Editing Fluctuation–dissipation theorem (section)

{{short description|Statistical physics theorem}}
The '''fluctuation–dissipation theorem''' ('''FDT''') or '''fluctuation–dissipation relation''' ('''FDR''') is a powerful tool in [[statistical physics]] for predicting the behavior of systems that obey [[detailed balance]]. Given that a system obeys detailed balance, the theorem is a proof that [[thermal fluctuations|thermodynamic fluctuations]] in a physical variable  predict the response quantified by the [[admittance]] or [[Electrical impedance|impedance]] (in their general sense, not only in electromagnetic terms) of the same physical variable (like voltage, temperature difference, etc.), and vice versa. The fluctuation–dissipation theorem applies both to [[classical physics|classical]] and [[quantum mechanics|quantum mechanical]] systems.

The fluctuation–dissipation theorem was proven by [[Herbert Callen]] and [[Theodore A. Welton|Theodore Welton]] in 1951<ref name=Callen-Welton>{{cite journal |author1 = H.B. Callen |author2 = T.A. Welton |authorlink1 = Herbert Callen |authorlink2 = Theodore A. Welton | year = 1951 | title = Irreversibility and Generalized Noise | journal = [[Physical Review]] | volume = 83 |issue = 1 | pages = 34&ndash;40 | bibcode = 1951PhRv...83...34C | doi = 10.1103/PhysRev.83.34 }}</ref>
and expanded by [[Ryogo Kubo]]. There are antecedents to the general theorem, including [[Albert Einstein|Einstein]]'s explanation of [[Brownian motion]]<ref>
{{cite journal 
 | last = Einstein 
 | first = Albert 
 | author-link = Albert Einstein 
 | title = Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen 
 | journal = [[Annalen der Physik]] 
 | volume = 322 
 | issue = 8 
 | pages = 549–560 
 | date=May 1905
 | doi = 10.1002/andp.19053220806
 | bibcode = 1905AnP...322..549E
 | url = http://sedici.unlp.edu.ar/handle/10915/2785 
 | doi-access = free 
 }}
</ref>
during his ''[[annus mirabilis]]'' and [[Harry Nyquist]]'s explanation in 1928 of [[Johnson–Nyquist noise|Johnson noise]] in electrical resistors.<ref>{{cite journal | author = Nyquist H |authorlink = Harry Nyquist | year = 1928 | title = Thermal Agitation of Electric Charge in Conductors | journal = [[Physical Review]] | volume = 32 |issue = 1 | pages = 110&ndash;113 | bibcode = 1928PhRv...32..110N | doi = 10.1103/PhysRev.32.110 }}</ref>