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If I have a crumpled paper I can put it under a heavy book. If I remove the book in a minute the paper will still be rather crumpled, but if I leave it on for a longer time it will flatten more.

But why? There is no movement involved, so where does the energy to flatten the paper come from?

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    $\begingroup$ It's kinda like putting a book on a spring (non-ideal) which compresses over time. $\endgroup$ – Hritik Narayan Jul 10 '17 at 7:45
  • $\begingroup$ Note that this is just a guess: Could diffusion of ambient humidity be responsible for the delayed effect? $\endgroup$ – engineer Jul 10 '17 at 7:48
  • $\begingroup$ @HritikNarayan Exactly. $\endgroup$ – trmdttr Jul 10 '17 at 13:25
  • $\begingroup$ @engineer Kind of like this? physics.stackexchange.com/q/23485/113352 $\endgroup$ – trmdttr Jul 10 '17 at 13:27
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"Practical Considerations for Humidifying and Flattening Paper" (2003) by Stephanie Watkins, a conservationist, has this to say about how to flatten paper (emphasis mine):

The aim of humidification is to reintroduce moisture into the paper support to relax the fibers... Gravity and time, or pressure and time, can be as effective, depending on the relative humidity of the storage area. Curled paper that is sturdy can be hung from flat clips, such as paper-protected bull clips, and left over a short time to slowly uncurl (e.g. panoramas, large blueprints, etc.). Protect the items from dust and light exposure during this process as it may take several weeks. However, humidification relaxes the paper in a faster manner and fibers are less likely to be stressed.

Thus:

  • Paper becomes flat once the microscopic cellulose fibers in the paper relax.
  • This process does not complete instantaneously upon application of a force, i.e. it takes time so the longer you leave it the flatter it becomes.
  • The energy should be coming from the book lowering ever so slightly as the creases in the paper disappear.
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