Do solid objects really behave like fluid matter on extremely long timescales? Freeman Dyson's fascinating paper Time without End: Physics and Biology in an Open Universe contains the following passage:

I next discuss a group of physical processes which occur in ordinary matter at zero temperature as a result of quantum-mechanical barrier penetration.
[...]
On a time scale of $10^{65}$ yr, every piece of rock behaves like a liquid, flowing into a spherical shape under the influence of gravity. Its atoms and molecules will be ceaselessly diffusing around like the molecules in a drop of water.

While the paper provides computations yielding the time estimate quoted above, there is no obvious justification given for quantum barrier penetration actually leading to liquid-like behavior.
Would solid matter really behave exactly like a liquid on extremely long timescales, or is this just an analogy? If barrier penetration is a random process, why doesn't matter just re-form into random shapes at such timescales rather than becoming spherical?
 A: I think what Dyson's saying is that, while a solid generally does not deform permanently unless enough pressure is applied to break bonds between atoms or molecules,  statistical properties of quantum mechanics, analogous to the probability of electron tunneling,  will lead to solids changing shape under the influence of gravitational fields.  It's not clear to me (being a run-of-the-mill dummy physicist) why the atoms wouldn't re-form into a crystalline structure after each tunneling event, but maybe they're trapped kind of the way dislocations occur in normal crystals.
A: The number of years mentioned appears even larger than total anticipated life span of universe (gravity) itself. One of these - Heat death, Big Rip, Big crunch would probably happen before the time frame mentioned. Therefore not sure what the answer is as the conditions mentioned may no even exists that long. For example, If a big rip happens, then one can say - solids behave like gasses over long enough time scales. And behave even stranger over even longer time times.
