Temperature depends on the energy landscape (Image: Ludwig Maximilian University of Munich)

Nothing is colder than absolute zero, so it seems nonsensical to talk about negative temperature – but now there is a substance that must have just that. The revelation could shake up our ideas about temperature and help us understand strange entities such as dark energy, as well as the interactions of subatomic particles.

Although we’re used to talking about negative temperatures, such as −10°C, all temperatures on an ordinary thermometer are actually positive when measured in kelvin, the scientific temperature scale that starts at absolute zero (−273.15°C).

On the kelvin scale, temperature is determined by the kinetic energy of particles, so a gas of slow particles is colder than a gas of fast-moving ones. Absolute zero corresponds to the point at which particles stop moving completely, which is why nothing can be colder.


That does not tell the whole story, however. Temperature also depends on the way in which the particle energies are distributed within the gas, which determines their entropy, or disorder.

Energy landscape

Above absolute zero, adding more energy corresponds to an increase in entropy. Picture a hill next to a valley (see image) with the height of the landscape corresponding to the energy of a particle – and the chance of finding a particle at a certain height representing entropy. At absolute zero, particles are motionless and all have no energy so are all at the bottom of the valley, giving a minimum entropy.

As the gas heats up, the average energy of the particles increases, with some gaining lots of extra energy but most just a small amount. Spread along the side of the hill, now the particles have different energies, so entropy is higher.

According to temperature’s entropic definition, the highest positive temperature possible corresponds to the most disordered state of the system. This would be an equal number of particles at every point on the landscape. Increase the energy any further and you’d start to lower the entropy again, because the particles wouldn’t be evenly spread. As a result, this point represents the end of the positive temperature scale.

In principle, though, it should be possible to keep heating the particles up, while driving their entropy down. Because this breaks the energy-entropy correlation, it marks the start of the negative temperature scale, where the distribution of energies is reversed – instead of most particles having a low energy and a few having a high, most have a high energy and just a few have a low energy. The end of this negative scale is reached when all particles are at the top of the energy hill.

The resulting thermometer is mind-bending with a scale that starts at zero, ramps up to plus infinity, then jumps to minus infinity before increasing through the negative numbers until it reaches negative absolute zero, which corresponds to all particles sitting at the top of the energy hill.

Cold atoms

“The temperature scale as we know it starts at zero and goes up to infinity, but it doesn’t stop there,” says Ulrich Schneider of the Ludwig Maximilian University of Munich in Germany.

To enter the negative realm, Schneider and his colleagues began by cooling atoms to a fraction above absolute zero and placing them in a vacuum. They then used lasers to place the atoms along the curve of an energy valley with the majority of the atoms in lower energy states. The atoms were also made to repel each other to ensure they remained fixed in place.

Schneider’s team then turned this positive temperature system negative by doing two things. They made the atoms attract and adjusted the lasers to change the atoms’ energy levels, making the majority of them high-energy, and so flipping the valley into an energy hill. The result was an inverse energy distribution, which is characteristic of negative temperatures.

The atoms can’t lose energy and “roll down” this hill because doing so would require them to increase their kinetic energy and this is not possible because the system is in a vacuum and there is no outside energy source. “We create a system with a lot of energy, but the particles cannot redistribute their energy so they have to stay on top of the hill,” says Schneider.

Dark temperature

Cold atoms are already used to simulate the interactions of some subatomic particles. The new negative temperature set-up could be used to create simulated interactions that are not possible with positive temperatures. “They are a new technical tool in the business of quantum simulations,” says Schneider.

Negative temperature may also have implications for cosmology. Dark energy, thought to explain the accelerating expansion of the universe, exerts negative pressure, which suggests it might have negative temperature – Schneider is currently discussing the idea with cosmologists.

“It is amazing experimental work,” says Allard Mosk of the University of Twente in the Netherlands, who originally outlined the theory behind the experiment in 2005.

Learning more about how negative temperature systems interact both with themselves and with positive temperatures might allow us to build ultra-efficient heat engines, but these are far off, he says. “I don’t think this will immediately give us new devices, but it will give us a deeper understanding about what temperature really is.”

Journal reference: Science, 10.1126/science.1227831