Is that still heat then in the way we talk about "hot" or is that actually colder in a naive sense?
Heat is the transfer of energy, so it will
always flow from −0 K (hot) to +0 K (cold).
Think of it this way.
+0 K, a uniform state of minimum entropy. All individual atoms possess the same minimum energy state. As you add energy the entropy increases, the average temperature increases, and the possible range of
energy states of individual atoms
increases.
−0 K, a uniform state of maximum entropy. all individual atoms possess the same maximum energy state. This because the system is entropy-saturated, meaning that entropy can no longer grow. As you add energy the entropy decreases, the average temperature decreases, and the possible range of
energy states of individual atoms
increases.
+0 K is the "coldest" possible uniform energy state; entropy (and temperature) increases as energy is added to the system.
+∞ K is the "hottest" possible non-uniform energy state; range of energy states increases as energy is added to the system.
−∞ K is the "coldest" possible non-uniform energy state; range of energy states increases as energy is added to the system.
−0 K is the "hottest" possible uniform energy state; entropy (and temperature) decreases as energy is added to the system.
Moving towards +∞ K means that the system is growing "hotter" and more "non-uniform". There is no limit to entropy, so the more energy you add, the "hotter" and more "non-uniform" it becomes, growing towards +∞ K.
If, however, a system has an entropy limit, it can become saturated. As you add energy the system will slowly become more uniform, reaching a maximum entropy, and once it is fully saturated all individual atoms are in a uniform (maximum) energy state. Greater "heat" and greater "temperature" means greater "entropy", so for a entropy-saturated system, any energy beyond the entropy limit cannot do any work, and entropy will actually decrease, thus also "heat" and "temperature".
Also, I believe that kinetic theory only applies to gases, maybe? Maybe solids as well, but once it gets hot enough it's no longer gas, it becomes plasma. As it gets even hotter, who knows, maybe you get a soup of quarks and electrons.
However, using kinetic theory, +0 K is a "cold" state where all atoms are "motionless" while −0 K is a "hot" state where all atoms are "motionless". Adding energy to either system will give the atoms "motion" — but for +0 K the entropy will increase, and for −0 K the entropy will decrease.
Oh, and I think this is strictly a quantum mechanical phenomenon, so you couldn't get a quantity of water with a negative temperature, I believe.
Even though I like physics, I wouldn't dare say I'm a physicist
And unfortunately there is no proper physicist around to properly explain it.
https://en.wikipedia.org/wiki/Negative_temperature