Solution
= Solution
If $x^T\mathbf1=0$, then $x^TQ=-Rx^T$. Induction gives $x^TQ^n=(-R)^nx^T$. Summing the matrix-exponential <series> yields
$$
\boxed{x^TP(t)=e^{-Rt}x^T.}
$$
Thus deviations of total mass zero decay with the single rate $R$.
= Solution
If $x^T\mathbf1=0$, then $x^TQ=-Rx^T$. Induction gives $x^TQ^n=(-R)^nx^T$. Summing the matrix-exponential <series> yields
$$
\boxed{x^TP(t)=e^{-Rt}x^T.}
$$
Thus deviations of total mass zero decay with the single rate $R$.