  Recently Hod proposes a lower bound on the relaxation time of a perturbed
thermodynamic system. For gravitational systems this bound transforms into a
condition on the fundamental quasinormal frequency. We test the bound in some
spacetimes whose quasinormal frequencies are calculated exactly, as the
three-dimensional BTZ black hole, the D-dimensional de Sitter spacetime, and
the D-dimensional Nariai spacetime. We find that for some of these spacetimes
their fundamental quasinormal frequencies do not satisfy the bound proposed by
Hod.
