Yes you can do compression, if the text is compressible. The playground [1] has a "run length encoding" example.
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.
You could package all your data into a zip using this language but you would also have a worthless stretch of memory seemingly filled with noise / things you’re not interested in.
Why do you think so? The code example shows that you can do RLE (run length encoding) without noise / additional space. I'm pretty sure you can do zip as well. It would just be very hard to implement, but it wouldn't necessarily require that the output contains noise.
Hmm. As a physicist my intuition is that information-preserving transformations are unitary (unitary transformations are 1-to-1). If a compression algorithm is going to yield a bit string (the zip file, for example) shorter than the original it can't be 1-to-1. So it must yield the zip file and some other stuff to make up for the space saved by the compression.
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.
[1] https://topps.diku.dk/pirc/?id=janusP