I have read the original PRL paper, and I think that the significant issue with it is that it conflates the complexity (C5 in the paper, a measure of the cluste

I have read the original PRL paper, and I think that the significant issue with it is that it conflates the complexity (C5 in the paper, a measure of the clustering of the gravitational objects) with entropy. I don't think that this leap is warranted. Complexity, as defined by the authors, is primarily a spatial dispersion measure without a corresponding measure of energy dispersion. As far as I can tell, this system should be subject to Liouville's theorem, which means that the apparent entropy decrease (the decrease in C5) that occurs when the system contracts is just hiding the entropy in the phase space of the particle velocities. So, as the particles get closer together, their velocities get farther apart. This same kind of effect occurs in particle beams when you try to squeeze the particle beam tighter. Assuming you aren't using some kind of beam cooling (like adding cold electrons, or using stochastic cooling), every time the beam gets squeezed, the beam gets tighter but the phase spread in the particles increases. When the beam spreads out again, the phase spread usually goes back down. It can get as low as its original value, but no lower. Just like entropy (cause that's what it really is). That's just my thoughts after a brief perusal. Feel free to point out any obvious errors in my logic.