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> But "understanding" requires much more than giving one simple definition without discussing the consequences of the definition. But I did discuss the consequ
by lisper 4y ago
> But "understanding" requires much more than giving one simple definition without discussing the consequences of the definition.
But I did discuss the consequences: my definition (well, Boltzmann and Shannon's) leads directly to the second law, and in a way that is much more general and intuitive than the thermodynamic approach. What, for example, is the entropy of a cryptographic key? On the thermodynamic approach that question doesn't even make sense to ask. It's a category error because the thermodynamic definition relies on the concept of temperature and cryptographic keys don't have temperatures.
> Using atoms and microstates to explain entropy makes the explanation shorter but it also makes it more complex because it now depends on the definition of atoms and microstates.
Complexity is in the eye of the beholder. The classical billiard-ball model of atoms is perfectly adequate to explain the second law -- both the thermodynamic and information theoretic version -- and most people have no trouble wrapping their brains around the idea of "lots of tiny billiard balls wiggling around".
> I am curious what do you claim is a simple statistical explanation of temperature?
Higher/lower temperatures mean that the billiard balls are, on average, moving faster/slower relative to each other, all else being equal. And yes, I know that is not entirely accurate, but neither is the idea that atoms are billiard balls in the first place. This model is perfectly adequate as a first-order approximation. It allows you to describe the qualitative features of a heat engine purely in terms of the Newtonian mechanics of colliding billiard balls, which most people have a pretty good intuition for. No, it's not 100% accurate in the thermodynamic case, but the benefit is that it is obvious how to apply the concept of entropy defined in statistical terms to computation and information. I think that's a worthwhile tradeoff. Knowing how to calculate the efficiency of a heat engine is not very useful to most people in today's world. On the other hand, knowing how to estimate the entropy of a password or cryptographic key is very handy.
> The joke is that it is whatever the thermometer says it is.
Yes. But that joke conceals a deep truth: actually describing (let alone defining) thermodynamic temperature without reference to atoms, and without resorting to the thermometer joke, is very, very hard.
(It is analogous to trying to explain quantum mechanics without reference to entanglement, which is how it was done for decades. The problem with that approach is that it leaves you waving your hands about what a "measurement" is, because measurements are entanglements. Once you understand that simple fact, all of the mysteries of QM simply evaporate.)
> if bodies A and B are in thermal equilibrium (no heat transfer)
And how can I tell if A and B are in "thermal equilibrium" without resorting to the joke?
(BTW, your definition as you've given it is actually wrong. I can have two systems that are different temperatures but with no heat transfer between them simply by separating them with a perfect insulator. So now you have to incorporate that into your definition somehow, which means you have to define "insulator", and I don't see how you're going to do that without going around in circles.)
> It is an arbitrary (ordered) scale.
No, it's not. If it were arbitrary, the concept of specific heat would be meaningless.
Ultimately you need to make a connection between heat and motion. That is, after all, the thermodynamic project. You can convert heat into motion, and you can convert motion into heat, but the latter is much, much easier than the former. Why?
The statistical answer is: because heat is motion. It's a particular kind of motion. But if you deny yourself a referent to the things that are moving in the case of heat (atoms) then you deny yourself access to this simple straightforward explanation of the fundamental question of thermodynamics.
> "Understanding" entropy is about understanding why these vastly different definitions (thermodynamic and statistical) are equivalent
I agree, but I think it's much easier to start with the statistical definition and show how the thermodynamic one follows (because that is straightforward) than to start with the thermodynamic definition and try to extend it to non-thermodynamical systems. I've never seen that done successfully.
There's a reason that the atomic theory is a thing.
- krastanov 4y agoI mostly agree with the first half of what you wrote, especially in terms of pedagogy, but when you delved in the nitty-gritty in the second half, there are a lot of mistakes that would impede understanding "advanced" concepts in physics. I believe that is at the root of our disagreement - you are perfectly right about early pedagogy, but understanding (which for me means "capability of advanced applications") requires more. Disdain for the thermodynamic definition limits ones toolbox. (Edit: "disdain" is a bad choice of words) My main claim is: building the notion of entropy without relying on atomic theory is crucial if you want to apply it to "interesting" things like quantum mechanics or black hole physics. Admittedly that does not contradict your earlier posts, but it does significantly contradict the philosophy of your last post. An assortment of issues I have with the second half of what you wrote as related to our discussion of what "understanding entropy" means: - Passwords and cryptographic keys do not have entropy. What we call password entropy is a useful heuristic, but it differs from the rigorous information theory notion of entropy (or the thermodynamic one). I claim that it is important to understand that difference as it leads to understanding the limitations of the heuristic. - The definition I have given is not wrong, it is one of the most standard ways scientist have been defining temperature for the last century. "Perfect insulators do not exist" is an extremely important theorem that you "derive" in theoretical physics and use for a vast array of incredibly important thought experiments on which much of our understanding of nature is build. Not taking seriously the thermodynamic definition of entropy thus limits your power to explain Nature. Edit: "perfect insulators do not exist" is not a statement about how difficult it is to solve some engineering problem. It is an absolute statement with certainty equal to that of "√2 is irrational" or "you can not solve the halting problem". - Temperature is indeed an arbitrary scale, again something that has been established in pretty much any textbook on statistical physics or thermodynamics. At this point I really think it is worthwhile to play the authority card: you are claiming multiple things that contradict standard physics textbooks on which the last hundred years of science are based. - The heat engine efficiency is indeed not something most people care about day to day, but most people do not care about entanglement either. Moreover, I do not care about the heat engine as a question of engineering. However, thought experiments that involve heat engines are crucially important for the derivation of many no-go theorems (including in quantum mechanics). - This is incredibly important: heat is NOT motion. This is incredibly limiting worldview that is insufficient for anything but the simplest of toy problems. Very useful early pedagogical tool, but it has to be discarded early on if you want your student to grow. Sure, it is reasonable to say that it is a bad pedagogy to start with the thermodynamic definition. I teach graduate classes both in physics and in quantum information science (theoretical CS) and I actually follow your way of presenting entropy in the first few lectures. But the atomic theory interpretation of entropy is actually limiting when it comes to advanced physics. Really, the only thing I disagree about with you is your insistence that one does not need the thermodynamic definition in order to "understand" entropy. Please excuse my use of the word "insistence" if that is not the case - the limitation of text-based conversation are creeping in. > I agree, but I think it's much easier to start with the statistical definition and show how the thermodynamic one follows (because that is straightforward) than to start with the thermodynamic definition and try to extend it to non-thermodynamical systems. 100% yes > I've never seen that done successfully. Most of the graduate classes I have taken have done that relatively well, but I would agree with you that undergrad classes need more work in the US. For what is worth, the French Class Prepa curriculum on this topic is absolutely outstanding. I particularly like classes/textbooks that take the differential geometry approach to thermodynamics. As long as the textbook treats stat physics and thermodynamics separately, it is probably a textbook that does it well.