We study large deviations in the clustering of diffusing systems, mainly through the lens of macroscopic fluctuation theory (MFT). Additionally we study optimal control forces in such ensembles.

First, we consider a one dimensional system of hard-core diffusing particles and focus on the large deviations of the clustering of all the particles. Using an optimal control approach to this large deviation problem we find the approximate effective interactions in different regimes of the system. We present analytic calculations for the system in a few of these regimes. In the low clustering regime we identify the hyperuniformity of the system and find that the effective interactions are long range and repulsive. Conversely, for high clustering, there exists a near equilibrium regime characterised by attractive forces that can be described by MFT. We also explore a far from equilibrium regime characterised by a large macroscopic gap.

Furthermore, we also explore the large deviations of local clustering in systems of interacting particles. By exploring how the bias couples to hydrodynamic nodes, we find long range correlations of local observables. This explains how the dynamical free energy has non-trivial scaling forms with system size in one dimension and two dimensions. Furthermore we describe the long range effects of biasing two particles in the one dimensional system.

Finally we investigate pressure and body forces in biased ensembles of interacting particles in 2D. We identify a dynamical phase transition when biasing all particles in two dimensions. Using the Irving-Kirkwood definition of the stress we then mechanistically access the optimal control force. With this physical force from the simulations we can significantly speed up the simulation of the biased ensemble and thus the sampling of the probability distribution of the system.