  We consider a macroscopic quantum system with unitarily evolving pure state
$\psi_t\in \mathcal{H}$ and take it for granted that different macro states
correspond to mutually orthogonal, high-dimensional subspaces $\mathcal{H}_\nu$
(macro spaces) of $\mathcal{H}$. Let $P_\nu$ denote the projection to
$\mathcal{H}_\nu$. We prove two facts about the evolution of the superposition
weights $\|P_\nu\psi_t\|^2$: First, given any $T>0$, for most initial states
$\psi_0$ from any particular macro space $\mathcal{H}_\mu$ (possibly far from
thermal equilibrium), the curve $t\mapsto \|P_\nu \psi_t\|^2$ is approximately
the same (i.e., nearly independent of $\psi_0$) on the time interval $[0,T]$.
And second, for most $\psi_0$ from $\mathcal{H}_\mu$ and most $t\in[0,\infty)$,
$\|P_\nu \psi_t\|^2$ is close to a value $M_{\mu\nu}$ that is independent of
both $t$ and $\psi_0$. The first is an instance of the phenomenon of dynamical
typicality observed by Bartsch, Gemmer, and Reimann, and the second modifies,
extends, and in a way simplifies the concept, introduced by von Neumann, now
known as normal typicality.
