Here's a well-written piece specifically on the physical meaning of negative temperature, using the same definitions as the parent post: http://math.ucr.edu/ho

Here's a well-written piece specifically on the physical meaning of negative temperature, using the same definitions as the parent post: http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/neg_temperature.html http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/neg... It provides a specific example of a scenario where a temperature below absolute zero would actually make sense: A spin-system of spin-1/2 atoms confined to a wire. The atoms aren't free to leave the wire, but they can change their spin state from spin-down (lowest energy) to spin-up (highest energy); thus, there is one lowest possible energy state (all atoms spin-down) and one highest possible energy state (all atoms spin-up). If you start with that system in the lowest possible energy state, adding energy takes the temperature from zero to approaching positive infinity (half of the atoms are spin-up), then approaches negative infinity, and climbs back to approaching zero, but still negative.