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Simulations are made of a probe particle diffusing through a complex fluid.Probe particle motions are described by the Mori-Zwanzig equation and Mori'sorthogonal hierarchy of random forces scheme, subject to the approximation thatthe fluid creates a rapidly-fluctuating random force corresponding to solventmotions and a slowly fluctuating random force corresponding to solute (e.~g.,matrix polymer) motions. The Gaussian diffusion approximation is seriouslyincorrect in this physically-plausible model system. $P(x,t)$ has exponentialwings. $g^{(1s)}(q,t)$ can differ from $\exp(-q^{2} \langle x^{2}\rangle/2)$ byup to orders of magnitude. Experimental interpretations that rely on theGaussian approximation, such as the Stejskal-Tanner equation forpulsed-field-gradient NMR or particle tracking, can not be assumed to bereliable in complex fluids.

The Gaussian Diffusion Approximation for Complex Fluids is Generally Invalid