KRÜGER, Matthias; SOLON, Alexandre; DÉMERY, Vincent; ROHWER, Christian; DEAN, David

doi:10.1063/1.5019424

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KRÜGER, Matthias
Max Planck Institute for Intelligent Systems [Tübingen]
4th Institute for Theoretical Physics

SOLON, Alexandre
Department of Physics [MIT Cambridge]

DÉMERY, Vincent
Laboratoire de Physique de l'ENS Lyon [Phys-ENS]
Laboratoire de Physico-Chimie Théorique [LPCT]

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Ce document a été publié dans

Journal of Chemical Physics. 2018, vol. 148, n° 8, p. 084503

American Institute of Physics

Résumé en anglais

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute to the Green-Kubo relation for the viscosity.< Réduire

DOI

http://dx.doi.org/10.1063/1.5019424

Project ANR

Interactions induites par des fluctuations entre interfaces molles dans les systèmes complexes

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Laboratoire Ondes et Matière d'Aquitaine (LOMA) - UMR 5798