Negative absolute temperatures

Question

I read that scientists created a substance that was below absolute zero. How is that possible? Is it some mathematical quirk in how they calculate temperature, or can it actually be said to be physically ‘colder’ than something at absolute zero? What are alternate definitions of temperature

In: Physics

Answer 1

I believe you’ve got a great answer from /u/r3dl3g but I just couldn’t leave this thread without attempting to explain entropy a bit more as he gave the thermodynamic view, the statistical physics one is the one for me…

So let’s say you’ve got some physical system (a glass of water for instance), in the micro scale this system is made of constituents, the water is basically a huge collection of water molecules right? now there are many ways to arrange those molecules and still in the macro scale, we would see the same glass of water, many microscopic arrangements lead to the same macroscopic one.

Entropy is just saying, if this water glass has this much energy, how many arrangements could possibly result in it? (for those interested Entropy = Kb * natural log (number of arrangements at given energy) where Kb is just some constant).

Now we can define temperature 1/T = dS/dU basically the temperature is the answer to the question “hey, if we where to add a bit of energy to this glass of water, how does the number of arrangements change?” normally we would expect the number of arrangements to increase, I mean the water molecules would be swooshing around faster and in more ways, makes intuitive sense at least right? increasing number of arrangements would mean positive temperature according to the definition, but who’s to say that they can’t decrease? that would mean negative temperature…

now going back to /u/r3dl3g’s answer, what he means in that negative temperatures are hotter is that the ordering of events goes : We add energy -> Entropy increases -> We add more energy -> Entropy increases even more -> We add more energy -> Ah, guys? I think we overdid it -> Entropy decreases as the current setup is unstable. To reach negative temperatures you must first pass through positive temperatures.