The possibility of negative temperatures was first predicted by Lars Onsager in 1949, in his analysis of classical point vortices confined to a finite area. Confined point vortices are a system with bounded phase space as their canonical momenta are not independent degrees of freedom from their canonical position coordinates. Bounded phase space is the essential property that allows for negative temperatures, and such temperatures can occur in both classical and quantum systems. As shown by Onsager, a system with bounded phase space necessarily has a peak in the entropy as energy is increased. For energies exceeding the value where the peak occurs, the entropy decreases as energy increases, and high-energy states necessarily have negative Boltzmann temperature.