Why is tearing paper irreversible? Consider a piece of paper.
If I pull on it in the right way it tears into two pieces.
However, if I push those two pieces together, they do not spontaneously form a single piece.
What happens at the microscopic level when the paper tears such that the process is irreversible?

My instinct is that in the fully formed piece of paper the fibers are strongly interwebbed, and so there is a large amount of (electrostatic?) energy stored at the boundaries between the fibers.
To tear the paper, one must overcome this barrier, but I don't see what could have happened to make it difficult to re-introduce all those surfaces with one another.
It almost seems like an entropy argument might work but I'm not sure how.
 A: Paper is a mesh of fibres usually mixed with a binder and some clay. The fibres will in turn have some microstructure depending on their origin (cloth, wood, etc). Ultimately the paper is composed mostly of cellulose molecules.
When you tear paper you are mostly pulling the mesh of fibres apart. If you look at the torn edge closely you'll be able to see the fibres sticking out of it. You will probably also fracture some fibres, and that fracture process will depend on the microstructure within the fibres. The clay particles are small and rigid, and they are likely to just separate from each other rather than fracturing. Some of them will spring off the surface as a fine dust.
Given all this complexity, the chances of you reassembling the torn pieces into anything approaching their original configuration are essentially zero.
A: I suspect that this question is resolved in the same way as for metal? Perhaps you've seen the famous (visionary) lecture by Feynman on nanoscience (before it existed), he argued for what is now known as cold welding, using an argument that I think applies to paper too. I reproduce a relevant quote from Feynman's celebrated "Feynman lectures on physics" here, which shows the main idea: 

The reason for this
  unexpected behavior is that when
  the atoms in contact are all of the
  same kind, there is no way for the
  atoms to “know” that they are in
  different pieces of copper. When
  there are other atoms, in the oxides
  and greases and more complicated
  thin surface layers of contaminants
  in between, the atoms “know”
  when they are not on the same
  part. 

The only thing is that, with paper, it's infinitely more complex to "put the pieces back together" in the right fashion because of the highly nontrivial structures at the edge. To be clear, the answer I'm proposing is: It isn't irreversible, in principle.
