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arXiv · 2509.25511

Non-Gaussian statistics of concentration fluctuations in free liquid diffusion

Marco Bussoletti·Mirko Gallo·Amir Jafari·Gregory L. Eyink
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Abstract

We show that the three-point skewness of concentration fluctuations is non-vanishing in free liquid diffusion, even in the limit of vanishingly small mean concentration gradients. We exploit a high-Schmidt reduction of nonlinear Landau-Lifshitz hydrodynamics for a binary fluid, both analytically and by a massively parallel Lagrangian Monte Carlo simulation. Non-Gaussian statistics result from nonlinear coupling of concentration fluctuations to thermal velocity fluctuations, analogous to the turbulent advection of a passive scalar. Concentration fluctuations obey no central limit theorem, counter to the predictions of macroscopic fluctuation theory for generic diffusive systems.

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Marco Bussoletti, Mirko Gallo, Amir Jafari, Gregory L. Eyink. 2025-09-29. Non-Gaussian statistics of concentration fluctuations in free liquid diffusion. https://doi.org/10.1103/d27z-4fxz

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