Editing Temperature

The '''temperature''' of a system in [[classical thermodynamics]] is  intimately related to the [[zeroth law of thermodynamics]]; two systems having to have the same temperature if they are to be in thermal equilibrium (i.e. there is no net [[heat]] flow between them).
However, it is most useful to have a temperature scale.
By making use of the [[Equation of State: Ideal Gas |ideal gas law]] one can define an absolute temperature

:<math>T = \frac{pV}{Nk_B}</math>

however, perhaps a better definition of temperature is 

:<math>\frac{1}{T(E,V,N)} = \left. \frac{\partial S}{\partial E}\right\vert_{V,N}</math>

where <math>S</math> is the [[entropy]]. That said, in the words of Landau and Lifshitz "''Like the entropy, the temperature is seen to be a purely statistical quantity, which has meaning only for macroscopic bodies''" <ref>L. D. Landau and E. M. Lifshitz "Statistical Physics", Course of Theoretical Physics volume 5 Part 1 3rd Edition (1984) ISBN 0750633727 p. 35</ref>. For small systems, where fluctuations become significant, things become more complicated <ref>[http://dx.doi.org/10.1119/1.1987181 Richard McFee "On Fluctuations of Temperature in Small Systems", American Journal of Physics '''41''' pp. 230-234 (1973)]</ref>
<ref>[http://dx.doi.org/10.1063/1.3486557  Grey Sh. Boltachev  and Jürn W. P. Schmelzer "On the definition of temperature and its fluctuations in small systems", Journal of Chemical Physics '''133''' 134509 (2010)]</ref>.
==Temperature scale==
Temperature has the SI units (Système International d'Unités) of ''kelvin'' (K) (named in honour of [[William Thomson]] <ref>William Thomson "On an Absolute Thermometric Scale, founded on Carnot's Theory of the Motive Power of Heat, and calculated from the Results of Regnault's Experiments on the Pressure and Latent Heat of Steam", Philosophical Magazine '''October''' pp.  (1848)</ref>) The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the [[triple point]] of [[water]]<ref>[http://dx.doi.org/10.1088/0026-1394/27/1/002 H. Preston-Thomas "The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' pp. 3-10  (1990)]</ref>
<ref>[http://dx.doi.org/10.1088/0026-1394/27/2/010 H. Preston-Thomas "ERRATUM: The International Temperature Scale of 1990 (ITS-90)", Metrologia '''27''' p. 107 (1990)]</ref>.
====Non-SI temperature scales====
'''Rankine temperature scale''' <br>
0°R corresponds to 0 kelvin, and 1.8 degrees Rankine is equivalent to 1 kevlin <ref>[http://pml.nist.gov/Pubs/SP811/appenB9.html#TEMPERATURE NIST guide to SI Units]</ref>. The Rankine temperature scale is named after [[William John Macquorn Rankine]].

==Kinetic temperature==
:<math>T = \frac{2}{3} \frac{1}{k_B} \overline {\left(\frac{1}{2}m_i v_i^2\right)}</math>
 
where <math>k_B</math> is the [[Boltzmann constant]].  The kinematic temperature so defined is related to the [[equipartition]] theorem; for more details, see [http://clesm.mae.ufl.edu/wiki.pub/index.php/Configuration_integral_%28statistical_mechanics%29 Configuration integral].

==Configurational temperature==
<ref>[http://dx.doi.org/10.1103/PhysRevLett.78.772 Hans Henrik Rugh "Dynamical Approach to Temperature", Physical Review Letters ''' 78''' pp. 772-774 (1997)]</ref>
<ref>[http://dx.doi.org/10.1063/1.480995 András Baranyai "On the configurational temperature of simple fluids", Journal of Chemical Physics '''112''' pp. 3964-3966 (2000)]</ref>
==Non-equilibrium temperature==
<ref>[http://dx.doi.org/10.1063/1.2743032     Alexander V. Popov and Rigoberto Hernandez "Ontology of temperature in nonequilibrium systems", Journal of Chemical Physics '''126''' 244506 (2007)]</ref>
<ref>[http://dx.doi.org/10.1063/1.2958913  J.-L. Garden, J. Richard, and H. Guillou "Temperature of systems out of thermodynamic equilibrium", Journal of Chemical Physics '''129''' 044508 (2008)]</ref>
==Inverse temperature==
It is frequently convenient to define a so-called [[inverse temperature]], <math>\beta</math>, such that

:<math>\beta := \frac{1}{k_BT}</math>
==Negative temperature==
<ref>[http://dx.doi.org/10.1103/PhysRev.103.20 Norman F. Ramsey "Thermodynamics and Statistical Mechanics at Negative Absolute Temperatures", Physical Review '''103''' pp.  20-28 (1956)]</ref>

==See also==
*[[Thermostats | Thermostats in molecular dynamics]]
==References==
<references/>
'''Related reading'''
*Hasok Chang  "Inventing Temperature: Measurement and Scientific Progress", Oxford University Press (2004) ISBN  978-0-19-517127-3
*[http://dx.doi.org/10.1103/PhysRevX.4.031019 M. Kliesch, C. Gogolin, M. J. Kastoryano, A. Riera, and J. Eisert "Locality of Temperature" Physical Review X '''4''' 031019 (2014)]


[[category: Classical thermodynamics]]
[[category: statistical mechanics]]
[[category: Non-equilibrium thermodynamics]]