Computing diffusivities from particle models out of equilibrium

Peter Embacher, Nicolas Dirr, Johannes Zimmer, Celia Reina

Research output: Contribution to journalArticlepeer-review

13 Citations (SciVal)
32 Downloads (Pure)


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.

Original languageEnglish
Article number20170694
JournalProceedings of the Royal Society A: Mathematical Physical and Engineering Sciences
Issue number2212
Early online date11 Apr 2018
Publication statusPublished - 25 Apr 2018


  • Coarse-graining
  • Fluctuation–dissipation
  • Non-equilibrium thermodynamics
  • Transport coefficients

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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