Macroscopic Fluctuation Theory and Current Fluctuations in Active Lattice Gases

TL;DR

This paper develops a macroscopic fluctuation theory for active lattice gases, revealing a dynamical phase transition and providing a detailed large deviation analysis of current fluctuations, including phase-separated states.

Contribution

It introduces an exact fluctuating hydrodynamics framework for active particles with MIPS, accounting for Poissonian noise and characterizing phase transitions and large deviations.

Findings

Identifies a dynamical phase transition between flat and phase-separated states.

Derives the large deviation function for current fluctuations in all phases.

Shows methods similar to equilibrium phase separation apply to nonequilibrium active systems.

Abstract

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. We show how the results can be obtained using methods similar to those of equilibrium phase separation, in spite of the nonequilibrium nature of the problem.