Average dynamics, fluctuating relaxation rates, and dynamic susceptibility in glass-forming liquids

We systematically examine the consequences of the assumption that dynamic heterogeneity in glass-forming liquids can be described in terms of locally fluctuating relaxation rates. We find that under mild assumptions, the time dependence of the dynamic susceptibility χ₄(t) for times of the order of the α-relaxation time τ_α is completely determined by the average dynamics, except for an overall scale factor. In particular, the shape and location (but not the overall scale) of the peak in χ₄(t) can be predicted from knowledge of the average relaxation function F₀(t).