Macroscopic Fluctuation Theory and Current Fluctuations in Active Lattice Gases

Understand

We study the current large deviations for a lattice model of interacting active particles displaying a motility-induced phase separation (MIPS).

• To do this, we first derive the exact fluctuating hydrodynamics of the model in the large system limit.
• On top of the usual Gaussian noise terms the theory also presents Poissonian noise terms, that we fully account for.
• We find a dynamical phase transition between flat density profiles and sharply phase-separated traveling waves, and we derive the associated phase diagram together with the large deviation function for all phases, including the one displaying MIPS.