  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
($\mu<0$).
