Remark: Nonmonotone full purity

For the default pure preparation with ${\gamma }_{\mathrm{d}}=0$, $S$ remains pure and $\mathrm{Tr}{\rho }^2=(1-q{)}^2+q^2$. At positive relaxation this decreases to $1/2$ at $t=(\log 2)/{\gamma }_{\mathrm{r}}$ and subsequently increases to one. At fixed $t>0$, it is also nonmonotone as a function of ${\gamma }_{\mathrm{r}}$. Vacuum convergence does not prove monotonicity in relaxation rate. The normalization in (eq:coherence) must likewise be separated from any claimed chain-length dynamical effect.