Could you really do general compression in this language? I was under the impression that the output is always the same size or larger than the input.
Maybe you meant sorting. You can implement sorting algorithms, as long as you store the information which entries were swapped. (To "unsort" the entries when running in reverse). So, an array that is already sorted doesn't need much additional information; one that is unsorted will require a lot of "undo" space. I think this is the easiest example to see the relation between reversible computing and thermodynamics: in thermodynamics, to bring "order" to a system requires "unorder" (heat) somewhere else.
There are also examples for encryption / decryption, but I find compression and sorting more interesting.