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][1]. A recent example is a recent Simons Foundation article [Time’s Arrow Traced to Quantum Source][2]. There is also an older [expository article][3] 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 systems. In particular that states on entropy decreasing trajectories are unstable and the smallest perturbations result in entropy increasing trajectories. This means that unless you can prepare systems with infinite precision, then any system you prepare is almost certain to be on an entropy increasing trajectory unless it is at equilibrium already.

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?


  [1]: http://en.wikipedia.org/wiki/Loschmidt%27s_paradox
  [2]: http://www.simonsfoundation.org/quanta/20140416-times-arrow-traced-to-quantum-source/
  [3]: http://mysite.du.edu/~jcalvert/phys/boltz.htm