Computing diffusivities from particle models out of equilibrium

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but it is otherwise allowed to undergo arbitr...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2018-04, Vol.474 (2212), p.20170694-20170694
Main Authors: Embacher, Peter, Dirr, Nicolas, Zimmer, Johannes, Reina, Celia
Format: Article
Language:English
Subjects:
Coarse-Graining
Equilibrium
Fluctuation–dissipation
Gradient flow
Mathematical models
Non-Equilibrium Thermodynamics
Partial differential equations
Transport Coefficients
Variations
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Summary:A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but it is otherwise allowed to undergo arbitrary out-of-equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation–dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero-range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2017.0694