Negative temperature

SI temperature/coldness conversion scale: Temperatures on the Kelvin scale are shown in blue (Celsius scale in green, Fahrenheit scale in red), coldness values in gigabyte per nanojoule are shown in black. Infinite temperature (coldness zero) is shown at the top of the diagram; positive values of coldness/temperature are on the right-hand side, negative values on the left-hand side.

Certain systems can achieve negative thermodynamic temperature; that is, their temperature can be expressed as a negative quantity on the Kelvin or Rankine scales. This should be distinguished from temperatures expressed as negative numbers on non-thermodynamic Celsius or Fahrenheit scales, which are nevertheless higher than absolute zero. A system with a truly negative temperature on the Kelvin scale is hotter than any system with a positive temperature. If a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system.^[1]^[2] A standard example of such a system is population inversion in laser physics.

Thermodynamic systems with unbounded phase space cannot achieve negative temperatures: adding heat always increases their entropy. The possibility of a decrease in entropy as energy increases requires the system to "saturate" in entropy. This is only possible if the number of high energy states is limited. For a system of ordinary (quantum or classical) particles such as atoms or dust, the number of high energy states is unlimited (particle momenta can in principle be increased indefinitely). Some systems, however (see the examples below), have a maximum amount of energy that they can hold, and as they approach that maximum energy their entropy actually begins to decrease.^[3]

^ Ramsey, Norman (1956-07-01). "Thermodynamics and Statistical Mechanics at Negative Absolute Temperatures". Physical Review. 103 (1): 20–28. Bibcode:1956PhRv..103...20R. doi:10.1103/PhysRev.103.20.
^ Tremblay, André-Marie (1975-11-18). "Comment on: Negative Kelvin temperatures: some anomalies and a speculation" (PDF). American Journal of Physics. 44 (10): 994–995. Bibcode:1976AmJPh..44..994T. doi:10.1119/1.10248.
^ Atkins, Peter W. (2010-03-25). The Laws of Thermodynamics: A Very Short Introduction. Oxford University Press. pp. 89–95. ISBN 978-0-19-957219-9. OCLC 467748903.

[1] Ramsey, Norman (1956-07-01). "Thermodynamics and Statistical Mechanics at Negative Absolute Temperatures". Physical Review. 103 (1): 20–28. Bibcode:1956PhRv..103...20R. doi:10.1103/PhysRev.103.20.

[2] Tremblay, André-Marie (1975-11-18). "Comment on: Negative Kelvin temperatures: some anomalies and a speculation" (PDF). American Journal of Physics. 44 (10): 994–995. Bibcode:1976AmJPh..44..994T. doi:10.1119/1.10248.

[3] Atkins, Peter W. (2010-03-25). The Laws of Thermodynamics: A Very Short Introduction. Oxford University Press. pp. 89–95. ISBN 978-0-19-957219-9. OCLC 467748903.

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