Editing Equipartition theorem (section)

===Sedimentation of particles===
{{See also|Sedimentation|Mason–Weaver equation|Brewing}}

Potential energies are not always quadratic in the position. However, the equipartition theorem also shows that if a degree of freedom {{math|''x''}} contributes only a multiple of {{math|''x''<sup>s</sup>}} (for a fixed real number {{math|''s''}}) to the energy, then in thermal equilibrium the average energy of that part is {{math|''k''<sub>B</sub>''T''/''s''}}.

There is a simple application of this extension to the [[sedimentation]] of particles under [[gravitation|gravity]].<ref name="tolman_1918" /> For example, the haze sometimes seen in [[beer]] can be caused by clumps of [[protein]]s that [[Rayleigh scattering|scatter]] light.<ref>{{cite journal |vauthors=Miedl M, Garcia M, Bamforth C |title=Haze formation in model beer systems |journal=J. Agric. Food Chem. |volume=53 |issue=26 |pages=10161–5 |year=2005 |pmid=16366710 |doi=10.1021/jf0506941|bibcode=2005JAFC...5310161M }}</ref> Over time, these clumps settle downwards under the influence of gravity, causing more haze near the bottom of a bottle than near its top. However, in a process working in the opposite direction, the particles also [[diffusion|diffuse]] back up towards the top of the bottle. Once equilibrium has been reached, the equipartition theorem may be used to determine the average position of a particular clump of [[buoyant mass]] {{math|''m''<sub>b</sub>}}. For an infinitely tall bottle of beer, the [[gravitational energy|gravitational potential energy]] is given by
<math display="block">H^{\mathrm{grav}} = m_\text{b} g z </math>
where {{mvar|z}} is the height of the protein clump in the bottle and ''[[Earth's gravity|g]]'' is the [[acceleration]] due to gravity. Since {{math|1=''s'' = 1}}, the average potential energy of a protein clump equals {{math|''k''<sub>B</sub>''T''}}. Hence, a protein clump with a buoyant mass of 10&nbsp;[[Dalton (unit)|MDa]] (roughly the size of a [[virus]]) would produce a haze with an average height of about 2&nbsp;cm at equilibrium. The process of such sedimentation to equilibrium is described by the [[Mason–Weaver equation]].<ref name="mason_1924">{{cite journal | last = Mason | first = M |author2=Weaver W | year = 1924 | title = The Settling of Small Particles in a Fluid | journal = [[Physical Review]] | volume = 23 | issue = 3 | pages = 412–426 | doi = 10.1103/PhysRev.23.412|bibcode = 1924PhRv...23..412M }}</ref>