Generalizing the running vacuum energy model and comparing with the
  entropic-force models
  We generalize the previously proposed running vacuum energy model by
including a term proportional to \dot{H}, in addition to the existing H^2 term.
We show that the added degree of freedom is very constrained if both low
redshift and high redshift data are taken into account. Best-fit models are
undistinguishable from LCDM at the present time, but could be distinguished in
the future with very accurate data at both low and high redshifts. We stress
the formal analogy at the phenomenological level of the running vacuum models
with recently proposed dark energy models based on the holographic or entropic
point of view, where a combination of \dot{H} and H^2 term is also present.
However those particular entropic formulations which do not have a constant
term in the Friedmann equations are not viable. The presence of this term is
necessary in order to allow for a transition from a decelerated to an
accelerated expansion. In contrast, the running vacuum models, both the
original and the generalized one introduced here contain this constant term in
a more natural way. Finally, important conceptual issues common to all these
models are emphasized.
