This news story has been gathering attention today: a team from Ludwig-Maximilians-Universität in Munich has created a quantum potassium gas with a temperature below absolute zero. As the claim sounds far-fetched, let’s take a closer look (with hand-drawn graphs!) and see what has happened.
Temperature is a statistical measure of the average energy of the particles in a substance. When a substance is hotter it has a higher average energy, and a lower energy when it is colder. We experience “hot” and “cold” when heat flows from the substance to us, or vice versa.
Absolute zero is the point at which a substance has no kinetic energy at all. Of course, you can’t take energy away from something that has no energy, so it follows that, seemingly, nothing can have a temperature lower than absolute zero.
But there’s more to the story.
It turns out that temperature is not simply a measure of thermal energy. It also involves entropy, a fundamental thermodynamic concept that is related to the disorder or the dispersal of energy in a system. Entropy increases as disorder increases or as energy is dispersed in a system.
Normally, temperature and entropy have a positive correlation. As energy increases, temperature increases and entropy increases. Consider a small sample of particles with a low distribution of energies. As energy is added, the temperature increases because more and more particles gain greater levels of energy. The entropy increases as well, because the particles become more distributed across the range of energy levels.
We can, therefore, think of temperature as a combined measurement of the energy and entropy of a system. As energy is added, both average energy and entropy increase together. Mathematically, this combined energy/entropy definition of temperature yields a positive number so long as the entropy and energy are both increasing.
Here’s where things get a bit stranger, though. A state of maximum entropy would occur when the particles were all evenly distributed across the range of energy levels. At this point, the particles cannot be any more dispersed than they already are. If we were to continue adding energy after this point, the system would increase in energy, but its entropy would in fact decrease because the particles would become more and more clustered at the high-energy level of the distribution. The entropy would therefore decrease, even as energy increased, as the system’s particles became less dispersed.
In this strange realm, energy and entropy have an inverse relationship. As energy increases, entropy decreases. (If we kept adding thermal energy, we’d theoretically reach a point where entropy was zero.) The upshot is that this inverse relationship between energy and entropy would mean that temperature would turn out, mathematically, to be negative.
As you can see in the high-tech graph below, temperatures in a substance with this kind of distribution would not range from zero to infinity, but would rather range from negative infinity to – 0. On the left are normal temperatures, from absolute zero up to infinity. Then the temperature scale suddenly shifts from positive infinity to negative infinity, and then tapers down to negative absolute zero (at which point there would be zero entropy.)

Of course, conditions like this don’t occur in the everyday world. Interactions between particles and between the system and its environment would normally prevent this kind of high-energy/low-entropy distribution from coming about. The team at Ludwig-Maximilians, however, was able to take the atoms of a supercold potassium gas and suspend them in a vacuum. They then used a combination of lasers and magnetic fields to cause the atoms to both obtain a high energy level and yet remain in place. Without the ability to interact with each other or their surroundings, the gas had exactly the high-energy distribution needed to find itself in the realm of negative absolute temperatures.
The team’s paper itself is published in Science, and more coverage can be found here and here.