  The perturbation theory based on typicality introduced in Ref. [1] and
further refined in Refs. [2, 3] provides a powerful tool since it is intended
to be applicable to a wide range of scenarios while relying only on a few
parameters. Even though the authors present various examples to demonstrate the
effectiveness of the theory, the conditions used in its derivation are often
not thoroughly checked. It is argued that this is justified (without analytical
reasoning) by the robustness of the theory. In the paper at hand, said
perturbation theory is tested on three spin-based models. The following
criteria are taken into focus: the fulfillment of the conditions, the accuracy
of the predicted dynamics and the relevance of the results with respect to a
mesoscopic case.
