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  • Letter
  • Open Access

Non-Gaussian statistics of concentration fluctuations in free liquid diffusion

Marco Bussoletti1,*, Mirko Gallo1, Amir Jafari2, and Gregory L. Eyink2,3,†

  • *Contact author: marco.bussoletti@uniroma1.it
  • †Contact author: eyink@jhu.edu
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Phys. Rev. Research 8, L012059 – Published 10 March, 2026

DOI: https://doi.org/10.1103/d27z-4fxz

Abstract

We show that the three-point skewness of concentration fluctuations is nonvanishing 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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Outline

Information

Phys. Rev. Research 8, L012059– Published 10 March, 2026
  • Received 5 September 2025
  • Accepted 12 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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