Repository: Freie Universit├Ąt Berlin, Math Department

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

Renger, M. (2018) Gradient and Generic systems in the space of fluxes, applied to reacting particle systems. SFB 1114 Preprint in arXiv:1806.10461 . pp. 1-29. (Unpublished)

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Official URL: https://arxiv.org/abs/1806.10461

Abstract

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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics
ID Code:2260
Deposited By: Silvia Hoemke
Deposited On:18 Jul 2018 08:25
Last Modified:14 Aug 2018 14:06

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