  Theoretical analyses of the random energy model with only two states and its
extension with a hierarchy of only two levels show that these models reproduce
out-of-equilibrium phenomena observed in experiments of glassy materials; the
rejuvenation effect (the chaos effect), i.e. the abrupt jump and subsequent
relaxation of the out-of-phase susceptibility as if the system rejuvenates when
the temperature is lowered, and the power-law relaxation of the two-time
correlation function. Our results suggest that also in an assembly of small
systems with relaxation times distributed broadly some of these interesting
out-of-equilibrium phenomena can be observed.
