which holds under the Fourier transform convention f ( ω ω ) = ∫ ∫ − − ∞ ∞ ∞ ∞ f ( t ) e − − i ω ω t d t . The left-hand side describes fluctuations in x , the right-hand side is closely related to the energy dissipated by the system when pumped by an oscillatory field f ( t ) = F sin ⁡ ⁡ ( ω ω t + ϕ ϕ ) . The spectrum of fluctuations reveal the linear response, because past fluctuations cause future fluctuations via a linear response upon itself.