Comment on "Equilibration Time Scales of Physically Relevant Observables"

Putting a generally valid upper bound on equilibration times of physically relevant observables is a much pursued endeavor. Recently, such a bound has been suggested by Garcia-Pintos et al. While the mathematical correctness of the bound as such is undisputed, its concrete calculation requires the knowledge of certain quantities, which Garcia-Pintos et al. assess by means of assumptions. We show that, e.g., in standard cases of slow, exponential equilibration, (at least) one of these assumptions is not valid. This demonstration highlights the difficulty to judge the validity of the above assumptions without further information. Such information is, in general, very hard to obtain.