  The theoretical cornerstone of statistical mechanics is the ergodic
assumption that all accessible configurations of a physical system are equally
likely. Here we show how such property arises when an open quantum system is
continuously perturbed by an external environment effectively observing the
system at random times while the system dynamics approaches the quantum Zeno
regime. In this context, by large deviation theory we analytically show how the
most probable value of the probability for the system to be in a given state
eventually deviates from the non-stochastic case when the Zeno condition is not
satisfied. We experimentally test our results with ultra-cold atoms prepared on
an atom chip.
