Editing Negative temperature (section)

== History ==

The possibility of negative temperatures was first predicted by [[Lars Onsager]] in 1949.<ref name = Ons1949>{{cite journal |last=Onsager |first=L. |year=1949 |title= Statistical Hydrodynamics |journal=Il Nuovo Cimento |volume= 6|issue=  2|pages=279–287 |doi=10.1007/BF02780991 |issn=1827-6121 |bibcode=1949NCim....6S.279O |s2cid=186224016 }}</ref>
Onsager was investigating [[Two-dimensional point vortex gas|2D vortices]] confined within a finite area, and realized that since their positions are not independent [[degrees of freedom]] from their momenta, the resulting [[phase space]] must also be bounded by the finite area. Bounded phase space is the essential property that allows for negative temperatures, and 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.

The limited range of states accessible to a system with negative temperature means that negative temperature is associated with emergent ordering of the system at high energies. For example in Onsager's point-vortex analysis negative temperature is associated with the emergence of large-scale clusters of vortices.<ref name=Ons1949 /> This spontaneous ordering in equilibrium statistical mechanics goes against common physical intuition that increased energy leads to increased disorder.

It seems negative temperatures were first found experimentally in 1951, when Purcell and Pound observed evidence for them in the nuclear spins of a [[lithium fluoride]] crystal placed in a magnetic field, and then removed from this field.<ref name = PuPo>{{cite journal |last1 = Purcell |first1 = E. M. |last2 = Pound|first2 = R. V. |year = 1951|title = A nuclear spin system at negative temperature|journal = Physical Review |volume = 81 | issue = 2|pages =279–280 |doi = 10.1103/PhysRev.81.279 |bibcode = 1951PhRv...81..279P }}</ref>  They wrote:

: A system in a negative temperature state is not cold, but very hot, giving up energy to any system at positive temperature put into contact with it. It decays to a normal state through infinite temperature.