Orateur
Description
Studying large scale dynamics of interacting many-particle systems is extremely demanding both analytical and numerical. Fortunately, there exist an effective asymptotic description, called hydrodynamics, based on averaging over local equilibrium states. Unfortunately, in general it is an open problem to understand its emergence, i.e. to connect the microscopic and the macroscopic description. This motivates to study the problem of hydrodynamic emergence in simple models with ex- act microscopic solutions, such as the integrable hard rods model (hard spheres in 1D). In arXiv:2408.04502, we had derived the diffusive-scale hydrodynamic equation. To our surprise the result was not of the expected Navier-Stokes type. To investigate this, we propose a radical strategy: to study the evolution of a single deterministic configuration, instead of a statistical ensemble of them. First, I will explain how one can meaningfully define hydrodynamics in this scenario. Then, I will use the new to show that diffusion is in fact absent in hard rods and that hydrodynamics even works for “unphysical” configurations very far from local equilibrium. In addition, the method also provides error bounds on the quality of the hydrodynamic approximation.
Based on arXiv:2507.17827.