WIAS Preprint No. 2516, (2018)

Gradient and Generic systems in the space of fluxes, applied to reacting particle systems


  • Renger, D. R. Michiel
    ORCID: 0000-0003-3557-3485

2010 Mathematics Subject Classification

  • 60F10 60J27 80A30 82C22 82C35

2010 Physics and Astronomy Classification Scheme

  • 05.70.Ln 82.40.Bj 82.60.-s 82.20.Db 82.20.Fd


  • Large deviations, fluxes, macroscopic fluctuation theory, Onsager-Machlup, gradient structures, Generic




In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager-Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or Generic system in the space of fluxes. In a general setting we study how flux gradient or generic systems are related to gradient systems of concentrations. The arguments are explained by the example of reacting particle systems, which is later expanded to include spatial diffusion as well.

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