"Normally, most particles have average or near-average energies, with only a few particles zipping around at higher energies. In theory, if the situation is reversed, with more particles having higher, rather than lower, energies, the plot would flip over and the sign of the temperature would change from a positive to a negative absolute temperature."
If more particles have higher energy, then wouldn't the average energy increase as well? And if the average energy increases, then shouldn't that still keep things in positive, rather than negative, territory?
Temperature is not really the average kinetic energy any more. The temperature of a system says something about how much the entropy increases as you add energy. Negative temperature simply means that the entropy decreases as you add energy.
This is possible if the number of high energy states is small, because then adding energy will result in the system being in one of a smaller number of high energy states, thus having lower entropy (the entropy of a system is basically the logarithm of the number of states we think the system could be in, so if the number of states is lower, then the entropy is lower). Another way of saying this is that is as follows. For positive temperatures our knowledge of the state of the system would decrease if we added energy (think about a box full of neatly arranged balls and giving it a kick). For negative temperatures our knowledge of the system would increase if we added energy. In the extreme case if the number of possible high energy states is 1, then adding energy can force the system into exactly that state, thus we would know all you can know about the system.
In particular in the experiment described in the article, if you removed energy from the system the particles would not be in the lattice arrangement and instead would go around randomly. Thus the entropy would increase if you removed energy.
A thought experiment where a cup of some substance manages to be observed at a stable negative temperature.
This substance is a liquid at its current temperature. But it is colder than the ambient temperature of the room. As the liquid warms up from the ambient room temperature, it freezes. But taken outside on a cold day, it will melt and then evaporate?
I know you're not going to get a cup of this stuff in reality, but am I at least understanding the idea? The "temperature" of the liquid would remain negative, it's not like it could ever "warm up" to the point it was positive? It could reach an equilibrium state with its environment, but it would still be negative?
Yes, that's the right idea (assuming it has lower entropy when it's frozen than when it's liquid). In the context of the liquid you describe, and assuming it has otherwise normal properties then yes you can't warm it up (= add energy) and make it positive again. And if you took it outside, the temperature would first become more and more negative and then flip to positive. However, as long as we are talking about exotic stuff it is conceivable that as you add energy, the entropy first decreases (i.e. negative temperature) but if you add more and more energy, the entropy starts to go up again. For example lets say that if you add a lot of energy to the frozen stuff, it becomes a gas. I'm not sure if a system like that where you go from positive to negative to positive is physically possible, but I don't currently see any reason why it wouldn't be.
An object with negative temperature is hotter than an object with positive temperature. So it's not possible for the cup of negative temperature liquid to be "cooler" than the ambient temperature of the room. The liquid's temperature will get more and more negative until it flips from negative infinity to positive infinity, and then cool down from there until it equilibrates with the ambient environment.
Are any laws of thermodynamics violated here[1]? If not, why is this experiment interesting? As a physics student, let me check: 0. Probably not. 1. Not directly applicable 2. Nope. 3. Nope.
I did not read the article (shame on me), but the story goes like this:
Normally, energy of a system is bounded from below (there's a lowest energy). Adding energy to the system increases the number of accessible microstates (individual particles may occupy energy levels from lowest to highest accessible one) and thus the entropy. Such a system is characterized by positive temperature.
Now, quantum systems may come with an energy bounded from above, and adding energy to the system will decrease the number of accessible microstates (individual particles are forced into the highest energy level and have nowhere else to go). Such a system is characterized by negative temperature.
A system with negative temperature is hotter than one with positive temperature in the sense that heat will flow from the system with negative temperature to the one with positive temperature.
Negative temperature is a quantum effect than can be tricky to produce experimentally.
There's nothing mysterious about negative temperature from the thermodynamical point of view, but there are no classical systems that exhibit this property.
But isn't the property, as described, simply a different way of reasoning about the same physical phenomenon? (Clearly it's not, I'm just not sure where the gap in my understanding is)
>"Normally, most particles have average or near-average energies, with only a few particles zipping around at higher energies. In theory, if the situation is reversed, with more particles having higher, rather than lower, energies, the plot would flip over and the sign of the temperature would change from a positive to a negative absolute temperature."
Unless I'm missing something that is complete nonsense. If more particles have higher rather than lower energies the average shifts up and the most particles have average energy with just a few with much more energy. There is nothing to limit the maximum energy of particles like absolute zero on the high end.
I didn't read the actual research article, but this fragment reads as the usual disfigurement of actual information commited by a journalist attempting to explain a concept he/she doesn't understand at all.
No, it's not... really nonsense--it's just really confusing if you haven't worked with entropy and canonical ensembles before. See my comment above, or http://en.wikipedia.org/wiki/Thermodynamic_beta.
"Normally, most particles have average or near-average energies, with only a few particles zipping around at higher energies. In theory, if the situation is reversed, with more particles having higher, rather than lower, energies, the plot would flip over and the sign of the temperature would change from a positive to a negative absolute temperature."
If more particles have higher energy, then wouldn't the average energy increase as well? And if the average energy increases, then shouldn't that still keep things in positive, rather than negative, territory?