Temperatures below absolute zero are hotter than infinity

A negative absolute temperature is not colder than absolute zero but hotter than any positive temperature, and in a study published in January 2013 physicists in Munich reported creating one in a gas of about 100,000 potassium atoms, at roughly minus a billionth of a kelvin. The team was led by Ulrich Schneider and Immanuel Bloch at Ludwig Maximilian University and the Max Planck Institute of Quantum Optics.

In an ordinary gas most particles sit in low-energy states and only a few in high ones. Heat it towards infinite temperature and the particles spread evenly over every energy. Push further, which is possible only if energy has an upper limit, and most particles crowd into the highest states. That inverted distribution carries a negative Kelvin value: the scale does not end at infinity but jumps to negative numbers. Heat would flow out of such a gas into anything at a positive temperature.

The Munich team built the ceiling with an optical lattice of laser beams that caps the atoms’ kinetic energy, limited their interaction and potential energy as well, then drove the atoms to the top.

Not the first, and not settled

The 2013 gas is often described as the first temperature below absolute zero. It was not: the team’s own paper notes that negative temperatures had already been demonstrated in localized systems with a fixed set of discrete energy levels. Theirs was the first for moving particles.

The idea itself is disputed. In 2014, Jörn Dunkel and Stefan Hilbert argued in Nature Physics that such claims rest on an inconsistent definition of entropy, and that with Gibbs’s definition temperature stays positive. Daan Frenkel and Patrick Warren replied that, far from being forbidden, negative temperatures are inevitable in systems with bounded energy.

The states behave strangely either way. The attracting atoms should have collapsed but stayed stable, a parallel the team drew with dark energy, and in principle such a gas could run a heat engine above 100% efficiency by drawing energy from the cold side too, without breaking energy conservation.