 Negative temperature

Negative absolute temperature can occur only for a system with an energy spectrum bounded above. Since $\beta =\partial S/\partial E<0$, higher-energy states are more populated than lower-energy states.

Negative temperature is a concept primarily found in statistical mechanics and thermodynamics, and it can be somewhat counterintuitive. While temperatures are usually thought of as being positive (0 K and above, where 0 K is absolute zero), negative temperatures can occur in systems with a limited number of energy states, such as certain magnetic systems or some types of dissipative systems.