  A recently proposed universal lower-bound to the characteristic relaxation
times of perturbed thermodynamic systems, derived from quantum information
theory and (classical) thermodynamics and known to be saturated for (certain)
black holes, is investigated in the light of the gravity/thermodynamics
connection. A statistical-mechanical property, unrelated to gravity, essential
for the validity of the generalized covariant entropy bound, namely the
existence of a lower-limiting value l* for the size of thermodynamic systems,
is found to provide a way to understand the universal relaxation bound, thus
regardless of the kind of foundations (i.e. whether conventional or
information-based) of the statistical-mechanical description. As a by-product
an example of a conventional system (i.e. not a black hole) seemingly
saturating the universal relaxation bound is provided.
