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Entropy as Disorder: History of a Misconception

90 points by Anon84 7y ago

bonoboTP 7y ago
I would say, in itself the oil being separated from and being above the Italian salad is something that in itself decreases the entropy (for now I assume we can think of this as two gases of different density). However! It is overcompensated by other factors and in total the entropy is lowest in this case. What factors? Imagine you could place the particles as you wished, and being encouraged by my first sentence you decide to mix it all up to achieve higher entropy. To make it all mixed up, you'd have to move the heavier, denser material towards the top, increasing the total potential energy. This would need the introduction of external energy into the system. We cannot do that with a closed system. We could only take the energy as heat from the salad, making it all colder. However, in making it colder, the motion of the particles becomes less uncertain, leading to a decrease in entropy. Ultimately the method of mixing it up fails to increase the entropy, showing that the separated configuration is indeed lower entropy. However it is not because of the separation, but in a certain sense despite it. The separation helps bring the particles into a higher inner-energy state, because the potential energy decreases as the denser material moves down. Without paying attention to the micro situation the effect wouldn't make sense.
- kgwgk 7y ago
  > (for now I assume we can think of this as two gases of different density) What does that mean? If they were gases they would mix (as the atmosphere, where you don’t see layers of gasses of different densities but an essentially homogeneous mixture).
  - bonoboTP 7y ago
    That could be wrong. I think the point still stands that the separation contributes to a decrease in entropy, however it enables another effect which increases entropy even more. If we were allowed to mix it up evenly by adding energy from the outside to lift the heavier material up (constant temperature), then we'd get an even higher entropy, agree?
    - kgwgk 7y ago
      I don’t understand what point you are trying to make. If you assume that’s the equilibrium state and therefore the highest entropy state given the constraints on the system then of course the entropy cannot spontaneously increase. And if it’s the highest entropy state despite looking “low entropy” under the flawed criteria of “looks ordered” then it’s obvious there is something else we’re missing that explains why the entropy is indeed maximal. Anyway, to increase the entropy you don’t just need to add energy, it has to be in the form of heat (something you can’t extract work from later). If you move the “heavy” layer on top of the “light” layer the (potential) energy has increased but if the temperature remains constant the entropy doesn’t change.
      - bonoboTP 7y ago
        I'm sorry, it is difficult to express my thought, although it is a simple thought that may be trivial to you. I mean that ceteris paribus the layering (separation of materials) causes a decrease in entropy. However, the system still does this, because it gains more entropy through a different "channel". If we could destroy the layering, thereby evenly mixing things up, but not changing anything else that affects entropy, we could increase the entropy. So it show that the layered version is lower entropy as long as all else is the same. The catch is, this would require adding extra energy into the system, because the mixed version has more potential energy. We could also imagine a mixed up configuration that has the same total energy, but then the temperature would be lower since more of the energy would be used up as potential energy, leaving less for heat. In that case the entropy would be lower. Main point: the layering, just the fact that it is layered, this property, if we know nothing else, is still something that is a low entropy thing. So our intuition is not broken that order corresponds to low entropy.
        kgwgk 7y ago
        > I mean that ceteris paribus the layering (separation of materials) causes a decrease in entropy. But it doesn’t, which is the reason why it happens. Because that intuition of “oh, there are two phases, this means order and entropy is disorder so the entropy is lower” doesn’t correspond to the reality of the physical concept of entropy (the thing that is maximized for a thermodynamic system In equilibrium). That’s the point of the article. Note that the discussion about potential energy is a red herring, phase separation does also happen in absence of gravity (you get droplets which don’t coalesce as easily, but it happens nevertheless).
dvt 7y ago
So it's an article on entropy (as disorder) without one mention of Shannon[1]? This seems like a pretty big oversight. In the context of information theory, entropy is absolutely a decay of information. I understand that this is physics (not math -- although the formulae are virtually identical), but there's a very clear, accurate, and formal use of "entropy" to mean exactly what the author purports it doesn't mean: chaos. [1] https://heliosphan.org/shannon-entropy.html https://heliosphan.org/shannon-entropy.html
- dr_dshiv 7y ago
  I don't think it's an oversight. Shannon entropy, Von Neumann entropy and other information theory entropies are useful, but not physically fundamental in the sense of the second law of thermodynamics. That said, I don't under whether Gibbs entropy or Boltzmann entropy is fundamental-- ?
  - dvt 7y ago
    > Shannon entropy, Von Neumann entropy and other information theory entropies are useful, but not physically fundamental... I have to disagree, especially given that one of the great mysteries of our generation (the Black Hole Information Paradox) hinges on what happens to information -- sure, it's information about particles, whatever that might mean. But Jacob Bekenstein (among others) argues that Thermodynamic entropy is analogous to information (Shannon) entropy[1]. [1] http://webhome.phy.duke.edu/~mkruse/Phy255/255S06_Joyce_Coppock_bh.pdf http://webhome.phy.duke.edu/~mkruse/Phy255/255S06_Joyce_Copp...
    - dr_dshiv 7y ago
      But, analogous?
    - hcs 7y ago
      I take your point, it might have been interesting to talk about how a lot of relativity and quantum mechanics can be thought of in terms of propagation and destruction of information. And for many students, talking about codes is a lot more interesting than pressure gradients in ideal gasses. A missed opportunity, perhaps.
dr_dshiv 7y ago
I liked this article. Really clear. I found some of my own misconceptions. For instance, that uniformity and gradients are ways of characterising entropy. The example of oil and water is great. While they are separated with a gradient, there is no latent tendency to flow together and mix. But, it's only gravity that makes the oil and water issue hard to understand. With no gravity, they would not be evenly divided. We still don't understand gravity, as it relates to entropy. Usually entropy makes things spread out, but gravity makes things come together. Weird.
- deleted 7y ago
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- archgoon 7y ago
  > We still don't understand gravity, as it relates to entropy. Usually entropy makes things spread out, but gravity makes things come together. Weird. If 'gravity' weirds you out, put the mixture in a centrifugal chamber and let it spin. You get the same gradiated separation. > Usually entropy makes things spread out, but gravity makes things come together. Weird. It's no weirder than saying that hydrogen atoms exist because the proton attracts the electron.
  - dr_dshiv 7y ago
    The centrifugal chamber is using energy, so I don't know about that comparison. But the attractive forces of protons and electrons ARE weird. Do know how attraction/integration can lower entropy?
- maciejw 7y ago
  I also liked the article. I lack theoretical knowledge to determine if the system that is affected by gravity can still be considered "isolated" as per 2nd law of thermodynamics. I think this is not really relevant here, as the article focuses more on the common mental model, that disorder always increases with time. This model is not only incorrectly labelled (as entropy), but also misleading when used to describe some processes in the world. This oil/vinegar example is immediately useful for other areas too. We have oil and vinegar in the dressing. They eventually become separated and we need to put effort to mix them together. Now replace oil and vinegar with leave/remain, blue/red or whatever else...
panic 7y ago
I was looking for more information on the oil/vinegar situation and found this explanation at https://chem.libretexts.org/Bookshelves/General_Chemistry/Book%3A_CLUE_(Cooper_and_Klymkowsky)/6%3A_Solutions/6.3%3A_Hydrogen_Bonding_Interactions_and_Solubility/6.3.1%3A_Entropy_and_Solubility%3A_Why_Don’t_Oil_and_Water_Mix%3F https://chem.libretexts.org/Bookshelves/General_Chemistry/Bo...: > When hydrocarbon molecules are dispersed in water, the water molecules rearrange to maximize the number of H-bonds they make with one another. They form a cage-like structure around each hydrocarbon molecule. This cage of water molecules around each hydrocarbon molecule is a more ordered arrangement than that found in pure water, particularly when we count up and add together all of the individual cages! It is rather like the arrangement of water molecules in ice, although restricted to regions around the hydrocarbon molecule. This more ordered arrangement results in a decrease in entropy. The more oil molecules disperse in the water, the larger the decrease in entropy. On the other hand, when the oil molecules clump together, the area of “ordered water” is reduced; fewer water molecules are affected. Therefore, there is an increase in entropy associated with the clumping of oil molecules —a totally counterintuitive idea!
- deleted 7y ago
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- cma 7y ago
  What about with heavy gases and light ones like helium? Do they eventually mix completely in large atmospheres under a big gravity gradient? I would think a mixture should gain kinetic energy as the heavier one settles more on the bottom, releasing photons from the heat which increases total entropy, but in a closed system where the photons are reflected back it would hit some equilibrium with heavier stuff at the bottom, but more kinectic and photonic energy which maybe both together give more degrees of freedom than a more evenly mixed mixture with less kinetic energy and higher gravitational potential energy.
  - kgwgk 7y ago
    > I would think a mixture should gain kinetic energy as the heavier one settles more on the bottom, But this is not what happens, or there would only be CO2 (and a small ammount of the heavier atoms and molecules) in the lower part of our atmosphere. > I would think a mixture should gain kinetic energy as the heavier one settles more on the bottom, But this is not what happens, or there would only be CO2 (and a small ammount of the heavier atoms and molecules) in the lower part of our atmosphere. Edit: Maybe you know this already, but in equilibrium the mixture does indeed have more kinetic energy (per unit of volume) as you go down because even though the temperature remains constant the pressure increases.
szemet 7y ago
Isn't this a too narrow definition of entopy? Ok. Pure physical entropy was the first and original usage, but now informational entropy can be used at higher level, and it correlates well with disorder at that level. If I sort an array its entropy will be lower - while due to thermodynamics the total entropy of the world will be increased. So there is the only the high level component I'm interested in: I see less macrostate in a sorted array(one) than in an undordered(n factorial) even if the microstates in the world have increased(I don't care). Same goes for the article examples, for me subjectively an ice statue can have many different forms (macrostates), if it melts it will have one form (a puddle) - so I see the entropy to decrease - of course the puddle have more microstates than the ice statue - just I do not differentiate between them... True: in the sbove examples things became more ordered at high level (entropy have decreased), meanwhile physical entropy have increased - but that increase was global and in our local point of interest it is still can be said (according to modern usage) that entropy have decreased! Of course the total sum have to be positive - that's the basis of how for example the Landauer principle is calculated, wich connects the above high level informational view with physical entropy...
- kgwgk 7y ago
  Note that this is an article for physics teachers and the conclusion is “we can warn our students that this is not the meaning of the word “entropy” in physics.”
ScottBurson 7y ago
Slightly OT, but I just saw this last night and thought it was hilarious: You should call it "entropy", for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage. — John von Neumann, suggesting to Claude Shannon a name for his new uncertainty function, as quoted in Scientific American Vol. 225 No. 3, (1971), p. 180.
- hcs 7y ago
  Schrödinger used the term "negentropy". And there's a story that Norbert Wiener used to wander around MIT telling anyone who would listen that information is negative entropy, including Shannon. (I'm having trouble finding it, will edit if I track it down) Edit: ah, it was Fano who told that story (quoted in "The Cybernetics Moment"): > Electrical engineer Robert Fano at MIT, recalled that sometime in 1947, Wiener "walked into my office ... announced 'information is entropy' and then walks out again. No explanation, no elaboration." More about Wiener's approach and another recounting of the story here: http://news.mit.edu/2011/timeline-wiener-0119 http://news.mit.edu/2011/timeline-wiener-0119
- kgwgk 7y ago
  The article in question: Energy and Information http://www.esalq.usp.br/lepse/imgs/conteudo_thumb/mini/Energy-and-Information.pdf http://www.esalq.usp.br/lepse/imgs/conteudo_thumb/mini/Energ... Another paper co-authored by Myron Tribus: Information Theory and Thermodynamics https://www.e-periodica.ch/cntmng?pid=hpa-001:1974:47::871 https://www.e-periodica.ch/cntmng?pid=hpa-001:1974:47::871
trhway 7y ago
Typical fallacy in entropy considerations is to consider system as isolated in the model while it is strongly connected to the environment in reality. The oil/vinegar (similar to the pennies and dimes mentioned in the article - when shaken in a jar would "magically" separate with pennies on top) has exported the entropy to the environment through the work of gravitational force in full accordance with the 2nd law - the system transitions following the gradient and thus increasing total entropy of the whole system. A similar mistake for example is when "life" is stated to be "anti-entropic" in any sense while it is a really a form of matter organization which generates even more entropy than the same amount of dead matter would.
kgwgk 7y ago
A couple of related articles from Lambert (https://en.m.wikipedia.org/wiki/Frank_L._Lambert https://en.m.wikipedia.org/wiki/Frank_L._Lambert): Shuffled Cards, Messy Desks, and Disorderly Dorm Rooms — Examples of Entropy Increase? Nonsense! http://entropysite.oxy.edu/shuffled_cards.html http://entropysite.oxy.edu/shuffled_cards.html Disorder — A Cracked Crutch For Supporting Entropy Discussions http://entropysite.oxy.edu/cracked_crutch.html http://entropysite.oxy.edu/cracked_crutch.html
foxes 7y ago
The definition of entropy from a statistical mechanics perspective, is roughly a count of the number of different (microscopic) configurations, \Omega, of a system. When all the configurations are equally probable, you get the formula S ~ log(\Omega) I don't think you see this definition in a physics education until you do a course on statistical mechanics? I feel like I certainly had teachers say "disorder". I think the connection being that if there are more configurations it's more "disordered" which isn't really a precise thing. Looking back, I think rambling about ideal gases/pressure/volumes is a boring way to teach this subject (at least at late high school/first year uni). You should probably introduce it by talking about configurations and information. You can think of some very clear examples (configurations of a list of objects for example, it doesn't necessarily have to be "physical"). Then maybe you would go on to show that this is connected to macroscopic physical properties.
- rstuart4133 7y ago
  > I don't think you see this definition in a physics education until you do a course on statistical mechanics? I'm over 60, and I only recent discovered the definition of entropy recently thanks to Leonard Susskind youtube videos. For 60 bloody years I only got the dumbed down version about "disorder" and it made absolutely no sense to me whatsoever. Now I see the same confusion in others - like here on HN were to people where duking it out over whether one arrangement of a pack of cards (all individually identifiable of course) had more entropy than the other. This dumbing down does nobody any favors whatsoever. It certainly doesn't promote understanding of the basic principles.
codesushi42 7y ago
The best book on the subject: https://www.amazon.com/Entropy-Demystified-Second-Reduced-Revised/dp/9812832254/ https://www.amazon.com/Entropy-Demystified-Second-Reduced-Re...
tullatulla 7y ago
The author seems to mix up Gibbs free energy with entropy. The remark that thermal equilibrium equals maximum entropy is simply wrong. All examples can be explained with minimization of the free energy: dG = dH - TdS dH == internal energy (chemical bonds) + pV dS == Entropy term T == Temperature Where entropy is the number of different states the system can be in for a given internal energy. A thermodynamic system in equilibrium will always tend to a state of lowest free energy. Example: a perfect crystal would be a totally ordered state (and with the lowest entropy), with the internal energy minimized due to the highest number of chemical bonds. For T -> 0, this would be the thermodynamically most stable configuration (however not always kinetically accessible, e.g. supercooled water). As Temperature goes up, the Gibbs free energy of a more disordered phase (e.g. crystal defects or a liquid/gas phase) becomes lower and will eventually lead to the melting of the crystal. For the oil/water example, the separated state minimizes the free energy since polar water molecules can form hydrogen bonds with themselves (lowering the internal energy), and push out the oil molecules, even though the entropy is lower than for a totally mixed state. At higher temperatures, this will change theoretically and the mixed-phase becomes favorable thermodynamically. From this point of view, seeing higher entropy as more disorder seems absolutely fine, where more disorder is "lower chance of guessing the exact configuration of all molecules in the system".
- kgwgk 7y ago
  Entropy is maximized for an isolated system (constant energy), free energy is minimized for a system in thermal equilibrium with a heat bath (can exchange energy with the environment). Gibbs free energy is minimized at constant pression and temperature, Helmholtz free energy is minimized at constant volume and temperature. If you put now the oil/water system into a isolated container the equilibrium state won't change substantially. It remains separated in two phases and that's now the maximum entropy state.

90 points by Anon84 7y ago

I would say, in itself the oil being separated from and being above the Italian salad is something that in itself decreases the entropy (for now I assume we can think of this as two gases of different density). However! It is overcompensated by other factors and in total the entropy is lowest in this case. What factors? Imagine you could place the particles as you wished, and being encouraged by my first sentence you decide to mix it all up to achieve higher entropy. To make it all mixed up, you'd have to move the heavier, denser material towards the top, increasing the total potential energy. This would need the introduction of external energy into the system. We cannot do that with a closed system. We could only take the energy as heat from the salad, making it all colder. However, in making it colder, the motion of the particles becomes less uncertain, leading to a decrease in entropy. Ultimately the method of mixing it up fails to increase the entropy, showing that the separated configuration is indeed lower entropy. However it is not because of the separation, but in a certain sense despite it. The separation helps bring the particles into a higher inner-energy state, because the potential energy decreases as the denser material moves down. Without paying attention to the micro situation the effect wouldn't make sense.

kgwgk 7y ago
> (for now I assume we can think of this as two gases of different density) What does that mean? If they were gases they would mix (as the atmosphere, where you don’t see layers of gasses of different densities but an essentially homogeneous mixture).
- bonoboTP 7y ago
  That could be wrong. I think the point still stands that the separation contributes to a decrease in entropy, however it enables another effect which increases entropy even more. If we were allowed to mix it up evenly by adding energy from the outside to lift the heavier material up (constant temperature), then we'd get an even higher entropy, agree?
  - kgwgk 7y ago
    I don’t understand what point you are trying to make. If you assume that’s the equilibrium state and therefore the highest entropy state given the constraints on the system then of course the entropy cannot spontaneously increase. And if it’s the highest entropy state despite looking “low entropy” under the flawed criteria of “looks ordered” then it’s obvious there is something else we’re missing that explains why the entropy is indeed maximal. Anyway, to increase the entropy you don’t just need to add energy, it has to be in the form of heat (something you can’t extract work from later). If you move the “heavy” layer on top of the “light” layer the (potential) energy has increased but if the temperature remains constant the entropy doesn’t change.
    - bonoboTP 7y ago
      I'm sorry, it is difficult to express my thought, although it is a simple thought that may be trivial to you. I mean that ceteris paribus the layering (separation of materials) causes a decrease in entropy. However, the system still does this, because it gains more entropy through a different "channel". If we could destroy the layering, thereby evenly mixing things up, but not changing anything else that affects entropy, we could increase the entropy. So it show that the layered version is lower entropy as long as all else is the same. The catch is, this would require adding extra energy into the system, because the mixed version has more potential energy. We could also imagine a mixed up configuration that has the same total energy, but then the temperature would be lower since more of the energy would be used up as potential energy, leaving less for heat. In that case the entropy would be lower. Main point: the layering, just the fact that it is layered, this property, if we know nothing else, is still something that is a low entropy thing. So our intuition is not broken that order corresponds to low entropy.
      - kgwgk 7y ago
        > I mean that ceteris paribus the layering (separation of materials) causes a decrease in entropy. But it doesn’t, which is the reason why it happens. Because that intuition of “oh, there are two phases, this means order and entropy is disorder so the entropy is lower” doesn’t correspond to the reality of the physical concept of entropy (the thing that is maximized for a thermodynamic system In equilibrium). That’s the point of the article. Note that the discussion about potential energy is a red herring, phase separation does also happen in absence of gravity (you get droplets which don’t coalesce as easily, but it happens nevertheless).

dvt 7y ago

So it's an article on entropy (as disorder) without one mention of Shannon[1]? This seems like a pretty big oversight. In the context of information theory, entropy is absolutely a decay of information. I understand that this is physics (not math -- although the formulae are virtually identical), but there's a very clear, accurate, and formal use of "entropy" to mean exactly what the author purports it doesn't mean: chaos. [1] https://heliosphan.org/shannon-entropy.html https://heliosphan.org/shannon-entropy.html

dr_dshiv 7y ago
I don't think it's an oversight. Shannon entropy, Von Neumann entropy and other information theory entropies are useful, but not physically fundamental in the sense of the second law of thermodynamics. That said, I don't under whether Gibbs entropy or Boltzmann entropy is fundamental-- ?
- dvt 7y ago
  > Shannon entropy, Von Neumann entropy and other information theory entropies are useful, but not physically fundamental... I have to disagree, especially given that one of the great mysteries of our generation (the Black Hole Information Paradox) hinges on what happens to information -- sure, it's information about particles, whatever that might mean. But Jacob Bekenstein (among others) argues that Thermodynamic entropy is analogous to information (Shannon) entropy[1]. [1] http://webhome.phy.duke.edu/~mkruse/Phy255/255S06_Joyce_Coppock_bh.pdf http://webhome.phy.duke.edu/~mkruse/Phy255/255S06_Joyce_Copp...
  - dr_dshiv 7y ago
    But, analogous?
  - hcs 7y ago
    I take your point, it might have been interesting to talk about how a lot of relativity and quantum mechanics can be thought of in terms of propagation and destruction of information. And for many students, talking about codes is a lot more interesting than pressure gradients in ideal gasses. A missed opportunity, perhaps.

dr_dshiv 7y ago

I liked this article. Really clear. I found some of my own misconceptions. For instance, that uniformity and gradients are ways of characterising entropy. The example of oil and water is great. While they are separated with a gradient, there is no latent tendency to flow together and mix. But, it's only gravity that makes the oil and water issue hard to understand. With no gravity, they would not be evenly divided. We still don't understand gravity, as it relates to entropy. Usually entropy makes things spread out, but gravity makes things come together. Weird.

deleted 7y ago
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archgoon 7y ago
> We still don't understand gravity, as it relates to entropy. Usually entropy makes things spread out, but gravity makes things come together. Weird. If 'gravity' weirds you out, put the mixture in a centrifugal chamber and let it spin. You get the same gradiated separation. > Usually entropy makes things spread out, but gravity makes things come together. Weird. It's no weirder than saying that hydrogen atoms exist because the proton attracts the electron.
- dr_dshiv 7y ago
  The centrifugal chamber is using energy, so I don't know about that comparison. But the attractive forces of protons and electrons ARE weird. Do know how attraction/integration can lower entropy?
maciejw 7y ago
I also liked the article. I lack theoretical knowledge to determine if the system that is affected by gravity can still be considered "isolated" as per 2nd law of thermodynamics. I think this is not really relevant here, as the article focuses more on the common mental model, that disorder always increases with time. This model is not only incorrectly labelled (as entropy), but also misleading when used to describe some processes in the world. This oil/vinegar example is immediately useful for other areas too. We have oil and vinegar in the dressing. They eventually become separated and we need to put effort to mix them together. Now replace oil and vinegar with leave/remain, blue/red or whatever else...

panic 7y ago

I was looking for more information on the oil/vinegar situation and found this explanation at https://chem.libretexts.org/Bookshelves/General_Chemistry/Book%3A_CLUE_(Cooper_and_Klymkowsky)/6%3A_Solutions/6.3%3A_Hydrogen_Bonding_Interactions_and_Solubility/6.3.1%3A_Entropy_and_Solubility%3A_Why_Don’t_Oil_and_Water_Mix%3F https://chem.libretexts.org/Bookshelves/General_Chemistry/Bo...: > When hydrocarbon molecules are dispersed in water, the water molecules rearrange to maximize the number of H-bonds they make with one another. They form a cage-like structure around each hydrocarbon molecule. This cage of water molecules around each hydrocarbon molecule is a more ordered arrangement than that found in pure water, particularly when we count up and add together all of the individual cages! It is rather like the arrangement of water molecules in ice, although restricted to regions around the hydrocarbon molecule. This more ordered arrangement results in a decrease in entropy. The more oil molecules disperse in the water, the larger the decrease in entropy. On the other hand, when the oil molecules clump together, the area of “ordered water” is reduced; fewer water molecules are affected. Therefore, there is an increase in entropy associated with the clumping of oil molecules —a totally counterintuitive idea!

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cma 7y ago
What about with heavy gases and light ones like helium? Do they eventually mix completely in large atmospheres under a big gravity gradient? I would think a mixture should gain kinetic energy as the heavier one settles more on the bottom, releasing photons from the heat which increases total entropy, but in a closed system where the photons are reflected back it would hit some equilibrium with heavier stuff at the bottom, but more kinectic and photonic energy which maybe both together give more degrees of freedom than a more evenly mixed mixture with less kinetic energy and higher gravitational potential energy.
- kgwgk 7y ago
  > I would think a mixture should gain kinetic energy as the heavier one settles more on the bottom, But this is not what happens, or there would only be CO2 (and a small ammount of the heavier atoms and molecules) in the lower part of our atmosphere. > I would think a mixture should gain kinetic energy as the heavier one settles more on the bottom, But this is not what happens, or there would only be CO2 (and a small ammount of the heavier atoms and molecules) in the lower part of our atmosphere. Edit: Maybe you know this already, but in equilibrium the mixture does indeed have more kinetic energy (per unit of volume) as you go down because even though the temperature remains constant the pressure increases.

szemet 7y ago

Isn't this a too narrow definition of entopy? Ok. Pure physical entropy was the first and original usage, but now informational entropy can be used at higher level, and it correlates well with disorder at that level. If I sort an array its entropy will be lower - while due to thermodynamics the total entropy of the world will be increased. So there is the only the high level component I'm interested in: I see less macrostate in a sorted array(one) than in an undordered(n factorial) even if the microstates in the world have increased(I don't care). Same goes for the article examples, for me subjectively an ice statue can have many different forms (macrostates), if it melts it will have one form (a puddle) - so I see the entropy to decrease - of course the puddle have more microstates than the ice statue - just I do not differentiate between them... True: in the sbove examples things became more ordered at high level (entropy have decreased), meanwhile physical entropy have increased - but that increase was global and in our local point of interest it is still can be said (according to modern usage) that entropy have decreased! Of course the total sum have to be positive - that's the basis of how for example the Landauer principle is calculated, wich connects the above high level informational view with physical entropy...

kgwgk 7y ago
Note that this is an article for physics teachers and the conclusion is “we can warn our students that this is not the meaning of the word “entropy” in physics.”

ScottBurson 7y ago

Slightly OT, but I just saw this last night and thought it was hilarious: You should call it "entropy", for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage. — John von Neumann, suggesting to Claude Shannon a name for his new uncertainty function, as quoted in Scientific American Vol. 225 No. 3, (1971), p. 180.

hcs 7y ago
Schrödinger used the term "negentropy". And there's a story that Norbert Wiener used to wander around MIT telling anyone who would listen that information is negative entropy, including Shannon. (I'm having trouble finding it, will edit if I track it down) Edit: ah, it was Fano who told that story (quoted in "The Cybernetics Moment"): > Electrical engineer Robert Fano at MIT, recalled that sometime in 1947, Wiener "walked into my office ... announced 'information is entropy' and then walks out again. No explanation, no elaboration." More about Wiener's approach and another recounting of the story here: http://news.mit.edu/2011/timeline-wiener-0119 http://news.mit.edu/2011/timeline-wiener-0119
kgwgk 7y ago
The article in question: Energy and Information http://www.esalq.usp.br/lepse/imgs/conteudo_thumb/mini/Energy-and-Information.pdf http://www.esalq.usp.br/lepse/imgs/conteudo_thumb/mini/Energ... Another paper co-authored by Myron Tribus: Information Theory and Thermodynamics https://www.e-periodica.ch/cntmng?pid=hpa-001:1974:47::871 https://www.e-periodica.ch/cntmng?pid=hpa-001:1974:47::871

trhway 7y ago

Typical fallacy in entropy considerations is to consider system as isolated in the model while it is strongly connected to the environment in reality. The oil/vinegar (similar to the pennies and dimes mentioned in the article - when shaken in a jar would "magically" separate with pennies on top) has exported the entropy to the environment through the work of gravitational force in full accordance with the 2nd law - the system transitions following the gradient and thus increasing total entropy of the whole system. A similar mistake for example is when "life" is stated to be "anti-entropic" in any sense while it is a really a form of matter organization which generates even more entropy than the same amount of dead matter would.

kgwgk 7y ago

A couple of related articles from Lambert (https://en.m.wikipedia.org/wiki/Frank_L._Lambert https://en.m.wikipedia.org/wiki/Frank_L._Lambert): Shuffled Cards, Messy Desks, and Disorderly Dorm Rooms — Examples of Entropy Increase? Nonsense! http://entropysite.oxy.edu/shuffled_cards.html http://entropysite.oxy.edu/shuffled_cards.html Disorder — A Cracked Crutch For Supporting Entropy Discussions http://entropysite.oxy.edu/cracked_crutch.html http://entropysite.oxy.edu/cracked_crutch.html

foxes 7y ago

The definition of entropy from a statistical mechanics perspective, is roughly a count of the number of different (microscopic) configurations, \Omega, of a system. When all the configurations are equally probable, you get the formula S ~ log(\Omega) I don't think you see this definition in a physics education until you do a course on statistical mechanics? I feel like I certainly had teachers say "disorder". I think the connection being that if there are more configurations it's more "disordered" which isn't really a precise thing. Looking back, I think rambling about ideal gases/pressure/volumes is a boring way to teach this subject (at least at late high school/first year uni). You should probably introduce it by talking about configurations and information. You can think of some very clear examples (configurations of a list of objects for example, it doesn't necessarily have to be "physical"). Then maybe you would go on to show that this is connected to macroscopic physical properties.

rstuart4133 7y ago
> I don't think you see this definition in a physics education until you do a course on statistical mechanics? I'm over 60, and I only recent discovered the definition of entropy recently thanks to Leonard Susskind youtube videos. For 60 bloody years I only got the dumbed down version about "disorder" and it made absolutely no sense to me whatsoever. Now I see the same confusion in others - like here on HN were to people where duking it out over whether one arrangement of a pack of cards (all individually identifiable of course) had more entropy than the other. This dumbing down does nobody any favors whatsoever. It certainly doesn't promote understanding of the basic principles.

codesushi42 7y ago

The best book on the subject: https://www.amazon.com/Entropy-Demystified-Second-Reduced-Revised/dp/9812832254/ https://www.amazon.com/Entropy-Demystified-Second-Reduced-Re...

tullatulla 7y ago

The author seems to mix up Gibbs free energy with entropy. The remark that thermal equilibrium equals maximum entropy is simply wrong. All examples can be explained with minimization of the free energy: dG = dH - TdS dH == internal energy (chemical bonds) + pV dS == Entropy term T == Temperature Where entropy is the number of different states the system can be in for a given internal energy. A thermodynamic system in equilibrium will always tend to a state of lowest free energy. Example: a perfect crystal would be a totally ordered state (and with the lowest entropy), with the internal energy minimized due to the highest number of chemical bonds. For T -> 0, this would be the thermodynamically most stable configuration (however not always kinetically accessible, e.g. supercooled water). As Temperature goes up, the Gibbs free energy of a more disordered phase (e.g. crystal defects or a liquid/gas phase) becomes lower and will eventually lead to the melting of the crystal. For the oil/water example, the separated state minimizes the free energy since polar water molecules can form hydrogen bonds with themselves (lowering the internal energy), and push out the oil molecules, even though the entropy is lower than for a totally mixed state. At higher temperatures, this will change theoretically and the mixed-phase becomes favorable thermodynamically. From this point of view, seeing higher entropy as more disorder seems absolutely fine, where more disorder is "lower chance of guessing the exact configuration of all molecules in the system".

kgwgk 7y ago
Entropy is maximized for an isolated system (constant energy), free energy is minimized for a system in thermal equilibrium with a heat bath (can exchange energy with the environment). Gibbs free energy is minimized at constant pression and temperature, Helmholtz free energy is minimized at constant volume and temperature. If you put now the oil/water system into a isolated container the equilibrium state won't change substantially. It remains separated in two phases and that's now the maximum entropy state.