Editing Negative temperature (section)

== Heat and molecular energy distribution ==
[[File:NegativeTemperature.webm|300px|thumb|right|When the temperature is negative, higher energy states are more likely to be occupied than low energy ones.]]Negative temperatures can only exist in a system where there are a limited number of energy states (see below). As the temperature is increased on such a system, particles move into higher and higher energy states, so that the number of particles in the lower energy states and in the higher energy states approaches equality.<ref>{{Cite book |last1=Kubo |first1=Ryōgo |title=Statistical mechanics: an advanced course with problems and solutions |last2=Ichimura |first2=Hiroshi |date=1981 |publisher=North-Holland |isbn=978-0-7204-0090-8 |edition=6. print |location=Amsterdam}}</ref>  This is a consequence of the definition of temperature in [[statistical mechanics]] for systems with limited states. By injecting energy into these systems in the right fashion, it is possible to create a system in which there are more particles in the higher energy states than in the lower ones. The system can then be characterized as having a negative temperature.

A substance with a negative temperature is not colder than [[absolute zero]], but rather it is hotter than infinite temperature.<ref name=":0" /> As Kittel and Kroemer put it,<ref>{{cite book |last1=Kittel |first1=C. |author1-link=Charles Kittel |title=Thermal Physics |last2=Kroemer |first2=H. |author2-link=Herbert Kroemer |publisher=[[W. H. Freeman]] |year=1980 |isbn=978-0-7167-1088-2 |edition=2nd |pages=462}}</ref>

{{blockquote|The temperature scale from cold to hot runs +0&thinsp;K,…, +300&thinsp;K,…,+∞&thinsp;K, −∞&thinsp;K,…, −300&thinsp;K,…, −0&thinsp;K. Note that if a system at −300&thinsp;K is brought into thermal contact with an identical system at 300&thinsp;K, the final equilibrium temperature is not 0&thinsp;K, but is ±∞&thinsp;K.
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The corresponding inverse temperature scale, for the quantity {{math|1=''β'' = {{sfrac|1|''kT''}}}} (where {{mvar|k}} is the [[Boltzmann constant]]), runs continuously from low energy to high as +∞, …, 0, …, −∞. Because it avoids the abrupt jump from +∞ to −∞, {{mvar|β}} is considered more natural than {{mvar|T}}. Although a system can have multiple negative temperature regions and thus have −∞ to +∞ discontinuities.

In many familiar physical systems, temperature is associated to the [[kinetic energy]] of atoms.<ref>{{Cite journal |last=Nettleton |first=R. E. |date=March 1994 |title=On the relation between thermodynamic temperature and kinetic energy per particle |url=https://cdnsciencepub.com/doi/10.1139/p94-017 |journal=[[Canadian Journal of Physics]] |volume=72 |issue=3–4 |pages=106–112 |doi=10.1139/p94-017 |bibcode=1994CaJPh..72..106N |issn=0008-4204|url-access=subscription }}</ref> Since there is no upper bound on the momentum of an atom, there is no upper bound to the number of energy states available when more energy is added, and therefore no way to get to a negative temperature.<ref name=":0" /> However, in statistical mechanics, temperature can correspond to other degrees of freedom than just kinetic energy (see below).