The main motivation of no-collapse interpretations is to emphasize that the unitary Schroedinger evolution is all there is.
In order to reconcile this with our experience a description considering 'many worlds' or 'many minds' and the 'splitting' of the universe into different 'branches' is often used:
The physicist does not kill the cat but really creates two worlds and then repeating this experiment doubles the number again and again.
It seems that the number N of 'branches' or different 'minds' etc. increases like N(t) ~ wt where w is some unknown constant. Now one can calculate something like an entropy S from it as S = log(N) and therefore S ~ t; time really is 'm.w.i entropy'.
But how does one reconcile all this with the time-reversible Schroedinger evolution?