I read with interest most well written articles explaining entropy. I often leave the article mildly satisfied that I understood it. Until the next day when I again have to figure out the difference between "high" and "low" entropy in a particular model, and invariably I mix up the two.
It took me 10 years to understand entropy
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Re: It took me 10 years to understand entropy
#22Entropy: "to describe energy loss in irreversible processes". We have no clue about what is or is not reversible. Complex systems exhibit self-organizing behavior for no reason (that we understand), and we continue to identify more conditions under which this occurs. How does a Nobel Prize get handed out for identifying/quantifying "self-organization" http://pespmc1.vub.ac.be/COMPNATS.html without bringing everything…
Welp, I suppose the author has another 10 years to work on their article about how it took them 20 years to actually understand entropy.
Re: It took me 10 years to understand entropy
#23Nice writeup! BTW statistical thermodynamics has a name for that set of possible microstates, perhaps the most pretentious sounding name in all of physics, the "canonical ensemble".
Nah, Ultraviolet Catastrophe is worse, then there's wavefunction collapse. And there's gotta be something in particle physics that puts these terms to shame. Given that the particle names are drawn from literature and whimsy. I looked up the dictionary definition of pretentious, and so it doesn't really apply, but the hERG channel is a critical ion channel and various drugs block this and cause Really Bad Things. hER…
"Ultraviolet Catastrophe"'s problem is that it sounds way cooler than it is. I mean, that's the title of a cyberpunk novel; more hyperbolic (and disappointing) than pretentious. Eigenthings would be second on my list of pretentiousness (oddly, not gedankenthings; I'm inconsistent I guess). Standard Model names strike me whimsical to the point of being undignified.
Re: It took me 10 years to understand entropy
#24Entropy: "to describe energy loss in irreversible processes". We have no clue about what is or is not reversible. Complex systems exhibit self-organizing behavior for no reason (that we understand), and we continue to identify more conditions under which this occurs. How does a Nobel Prize get handed out for identifying/quantifying "self-organization" http://pespmc1.vub.ac.be/COMPNATS.html without bringing everything…
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Re: It took me 10 years to understand entropy
#25One aspect of entropy that I always find counterintuitive is that unlike mass, charge, etc. it is not a physical quantity. In fact, from the point of view of an experimenter with perfect information about a physical system, the entropy of the system is exactly conserved over time (as made precise by Liouville's Theorem). The Second Law survives in this setting only in the most trivial sense that a constant function does not decrease.
It's only when you start making crude measurements---lumping positions into pixels, clouds of particles each with their own kinetic energy into a single scalar called "temperature," etc---that you start to see a nontrivial entropy and Second Law. Different ways of lumping microstates into macrostates will give you different (and inconsistent) notions of entropy.
Re: It took me 10 years to understand entropy
#26Small nit in case the author sees this: the image labelled "Entropy of each configuration of system with two dices where the observed macrostate is their sum" is either incorrect or mislabeled.
For example, 2 and 12 each have 1 microstate, and ln 1 = 0, so the entropy of 2 and 12 is 0, but the image says 0.028 (which is the probability of 2 or 12, not the entropy).
Re: It took me 10 years to understand entropy
#27Entropy: "to describe energy loss in irreversible processes". We have no clue about what is or is not reversible. Complex systems exhibit self-organizing behavior for no reason (that we understand), and we continue to identify more conditions under which this occurs. How does a Nobel Prize get handed out for identifying/quantifying "self-organization" http://pespmc1.vub.ac.be/COMPNATS.html without bringing everything…
Entropy isn’t measuring a loss of energy, but the loss of the ability for a closed system to do useful work.
Order is often used to describe what’s going on but it’s not the kind of order we normally think of. Sufficient cold water in a warm room is just as capable of preforming work as warm water in a cold room.
Re: It took me 10 years to understand entropy
#28This reminds me of a great article that I saw on Hacker news that really helped explain the concept of Entrophy to me. Linked here: https://news.ycombinator.com/item?id=24140808
Gotta love these interactive websites.
Re: It took me 10 years to understand entropy
#29One aspect of entropy that I always find counterintuitive is that unlike mass, charge, etc. it is not a physical quantity. In fact, from the point of view of an experimenter with perfect information about a physical system, the entropy of the system is exactly conserved over time (as made precise by Liouville's Theorem). The Second Law survives in this setting only in the most trivial sense that a constant function d…
If I can pick your brain, there’s a related concept — entropy production. How does that relate with these ideas?
Re: It took me 10 years to understand entropy
#30Entropy: "to describe energy loss in irreversible processes". We have no clue about what is or is not reversible. Complex systems exhibit self-organizing behavior for no reason (that we understand), and we continue to identify more conditions under which this occurs. How does a Nobel Prize get handed out for identifying/quantifying "self-organization" http://pespmc1.vub.ac.be/COMPNATS.html without bringing everything…
Complex systems are net increases in entropy. The water is flowing downhill, but it takes a really weird organism-shaped path to get there. Self organization is supposedly interesting because we don't know why such a path manifests. Thus far, nothing has given the second law a second's (ha ha) pause. It's not impossible, but considering most of our foundational physics is time-symmetric it makes sense to call entropy irreversible. Even if it could be reversed (and don't hold your breath on that one), it's still the cause of the arrow of time.