walk dynamics defined over a finite set of states. The persistence in a given state or the transition to another one depends on the whole previous temporal history of the system. A set of waiting time distributions, associated to each state, sets the random times between consecutive steps. Their mean value is finite for all states. The probability density of time-averaged observables is obtained for different memory mechanisms. This statistical object explicitly shows departures between time and ensemble averages. While the residence time in each state may have a divergent mean value, we demonstrate that this condition is in general not necessary for breaking ergodicity. Hence, we conclude that global memory effects are an alternative mechanism able to induce ergodicity breaking without involving power-law statistics. Analytical and numerical calculations support these results.