Microscopic Fluctuation Theory (mFT) for interacting Poisson processes

While the Macroscopic Fluctuation Theory (MFT) is a renormalized theory in the hydrodynamic limit based on a space-time local Lagrangian that is Gaussian with respect to the empirical current, C. Maes, K. Netocny and B. Wynants [Markov Proc. Rel. Fields. 14, 445 (2008)] have derived a microscopic Fluctuation Theory (mFT) for independent Markov jump processes based on a space-time local Lagrangian that is Poissonian with respect to the empirical flow, in direct relation with the general theory of large deviations at 'Level 2.5' for Markovian processes. Here we describe how this approach can be generalized to the presence of interactions, that can be either zero-range or involve neighbors, either for closed systems or for open systems with reservoirs.