I don’t know about the soda can but in the case of the rubber band, here’s what I think is happening. When you stretch it out, you are adding energy to it and it warms up (I don’t know the exact mechanism but most things heat up when you deform them from their equilibrium; once I got a burn from picking up a anil whose head I had ). The heat dissipates into the air, then when you let it contract again, cools down more, the reverse of what happened when you stretched it. This is a little like what happens to your freon in the air conditioner, only you add energy by stretching the rubber band, and by compressing the freon.
I remember we discussed your rubber band example in a thermodynamics course back in college. It is a real phenomenon.
A stretched rubber band has a good deal of energy in the form of the chemical bonds in the elastomer polymer in it. Stretching not only puts the “stretch” energy into the band, it also causes the elastomers within the band to take on a somewhat more ordered form - which is more energy.
When you take the tension off, that energy is released. Since the rubber band is releasing energy to the environment, it feels cold.
Conversely - if you take a limp rubber band and rapidly stretch it, then touch it it will feel warm.
Huh. I’ll be damned, you’re right. Anyway the reason is entropy, and rather than try to explain it myself (which I probably wouldn’t be able to do), I’ll direct your attention here.