# nLab fluctuation-dissipation theorem

The fluctuation-dissipation theorem (fluctuation-dissipation relation) is one of the central results of statistical mechanics. The original formulation is due Nyquist (1928) and proven by

• H. B. Callen, T. A. Welton, Irreversibility and generalized noise, Physical Review. 83: 34 (1951) doi

The classical form is obtained from the linear response theory by Kubo.

• Ryogo Kubo, The fluctuation-dissipation theorem, pdf

• R. Kubo, M. Toda, Statistical physics I, II, Springer (see vol. II)

• Robert Zwanzig, Nonequilibrium statistical mechanics, Oxford University Press 2001

• U.M.B. Marconi, A. Puglisi, L. Rondoni, A. Vulpiani, Fluctuation-dissipation: response theory in statistical physics, Physics Reports. 461 (4–6): 111–195 (2008)arXiv:0803.0719 doi

There are now generalizations in nonequilibrium thermodynamics.

• G. N. Bochkov, Yu. E. Kuzovlev, Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: I. Generalized fluctuation-dissipation theorem, Physica A, 106: 443B (1991) doi

Related $n$Lab entries include statistical physics, thermodynamics, stochastic process, Langevin equation, Brownian motion, white noise