### Abstract

Original language | English |
---|---|

Article number | 20170694 |

Pages (from-to) | 20170694 |

Journal | Proceedings of the Royal Society of Edinburgh Section A - Mathematics |

Volume | 474 |

Issue number | 2212 |

DOIs | |

Publication status | Published - 11 Apr 2018 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Proceedings of the Royal Society of Edinburgh Section A - Mathematics*,

*474*(2212), 20170694. [20170694]. https://doi.org/10.1098/rspa.2017.0694

**Computing diffusivities from particle models out of equilibrium.** / Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of Edinburgh Section A - Mathematics*, vol. 474, no. 2212, 20170694, pp. 20170694. https://doi.org/10.1098/rspa.2017.0694

}

TY - JOUR

T1 - Computing diffusivities from particle models out of equilibrium

AU - Embacher, Peter

AU - Dirr, Nicolas

AU - Zimmer, Johannes

AU - Reina, Celia

PY - 2018/4/11

Y1 - 2018/4/11

N2 - 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.

AB - 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.

KW - Coarse-graining

KW - Fluctuation–dissipation

KW - Non-equilibrium thermodynamics

KW - Transport coefficients

UR - http://www.scopus.com/inward/record.url?scp=85046464513&partnerID=8YFLogxK

U2 - 10.1098/rspa.2017.0694

DO - 10.1098/rspa.2017.0694

M3 - Article

VL - 474

SP - 20170694

JO - Proceedings of the Royal Society of Edinburgh Section A - Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A - Mathematics

SN - 0308-2105

IS - 2212

M1 - 20170694

ER -