Pré-Publication, Document De Travail Année : 2026

A bottom-up approach to fluctuating hydrodynamics: Coarse-graining of stochastic lattice gases and the Dean-Kawasaki equation

Résumé

Fluctuating hydrodynamics provides a quantitative, large-scale description of many-body systems in terms of smooth variables, with microscopic details entering only through a small set of transport coefficients. Although this framework has been highly successful in characterizing macroscopic fluctuations and correlations, a systematic derivation of fluctuating hydrodynamics from underlying stochastic microscopic dynamics remains obscure for broad classes of interacting systems. For stochastic lattice-gas models with gradient dynamics and a single conserved density, we develop a path-integral based coarse-graining procedure that recovers fluctuating hydrodynamics in a controlled manner. Our analysis highlights the essential role of local-equilibrium averages, which go beyond naïve mean-field–type gradient expansions. We further extend this approach to interacting Brownian particles by coarse-graining the Dean–Kawasaki equation, revealing a mobility proportional to the density and a diffusivity determined by the thermodynamic pressure.

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hal-05546488 , version 1 (10-03-2026)

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Soumyabrata Saha, Sandeep Jangid, Thibaut Arnoulx de Pirey, Juliane U. Klamser, Tridib Sadhu. A bottom-up approach to fluctuating hydrodynamics: Coarse-graining of stochastic lattice gases and the Dean-Kawasaki equation. 2026. ⟨hal-05546488⟩
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