Macroscopic fluctuation theory and current fluctuations in active lattice gases

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.

Current fluctuations in an interacting active lattice gas

“…These fluctuations are conjectured through an exact mapping with the ABC model [49,50]. However, the noise η K coming from tumbling events follows Poissonian statistics [31]. They come from slow local tumbling events of the + and the − particles.…”

“…This exact expression for L K has been derived in [31] by considering the underlying Poisson process for the tumble events. For typical small fluctuations, the noise arising due to the flipping of states can be approximated as a Gaussian noise, and the above expression for the Lagrangian density reduces to…”

“…This framework can therefore be used to study the dynamics of interacting active particles, and corroborate the predictions of the hydrodynamic theory with microscopic simulations. Recent studies have extended this framework to a fluctuating hydrodynamics description [30], as well as macroscopic fluctuation theory (MFT) [31,32], which accounts for the Poissonian noise arising due to the flipping of the velocities of the particles. This allows for an investigation of several interesting aspects, such as diverging correlation lengths, dynamical correlation functions, current fluctuations, large deviation functions, as well as entropy production [31,32].…”

“…This is different from the SSEP case, where the variance of the integrated current grows as √ T at all times. In this work, we extend the recently developed MFT framework to study the integrated density current fluctuations for the interacting active particle model studied in [31,32], but for quenched initial conditions. Interestingly, we find that the variance of the integrated current for the interacting active lattice gas with diffusion exhibits three regimes: a short-time regime where the variance grows as √ T , which can be described by the SSEP, a cross-over regime, and a large-time regime where the variance grows again as √ T .…”

“…In sections 3 and 4, we explain the hydrodynamics and fluctuating hydrodynamics framework for this model developed in previous studies for completeness. We extend the MFT framework introduced in [31] to compute the integrated current fluctuations in sections 5 and 6. We provide the details of the perturbative techniques used in the study and the expressions for the cumulants of the integrated current for general initial conditions in section 7.…”