Let x ( t ) be an observable of a dynamical system with Hamiltonian H 0 ( x ) subject to thermal fluctuations. The observable x ( t ) will fluctuate around its mean value ⟨ ⟨ x ⟩ ⟩ 0 with fluctuations characterized by a power spectrum S x ( ω ω ) = ⟨ ⟨ x ^ ^ ( ω ω ) x ^ ^ ∗ ∗ ( ω ω ) ⟩ ⟩ . Suppose that we can switch on a time-varying, spatially constant field f ( t ) which alters the Hamiltonian to H ( x ) = H 0 ( x ) − − f ( t ) x . The response of the observable x ( t ) to a time-dependent field f ( t ) is characterized to first order by the susceptibility or linear response function χ χ ( t ) of the system