General treatment for dark energy thermodynamics

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 derive 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 ($\mu<0$).