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It is shown that time reversibility of Hamiltonian microscopic dynamics andGibbs canonical statistical ensemble of initial conditions for it togetherproduce an exact virial expansion for probability distribution of path ofmolecular Brownian particle in a fluid. This expansion leads to inequalityconnecting logarithmic derivative of the distribution with respect to fluiddensity and characteristic volume occupied by pair statistical correlationbetween the path and fluid molecules. Due to the inequality, finiteness of thisvolume means that asymptotic of the distribution is essentially non-Gaussian.For principal case when fluid is dilute gas it is demonstrated that the paircorrelation volume is actually finite and bounded above. Therefore even underthe Boltzmann-Grad limit the path distribution possess power-law long tails(cut off at distances of ballistic flight).

Thermodynamic restrictions on statistics of molecular random walks