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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 thermodynamic fluctuations in a physical variable predict the response quantified by the admittance or impedance of the same physical variable, and vice versa. The fluctuation–dissipation theorem applies both to classical and quantum mechanical systems. The fluctuation–dissipation theorem was proven by Herbert Callen and Theodore Welton in 1951 and expanded by Ryogo Kubo. There are antecedents to the general theorem, including Einstein's explanation of Brownian motion
during his annus mirabilis and Harry Nyquist's explanation in 1928 of Johnson noise in electrical resistors.