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Entropy of position and wave packet spreading.

Why do wave packets spread out over time?

Wave packet of the universe and its  spreading.

Why was the universe in such an extraordinarily low entropy state right after the big bang?

Is there a connection between the spreading of the wave packet of the universe and the time arrow  , despite the reversible character of physical laws? Could this be an explanation of the low entropy state of the early universe?

In other words, could wave packet spreading  of the universe  explain the low entropy (low compared to later entropy) of the early universe? Note that the wave packet spreading of the early universe can be justified mathematically, with no need for any physical hypothesis.

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