fluctuationdissipationteorin

Fluctuationdissipationteorin is the Swedish name for the fluctuation–dissipation theorem, a central result in statistical physics and linear response theory. It relates spontaneous fluctuations in an equilibrium system to the way that system dissipates energy when driven slightly out of equilibrium. In other words, spontaneous microscopic variability and macroscopic susceptibility to applied perturbations are two aspects of the same underlying dynamics.

Historically, the idea appears in work on electrical noise by Johnson and Nyquist and was formalized in quantum and statistical contexts by Callen, Welton and Kubo. The theorem applies to systems near thermal equilibrium and assumes linear response to small external forces. In frequency space, the power spectrum of equilibrium fluctuations is proportional to the imaginary (dissipative) part of the system’s response function, with a temperature-dependent factor; the classical limit reduces to a simple factor proportional to temperature, while the full quantum form includes the Bose occupation factor.

Practical applications span condensed matter physics, electrical engineering (Johnson–Nyquist noise), Brownian motion and diffusion (Einstein relation), and spectroscopy. The theorem provides a powerful tool for predicting dissipation from equilibrium measurements and vice versa, and it underpins many theoretical and experimental analyses of noise, transport coefficients and relaxation processes. Limitations arise outside the linear regime or far from equilibrium, where generalized or non-equilibrium extensions are required.