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arXiv · 2501.15862

Hydrodynamic limit for an active-passive exclusion process

Deyue Li
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Abstract

The collective non-equilibrium dynamics of multi-component mixtures of interacting active (self-propelled) and passive (diffusive) particles have garnered great interest in the physics community. However, the mathematical understanding of these systems remains partial. In this work, we consider a lattice gas model of active-passive particle mixtures with exclusion, where the self-propulsion orientations of active particles undergo Brownian motion on a torus. We derive the hydrodynamic equations governing the particle densities. Due to the presence of two types of particles with continuous-valued orientations, further generalizations of non-gradient decomposition and spectral gap estimation developed for the pure active case are necessitated, which entails novel challenges and new proofs.

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Deyue Li. 2025-01-27. Hydrodynamic limit for an active-passive exclusion process. https://arxiv.org/abs/2501.15862

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