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?

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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 at the boundaries between the fibers.
Tearing the paper 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.