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Equation (**) implies a discontinuous step-function response for $\langle x(t)\rangle -\langle x\rangle _{0}$ at t=0, which is incorrect. As t approaches zero from minus infinity, $\langle x(t)\rangle -\langle x\rangle _{0}$ adiabatically approaches $\ \beta f_{0}A(0)$. Equation (**) can be corrected by removing the outer parentheses on the right-hand side. As a consequence of this change, the outer parentheses in the second term on the right-hand side in the final equation of the derivation must also be removed. Thus the derivation beginning with equation (**) should read:

$(**)-\chi (t)=\beta {\operatorname {d} A(t) \over \operatorname {d} t}\theta (t).$

For stationary processes, the Wiener-Khinchin theorem states that the power spectrum equals twice the Fourier transform of the auto-correlation function

$S_{x}(\omega )=2{\tilde {A}}(\omega ).$

The last step is to Fourier transform equation (**) and to take the imaginary part. For this it is useful to recall that the Fourier transform of a real symmetric function is real, while the Fourier transform of a real antisymmetric function is purely imaginary. We can split ${\operatorname {d} A(t) \over \operatorname {d} t}\theta (t)$ into a symmetric and an anti-symmetric part

$2{\operatorname {d} A(t) \over \operatorname {d} t}\theta (t)\ ={\operatorname {d} A(t) \over \operatorname {d} t}+{\operatorname {d} A(t) \over \operatorname {d} t}{\rm {sign}}(t).$

Now the fluctuation-dissipation theorem follows.

(Remark to reviewer, not to be included in the actual article: Observe that the corrected derivation above does not change the imaginary (absorptive) part of chi, but it does modify the real (dispersive) part.)