No. The fundamental disconnect is this:
Information theory and QM tell us there is "conservation of information".
But the Second Law of thermodynamics tells us "entropy always increases".
They can't both be true.
There is a mistake in the logic, of transitioning from single elements to the ensemble.
The mistake is viewing information in terms of order.
They're not the same thing. And I think I can prove it. Order is a "form of" information, a subset. But it's a mistake to generalize it.
Information has to do with partitioning, not with the number of available orders. "In some cases" there is a relationship, but not always.
The mistake has to do with separability, and you can see it easily in a directed acyclic graph.
In fact this is covered by Reichenbach's causal logic, which is corrected and treated formally by von Neumann algebras.