This is the Version of Record (VoR) of the following article: Bussoletti, M., Gallo, M., Jafari, A., & Eyink, G.L. (2026). Non-Gaussian statistics of concentration fluctuations in free liquid diffusion. Physical Review Research, 8, L012059. https://doi.org/10.1103/d27z-4fxz The three-point skewness of concentration fluctuations is shown to be nonvanishing in free liquid diffusion, even in the limit of vanishingly small mean concentration gradients. A high-Schmidt reduction of nonlinear Landau-Lifshitz hydrodynamics for a binary fluid is exploited, 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. Funded by the European Union. Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. This work is supported by an ERC grant (ERC-STG E-Nucl. Grant agreement ID: 101163330). Data availability. The final data supporting this research are publicly available at 10.5281/zenodo.18235038.
Bussoletti et al. (Tue,) studied this question.