Evolution of dissipative and non-dissipative universes in holographic
  cosmological models with a power-law term
  Density perturbations related to structure formations are expected to be
different in dissipative and non-dissipative universes, even if the background
evolution of the two universes is the same. To clarify the difference between
the two universes, first-order density perturbations are studied, using two
types of holographic cosmological models. The first type is a "$\Lambda(t)$
model" similar to a time-varying $\Lambda(t)$ cosmology for the non-dissipative
universe. The second type is a "BV model" similar to a bulk viscous cosmology
for the dissipative universe. To systematically examine the two different
universes, a power-law term proportional to $H^{\alpha}$ is applied to the
$\Lambda(t)$ and BV (bulk-viscous-cosmology-like) models, assuming a flat
Friedmann--Robertson--Walker model for the late universe. Here, $H$ is the
Hubble parameter and $\alpha$ is a free parameter whose value is a real number.
The $\Lambda(t)$-$H^{\alpha}$ and BV-$H^{\alpha}$ models are used to examine
first-order density perturbations for matter, in which the background evolution
of the two models is equivalent. In addition, thermodynamic constraints on the
two models are discussed, with a focus on the maximization of entropy on the
horizon of the universe, extending previous analyses [Phys. Rev. D 100, 123545
(2019) (arXiv:1911.08306); 102, 063512 (2020) (arXiv:2006.09650)].
Consequently, the $\Lambda(t)$-$H^{\alpha}$ model for small $|\alpha|$ values
is found to be consistent with observations and satisfies the thermodynamic
constraints, compared with the BV-$H^{\alpha}$ model. The results show that the
non-dissipative universe described by the $\Lambda(t)$-$H^{\alpha}$ model
similar to lambda cold dark matter models is likely favored.
