  We give a microscopic explanation of both Debye and non-Debye thermalization
processes that have been recently reported by Gall and Kutner (Physica A 352,
347 (2005)). Due to reduction of the problem to first passage phenomena we
argue that relaxation functions f(t) introduced by the authors directly
correspond to survival probabilities S(t) of particles in the considered
systems. We show that in the case of broken ergodicity (i.e. in the case of
mirror collisions) the survival probability decays as a power law S(t)=\tau/t.
