Anyway, it seems that - like many others - I just misunderstood the “little need for all the mystery” remark.
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.)
But that’s fine, I accept that you may think that it’s just a little detail.
(Quantum mechanics has no mystery either.
ih/2pi dA/dt = AH - HA
That’s it. The only thing one needs to add is a choice of operators.)
Obviously one first introduces the relevant probability distributions (at least the micro-canonical ensemble). But once you have those, your comment still does not offer a better way to introduce entropy other than what I wrote. What did you have in mind?
In other words, how did you think I should change this part of my course?