Editing Absolute zero (section)

==Negative temperatures==
{{Main|Negative temperature}}

Temperatures that are expressed as negative numbers on the familiar Celsius or Fahrenheit scales are simply colder than the zero points of those scales. Certain [[Thermodynamic system|systems]] can achieve truly negative temperatures; that is, their [[thermodynamic temperature]] (expressed in kelvins) can be of a [[Negative number|negative]] quantity. A system with a truly negative temperature is not colder than absolute zero. Rather, a system with a negative temperature is hotter than ''any'' system with a positive temperature, in the sense that if a negative-temperature system and a positive-temperature system come in contact, heat flows from the negative to the positive-temperature system.<ref name="Chase">{{Cite web |last=Chase |first=Scott |title=Below Absolute Zero -What Does Negative Temperature Mean? |url=http://www.phys.ncku.edu.tw/mirrors/physicsfaq/ParticleAndNuclear/neg_temperature.html |url-status=dead |archive-url=https://web.archive.org/web/20110815144418/http://www.phys.ncku.edu.tw/mirrors/physicsfaq/ParticleAndNuclear/neg_temperature.html |archive-date=15 August 2011 |access-date=2 July 2010 |website=The Physics and Relativity FAQ}}</ref>

Most familiar systems cannot achieve negative temperatures because adding energy always increases their [[entropy]]. However, some systems have a maximum amount of energy that they can hold, and as they approach that maximum energy their entropy actually begins to decrease. Because temperature is defined by the relationship between energy and entropy, such a system's temperature becomes negative, even though energy is being added.<ref name="Chase" /> As a result, the Boltzmann factor for states of systems at negative temperature increases rather than decreases with increasing state energy. Therefore, no complete system, i.e. including the electromagnetic modes, can have negative temperatures, since there is no highest energy state,{{citation needed|date=October 2016}} so that the sum of the probabilities of the states would diverge for negative temperatures. However, for quasi-equilibrium systems (e.g. spins out of equilibrium with the electromagnetic field) this argument does not apply, and negative effective temperatures are attainable.

On 3 January 2013, physicists announced that for the first time they had created a quantum gas made up of potassium atoms with a negative temperature in motional degrees of freedom.<ref>{{Cite journal |last=Merali |first=Zeeya |year=2013 |title=Quantum gas goes below absolute zero |journal=Nature |doi=10.1038/nature.2013.12146 |s2cid=124101032 |doi-access=free}}</ref>