### Abstract

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 language | English |
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Article number | 20170694 |

Journal | Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences |

Volume | 474 |

Issue number | 2212 |

Early online date | 11 Apr 2018 |

DOIs | |

Publication status | Published - 25 Apr 2018 |

### Keywords

- 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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## Profiles

### Johannes Zimmer

- Department of Mathematical Sciences - Professor, Visiting Professor (from 1 Sept 20)
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Probability Laboratory at Bath

Person: Research & Teaching, Honorary / Visiting Staff

## Datasets

### Codes for "Computing diffusivities from particle models out of equilibrium"

Zimmer, J. (Creator), Embacher, P. (Creator), Dirr, N. (Creator) & Reina, C. (Creator), University of Bath, 11 Apr 2018

DOI: 10.15125/BATH-00488

Dataset

## Cite this

Embacher, P., Dirr, N., Zimmer, J., & Reina, C. (2018). Computing diffusivities from particle models out of equilibrium.

*Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences*,*474*(2212), [20170694]. https://doi.org/10.1098/rspa.2017.0694