Please don’t bring in thermodynamics! lol.
I’m recommending that you use entropy because that’s what the texts use. I was struck by the absence of the word information in the Cover and Thomas text. It was all about entropy (not meant to be taken too literally please).
A simple google search on relative information joint information and conditional information is revealing.
Whatever language people are speaking they seem to prefer the term entropy, and it has nothing to do with thermodynamics.
cheers!