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Basing on main principles of statistical mechanics only, an exact virialexpansion for path probability distribution of molecular Brownian particle in afluid is derived which connects response of the distribution to perturbationsof the fluid and statistical correlations of its molecules with Brownianparticle. The expansion implies that (i) spatial spread of these correlationsis finite, (ii) this is inconsistent with Gaussian distribution involved by the``molecular chaos'' hypothesis, and (iii) real path distribution possessespower-law long tails. This means that actual Brownian path never can bedisjointed into statistically independent fragments, even in the Boltzmann-Gradgas, but behaves as if Brownian particle's diffusivity undergoes scalelesslow-frequency fluctuations.

Virial expansion of molecular Brownian motion versus tales of "statistical independency"