How is the universe both non-ergodic and quantum?

Question

From Ted Jacobson we know relativity is thermodynamical. This also (I think?) must mean relativity, as a classical analysis, assumes space-time to be ergodic, i.e. a system that can reach thermal  equilibrium and ‘forget’ its initial conditions, aka ‘no deep history’, or alternatively, no external time.

Non-ergodic systems on the other hand, do not visit all of their possible states, and do have ‘history’. Rather like the absolute time of quantum mechanics. However, it seems to me that there is a general consideration that quantum mechanics is also ergodic, (e.g. von Neumann) but -

Q) The universe is clearly non-ergodic (like human individuals), and so how can QM be ergodic?

Note – I also came across this paper, maybe related

gandalf61 · Answer

General relativity and quantum mechanics are both models of reality. They are very successful models, in that their predictions very closely match the results of experimental observations, and no known observations contradict either model.
However, neither model can be a complete model of reality because they are inconsistent. GR is a classical deterministic model in which any set of parameters can, in principle, be determined to any degree of precision. QM is a stochastic theory in which there are limits to the precision with which certain pairs of parameters can be simultaneously measured. One aspect of this difference gives rise to the black hole information paradox.
I am not sure what you mean when you say that the universe is "clearly non-ergodic". Do you mean it is clear that information is lost ? Yes, parts of the universe (such as each human being) lose information, run down and decay, but they are not closed systems. Information may still be conserved across the universe as a whole.

How is the universe both non-ergodic and quantum?

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