WIAS Preprint No. 2375, (2017)

Flux large deviations of independent and reacting particle systems, with implications for macroscopic fluctuation theory



Authors

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

2010 Mathematics Subject Classification

  • 46N55 60F10 60J27 82C35

2008 Physics and Astronomy Classification Scheme

  • 05.40.-a 05.70.Ln 82.40.Bj 82.20.Fd

Keywords

  • empirical measure, empirical flux, discrete space, large deviations, Macroscopic Fluctuation Theory

DOI

10.20347/WIAS.PREPRINT.2375

Abstract

We consider a system of independent particles on a finite state space, and prove a dynamic large-deviation principle for the empirical measure-empirical flux pair, taking the specific fluxes rather than net fluxes into account. We prove the large deviations under deterministic initial conditions, and under random initial conditions satisfying a large-deviation principle. We then show how to use this result to generalise a number of principles from Macroscopic Fluctuation Theory to the finite-space setting.

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