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Heating Up by Cooling Down, Just Another Craziness That Is Quantum Physics

Let's face it: nothing makes sense in the topsy turvy world of quantum physics. Light can be both wave and particle. Schrödinger's cat is both dead and alive. Things can simultaneously sync up, even when they're separated by a large distance.

Why, it's enough to make Einstein throw up his hands and despair!

Well, add this to the weirdness that is quantum physics: quantum systems can heat up by cooling down.

Nemoto and her team examined a double sub-domain system coupled to a single constant temperature reservoir. Each sub-domain contained multiple spins -- a form of angular momentum carried by elementary particles such as electrons and nuclei. The researchers considered the situation where the spins within each sub-domain are aligned with respect to each other but the sub-domains themselves are oppositely aligned (for instance all up in one and all down in the second). This creates a certain symmetry in the system.

As time progresses, the components of the subdomain decay in a process called relaxation.

"Usually, we expect both domains to decay to the reservoir temperature; however, when the two domains coupled with a reservoir maintain a certain symmetry, the decay process can apparently heat the smaller domain up, even beyond the high temperature limit," Nemoto said.

See if you can understand what's going on in this article over at Science Daily, then tell the rest of the class, mkay? (Image: Future Quantum Physicist by Mike Jacobsen)

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I won't pretend to understand quantum physics, but I'm always amazed by how counterintuitive it can be.

And thank you for the detailed explanation! I quite enjoyed reading it (especially the bit about how temperature's definition has changed).
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I wouldn’t say that the research is earth-shattering, but is notable enough to be in PRL. The Science Daily article seems to only throw out a few definitions without much context, which sucks, because even if the research itself ends up being a bit boring, the background concepts might be interesting enough. On the other hand, I can understand not wanting to rewrite background material over and over again, especially when it might be already written elsewhere.

This research at the high level doesn’t actually need much quantum mechanics (QM), and instead needs more of a background in what temperature and spin have to do with each other.

Most people are taught that temperature is some sort of proxy for energy in a system, specifically random kinetic energy for those that paid attention. The idea that the hotter something is, the more random jiggling done by the constituent particles, goes back to the kinetic theory of gas work by Maxwell and Boltzmann in the 1860s-1870s. Before then, a lot of thermodynamics concepts, like temperature, were macroscopic ideas empirically worked out, but without much idea of what was mechanically happening on the microscopic level.

Although by the 1850s, Clausius already worked out something he called entropy that is closely connected to temperature and the state of the system (and important for things like the 2nd law and absolute limits on thermal efficiency of engines). Boltzmann’s work also started to give a microscopic mechanism to entropy, showing entropy is basically how much freedom a system has to move around. Over 1870s-1900ish, people like Gibbs, further refined entropy, showing that it is related to the number of equivalent states a system can be in.

This is relevant to temperature, because the end result is you define temperature in terms of entropy: temperature tells you how many more states you can access for an extra bit of energy. This ends up being equivalent to the kinetic idea, but way more general. The more energy you have, the more ways you can spread out between different jiggling particles, hence the more states you can access. An analogy to temperature would be money, in that the more money you have, the more different ways you can split the money up between a group of people for a given total amount of money.

Many fundamental particles have an innate spin to them, and for charged particles this means they act like little bar magnets. As a result, more complicated combinations, like atoms, can also have this innate spin from the combination of all of the individual parts. The only relevant bit here is that because they act like bar magnets, they will try to line up with a background magnetic field like the needle in a compass. Since you have to push on the particle to make it point away from the field, it takes more energy to make the spin point the “wrong” way. The one piece of QM needed here, is that the energy can only come in certain big steps, so for fundamental particles and certain atoms, there are only two possible orientations of the spin: with the background magnetic field (let’s assume this is pointing down) and against (let’s then call this pointing up).

Let’s say we had ten such atoms, and they are spread out enough to not interact with each other, just the background magnetic field. The lowest energy setup would be to have them all point down. The next lowest would be to add one unit of energy so we have one pointing up, and nine pointing down. If we randomly pick which one points up, there are ten possible choices, hence there are ten possible states for that amount of energy. If we put in two units of energy so there would be two ups and eight downs, there are 45 possible states, while the original lowest energy option only had one possible state. Adding energy opens up more states, giving more entropy and lets you define a temperature that increases with energy just like in the classical situation of gas atoms bouncing around in a box. All of the other ideas behind temperature work here, and you can take different groups of atoms and let heat flow between them and their temperature reach equilibrium, etc, with the same thermodynamic principles holding.

But something odd happens as you keep adding energy. At 5 units, you have 5 up and 5 down pointing spins, which gives you 252 ways to arrange those spins, but at 6 units you end up with 6 up and 4 down, with only 210 ways to arrange the spins. At the extreme, with 10 units of energy, all of the spins have to point up, and there is only one possible state. Because the number of states and hence entropy is going down with more energy, which is backwards in a sense, the temperature then becomes a negative number on an absolute scale. So in some finite systems, where there is a maximum possible energy, you also get a maximum temperature and then a negative temperature that just means adding energy makes the system more constrained.

Relaxation to Negative Temperatures in Double Domain Systems:

This is the title of the paper referenced in the story, and the story doesn’t even seem to mention the negative temperature bit (can’t blame them, it often turns online discussions into a quagmire).

By double domain, they mean they have two of these groups of particles with spin, where all of them within a group point the same way (like domains in a piece of iron, where there are sections of iron that have all of the atoms pointing together). The domains don’t directly interact with each other, but both instead interact with a common reservoir, and the researchers are studying how the domains reach an equilibrium temperature with the reservoir. In a sense, this is like studying two hunks of metal at different temperatures, and how that temperature changes when you dunk them at the same time into a giant tank of water (i.e. something that can suck up or give out a lot of heat without changing temperature).

The other special part of their setup though, is that they are setting up the two domains to be “superradiant.” When energy is exchanged between the reservoir and the domains, the size of the waves (e.g. radio or light waves) is much bigger than the domains, so that can cause weird indirect coupling, where one domain emitting or receiving energy affects the other because they are essentially both bathed in the same light. It also means there are some special symmetries involved, and importantly, no way to break them.

The end result is that there are constraints on what spins can flip or not flip as the temperature changes. If you start with one domain where everything is pointed up (high energy) and in the other everything is pointed down (low energy), and the reservoir at some medium temperature, normally the former would cool off and the latter heat up. But the constraints limit how many states you can access at each energy amount, thus changing how much entropy there is for a given amount of energy. As temperature comes from the relationship between entropy and energy, this changes the behaviour of the temperature for combined system: the system is more than just two parts stuck together. The combined system drifts toward the same temperature as the reservoir, but how energy gets spread out or taken from the individual domains gets constrained, and can cause their individual temperatures to do weird things. For example, having a large domain pointing up and a small domain pointing down, the system drifts to most of the large domain pointing down (cooling off) but all of the small domain pointing up (a negative temperature). If you had only the reservoir and a small domain initially pointing down, the small domain would stay mostly pointed down. Hence the two domain system causes the small domain to absorb more energy than it would without the large domain.

(I am glossing over a lot due to length and having only skimmed the actual paper, which is freely available on ArXiV.)
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