Hydrodynamics of a hard-core active lattice gas

TL;DR

This paper develops a fluctuating hydrodynamic framework for an active lattice gas with excluded volume interactions, analyzing phase separation and correlations, and validating predictions with simulations.

Contribution

It introduces a hydrodynamic description for an active lattice gas model with phase separation, including noise effects, and compares it with simulations.

Findings

Quantitative bounds on phase boundary for motility-induced phase separation.

Stationary correlations decay exponentially in the homogeneous phase.

Hydrodynamic predictions align well with Monte Carlo simulations.

Abstract

We present a fluctuating hydrodynamic description of an active lattice gas model with excluded volume interactions that exhibits motility-induced phase separation under appropriate conditions. For quasi-one dimension and higher, stability analysis of the noiseless hydrodynamics gives quantitative bounds on the phase boundary of the motility-induced phase separation in terms of spinodal and binodal. Inclusion of the multiplicative noise in the fluctuating hydrodynamics describes the exponentially decaying two-point correlations in the stationary-state homogeneous phase. Our hydrodynamic description and theoretical predictions based on it are in excellent agreement with our Monte Carlo simulations and pseudospectral iteration of the hydrodynamics equations. Our construction of hydrodynamics for this model is not suitable in strictly one-dimension with single-file constraints, and we argue that this breakdown is associated with micro-phase separation.