Flux Large Deviations of Independent and Reacting Particle Systems, with Implications for Macroscopic Fluctuation Theory

We consider a system of independent particles and a system of reacting particles on a discrete state space. For the independent case, we rigorously prove a dynamic large-deviation principle for the empirical measure-integrated flux pair, taking the one-way 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 formally calculate similar one-way flux large deviations for the more general reacting particles case. Next, we use these results to derive a number of principles from Macroscopic Fluctuation Theory like time-reversal principles and generalised gradient structures.