I have seen several claims to that quantum mechanics is required to explain the arrow of time which I take to mean the macroscopic irreversibility of physical systems. This is presumably to resolve Loschmidt's paradox. A recent example is a recent Simons Foundation article Time’s Arrow Traced to Quantum Source. Another example from is A quantum solution to the arrow-of-time dilemma. There is also an older expository article that contains the following rather strongly worded paragraph:
The application of classical mechanics to the explanation of thermodynamics resulted in a complex and disgusting mess that explains nothing, though great efforts were expended along this line. This is not surprising, since thermodynamics depends sensitively on mechanics at an atomic scale, for which classical mechanics fails spectacularly. ... with the introduction of quantum mechanics, it has been possible to understand entropy clearly and completely ...
However, as I understand, coarse grain irreversibility has been been demonstrated for theoretically and by numerical simulations for purely classical idealized systems like "billiards" and "gasses" in 2 and 3 dimensions. I am particularly thinking of Simanyi's results on ergodicity and the numerical investigations of Orban & Bellemans, Levesque & Vertlet and Komatsu & Abe. These would suggest that macroscopic irreversibility comes from the geometrical structure of the vector field on the phase space representing the evolution of the systems. States on entropy decreasing trajectories are unstable and the smallest perturbations result in trajectories that become entropy increasing after time. This means that unless systems can are prepared with infinite precision, then any system prepared is almost certain to be on an entropy increasing trajectory unless it is at equilibrium already. What is required is that the dynamics allow trajectories in phase space to diverge nonlinearly.
This would imply that, although there are deep connections between quantum mechanics and irreversibility, quantum mechanics is not strictly required for irreversibility as some articles seem to be claiming. What is still left to explain why the universe is in a far from equilibrium state, but the articles cited at the beginning do not seem to be addressing this aspect either.
What am I missing?