> is far from “being it” as a definition of the concept of entropy in physics.

I simply do not understand why you say this. Entropy in physics is defined using exactly the same equation. The only thing I need to add is the choice of probability distribution (i.e. the choice of ensemble).

I really do not see a better "definition of the concept of entropy in physics".

(For quantum systems one can nitpick a bit about density matrices, but in my view that is merely a technicality on how to extend probability distributions to Hilbert spaces.)