Thermodynamics of viscous dark energy for the late future time universe
  In this work we explore the thermodynamic aspects of dark energy for late
future time universe in two different scenarios: as a perfect fluid with
constant and variable equation of state parameter; and as dissipative fluid
described by a barotropic equation of state with bulk viscosity in the
framework of the Eckart theory and the full Israel-Stewart theory. We explore
cosmological solutions for a flat, homogeneous and isotropic universe; and we
assume the late future time behavior when the dark energy dominates the cosmic
evolution. When modeled as a perfect fluid with a dynamical equation of state,
$p=w(a)\rho$, the dark energy has an energy density, temperature and entropy
well defined and an interesting result is that there is no entropy production
even though been dynamical. For dissipative dark energy, in the Eckart theory
two cases are studied: $\xi=const.$ and $\xi =(\beta/\sqrt{3}) \rho^{1/2}$; it
is found that the entropy grows exponentially for the first case and as a
power-law for the second. In the Israel-Stewart theory we consider a $\xi
=\xi_0 \rho^{1/2}$ and a relaxation time $\tau = \xi/\rho$; an analytical Big
Rip solution is obtained with a power-law entropy. In all cases a power-law
relation between temperature and energy density is obtained. In order to
maintain the second law of thermodynamics theoretical constraints for the
equation of state are found in the different dark energy models studied. A
barotropic dark fluid with $w<-1$ is thermodynamically difficult to support,
but the overall effect of bulk viscosity in certain cases allows a phantom
regime without thermodynamic anomalies.
