Misconceptions about entropy are misconceptions about physics. You can’t dispell them focusing on the maths and ignoring the physics entirely - especially if you just write an equation without any conceptual discussion, not even mathematical.
I didn't say to only focus on the mathematics. Obviously wherever you apply the concept (and it's applied to much more than physics) there will be other sources of confusion. But just knowing that entropy is a property of a distribution, not a state, already helps clarify your thinking.
For instance, you know that the question "what is the entropy of a broken egg?" is actually meaningless, because you haven't specified a distribution (or a set of micro/macro states in the stat mech formulation).
Ok, I don’t think we disagree. But knowing that entropy is a property of a distribution given by that equation is far from “being it” as a definition of the concept of entropy in physics.
Anyway, it seems that - like many others - I just misunderstood the “little need for all the mystery” remark.
> 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.)
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.)
Sarcasm aside, I really do not think you are making much sense.
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?
