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- ItemLarge deviations of specific empirical fluxes of independent Markov chains, with implications for Macroscopic Fluctuation Theory(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Renger, D.R. MichielWe 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.
- ItemGradient and Generic systems in the space of fluxes, applied to reacting particle systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Renger, D.R. MichielIn 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.