Large Deviation Functions for active Brownian particles

Large deviation Functions (LDFs) characterize fluctuations of extensive observables away from equilibrium and offer a route to relate those fluctuations to the systems response to external perturbations. LDFs are difficult to calculate analytically and sometimes numerically for complex interacting systems. For a system of interacting active Brownian particles, we show how a weighted many body expansion can be used to calculate LDFs for a wide variety of relevant observables such as the mass current, active work, and activity. These in turn can be used to understand diverse phenomena such as the Motility Induces Phase Separation (MIPS) and active transport.