Consider Each of the Following Processes $d S=\frac{d Q}{T}$ (That $N$ Be Fixed and That the Process Not Involve Any Energy

Consider each of the following processes. Is the process consistent (C) or inconsistent (D) with the limitations on equation T8.12 $d S=\frac{d Q}{T}$ (that $N$ be fixed and that the process not involve any energy transfer that is neither heat nor work due to a quasistatic volume change)?
-Consider two $q$ -vectors $|u\rangle$ and $|w\rangle$ with possibly complex components. Their inner product $\langle u \mid w\rangle$ is a real number.