I'm not sure. Maybe when I've completely nutted out Brent's answer below
it'll make sense, but it seems to me that a universe in thermodynamic
equilibrium will still continue to diverge more than it merges, it's just
that the different configurations of matter/energy will look much alike. In
fact the number of possible equilibrium states is immense compared to the
ordered states (hence the arrow at all), so why shouldn't the multiverse
continue to branch out into more and more non-identical but similar-looking
states?

I can't see why it would when there are no more microstates available in
one time direction than the other. Assuming time symmetry of the underlying
physics, a universe at thermodynamic equilibrium could play out with equal
probability forwards or backwards, which would surely include MWI
splitting/merging?

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