Memory effects in the two-level model for glasses

We study an ensemble of two-level systems interacting with a thermal bath. This is a well-known model for glasses. The origin of memory effects in this model is a quasistationary but nonequilibrium state of a single two-level system, which is realized due to a finite-rate cooling and slow thermally activated relaxation. We show that single-particle memory effects, such as negativity of the specific heat under reheating, vanish for a sufficiently disordered ensemble. In contrast, a disordered ensemble displays a collective memory effect [similar to the Kovacs effect], where nonequilibrium features of the ensemble are monitored via a macroscopic observable. An experimental realization of the effect can be used to further assess the consistency of the model.