Time dependence of reflected entropy in rational and holographic conformal field theories

We calculate the time dependence of the reflected entropy of two disconnected regions after a global quench in $(1+1)$-dimensional conformal field theories and in large temperature limit. For rational conformal field theories, we find that the time evolution of the reflected entropy is the same as that of the mutual information. We get the same result for holographic theories in the limit where the separation between disconnected regions is much smaller than their respective sizes. We discuss how this result is consistent with the quasi-particle picture of Calabrese and Cardy \cite{calabrese-cardy}.