  We explore some thermodynamical consequences of accelerated universes driven
by a running cosmological constant (CC) from the renormalization group (RG).
Application of the generalized second law (GSL) of gravitational thermodynamics
to a framework where the running of the CC goes at the expense of energy
transfer between vacuum and matter, strongly restricts the mass spectrum of a
(hypothetical) theory controlling the CC running. We find that quantum effects
driving the running of the CC should be dominated by a trans-planckian mass
field, in marked contrast with the GUT-scale upper mass bound obtained by
analyzing density perturbations for the running CC. The model shows compliance
with the holographic principle.
