We know that the Von Neumann entropy can be given by the following formula (up to constants):
$S=-\text{Tr}(\rho \log(\rho))$
Where $\rho$ is the density matrix.
Now for situations such as Electromagnetically Induced Transparency then time evolution and superpositions are involved, we get that $\rho=\rho^\dagger\in\mathbb{C}$. With this in mind, my question is this:
Does this imply that in some cases we get that $S\leq0$?