Relaxation in two-level long-range-memory systems

Recently, new rigorous results concerning integrals of exact memory functions in the time-convolution Generalized Master Equations (GME) for state occupation probabilities, governing relaxation of open quantum systems, have been obtained. They include that a) time integrals of exact memories and b) memories w _ij(t) have tails unobtainable by perturbational arguments which cause that does not exist or is infinite. For a two-level system, a simple model for such memories is considered and solved. It is concluded that GME may yield that with increasing time, the system unphysically more and more deviates from equilibrium, indicating thus instability of the equilibrium distribution. Thus, in contrast to, e.g., the famous Boltzmann equation, the mathematical structure of GME alone does not guarantee the stability of the equilibrium state.