It bugs me that they describe it as being "below" absolute zero, because that's misleading. Negative temperatures are
hotter than positive ones, in the sense that heat would flow out of the negative temperature system into one with a positive temperature. A more accurate description would be to think of a number line:
<--negative infinity, -3, -2, -1, 0, 1, 2, 3, infinity-->
But instead of the negative end being to the left of the positive end, you pick it up and tack it onto the
right side:
+0, 1, 2, 3, infinity--><--negative infinity, -3, -2, -1, -0
Now positive infinity is pretty much the same thing as negative infinity, and +0.000001 is super far away from -0.000001. This all seems strange, because we usually think of temperature as average energy or motion of particles, but the temperature they're talking about in the article is dQ/dS, AKA "how much energy do I need to add to increase the entropy of something by a fixed amount?" Temperature goes up as you add energy, because you get diminishing returns. For most stuff, the story ends there, but if you limit your system in such a way that there is a
maximum amount of energy it can hold, once you've filled it up about half way, it turns out that adding more energy starts to
decrease your entropy (microstates, yo), and you've suddenly made the slope of your energy/entropy line (AKA temperature) go negative. Fill it to the max, and you're at that "-0" spot on the temperature line.