I’d say that the concept of entropy “in physics” is about (even better: starts with) the choice of a probability distribution. Without that you have just a number associated with each probability distribution - distributions without any physical meaning so those numbers won’t have any physical meaning either.

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.)