fluctuation–dissipation theorem

E31542

physical law theorem in statistical mechanics

The fluctuation–dissipation theorem is a fundamental principle in statistical physics that links the random microscopic fluctuations in a system at thermal equilibrium to its macroscopic response to external perturbations.

Aliases (2)

Green–Kubo relations ×1
Johnson–Nyquist noise formula ×1

Statements (49)

Predicate	Object
instanceOf	physical law → theorem in statistical mechanics →
appliesTo	systems in thermal equilibrium → systems near thermal equilibrium →
assumes	linearity of response to small perturbations → thermal equilibrium of the unperturbed system → time-translational invariance in equilibrium →
characterizes	random forces in Brownian motion → thermal noise in resistors →
connects	random microscopic fluctuations → response to external perturbations →
describes	relation between equilibrium fluctuations and linear response →
field	condensed matter physics → nonequilibrium statistical mechanics → statistical physics →
hasFormulation	classical formulation → frequency-domain formulation → quantum formulation → time-domain formulation →
implies	Onsager reciprocal relations under certain conditions → response functions are determined by equilibrium correlation functions →
involves	correlation functions → linear response theory → response function → susceptibility → temperature → thermal noise →
isRelatedTo	Fokker–Planck equation → fluctuation–dissipation theorem → surface form: "Green–Kubo relations" Johnson–Nyquist noise → Langevin dynamics → surface form: "Langevin equation" Nyquist theorem →
isSpecialCaseOf	Kubo formula →
relates	macroscopic dissipation → microscopic fluctuations →
relatesQuantity	dissipation of energy → imaginary part of susceptibility → power spectral density of fluctuations →
usedIn	Brownian motion theory → Langevin equation modeling → electrical noise analysis → magnetic susceptibility calculations → noise thermometry → optical response of materials → transport theory → viscoelasticity →
wasDevelopedBy	Herbert B. Callen → Ryogo Kubo → Theodore A. Welton NERFINISHED →

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Boltzmann constant → appearsIn → fluctuation–dissipation theorem →

this entity surface form: "Johnson–Nyquist noise formula"

fluctuation–dissipation theorem → isRelatedTo → fluctuation–dissipation theorem →

this entity surface form: "Green–Kubo relations"

Einstein–Smoluchowski relation → isSpecialCaseOf → fluctuation–dissipation theorem →

Langevin dynamics → satisfies → fluctuation–dissipation theorem →