In this work we discuss a general approach for the dark energy thermodynamics considering a varying equation of state (EoS) parameter of the type $omega(a)=omega_0+F(a)$ and taking into account the role of a non-zero chemical potential $mu$. We deriv
e generalized expressions for the entropy density, chemical potential and dark energy temperature $T$ and use the positiveness of the entropy to impose thermodynamic bounds on the EoS parameter $omega(a)$. In particular, we find that a phantom-like behavior $omega(a)< -1$ is allowed only when the chemical potential assumes negative values ($mu<0$).
A phenomenological attempt at alleviating the so-called coincidence problem is to allow the dark matter and dark energy to interact. By assuming a coupled quintessence scenario characterized by an interaction parameter $epsilon$, we investigate the p
recision in the measurements of the expansion rate $H(z)$ required by future experiments in order to detect a possible deviation from the standard $Lambda$CDM model ($epsilon = 0$). We perform our analyses at two levels, namely: through Monte Carlo simulations based on $epsilon$CDM models, in which $H(z)$ samples with different accuracies are generated and through an analytic method that calculates the error propagation of $epsilon$ as a function of the error in $H(z)$. We show that our analytical approach traces simulations accurately and find that to detect an interaction {using $H(z)$ data only, these must reach an accuracy better than 1%.
We use current measurements of the expansion rate $H(z)$ and cosmic background radiation bounds on the spatial curvature of the Universe to impose cosmological model-independent constraints on cosmic opacity. To perform our analyses, we compare opaci
ty-free distance modulus from $H(z)$ data with those from two supernovae Ia compilations: the Union2.1 plus the most distant spectroscopically confirmed SNe Ia (SNe Ia SCP-0401 $z=1.713$) and two Sloan Digital Sky Survey (SDSS) subsamples. The influence of different SNe Ia light-curve fitters (SALT2 and MLCS2K2) on the results is also verified. We find that a completely transparent universe is in agreement with the largest sample in our analysis (Union 2.1 plus SNe Ia SCP-0401). For SDSS sample a such universe it is compatible at $< 1.5sigma$ level regardless the SNe Ia light-curve fitting used.
