On the Hydrodynamics of Active Matter Models on a Lattice

C. Erignoux

2024, v.30, Issue 1, 57-80

ABSTRACT

Active matter has been widely studied in recent years because of
its rich phenomenology, whose mathematical understanding is still partial. We
present some results, based on [8, 17] linking microscopic lattice gases to their
macroscopic limit, and explore how the mathematical state of the art allows to
derive from various types of microscopic dynamics their hydrodynamic limit.
We present some of the crucial aspects of this theory when applied to weakly
asymmetric active models. We comment on the specific challenges one should
consider when designing an active lattice gas, and in particular underline mathematical and phenomenological differences between gradient and non-gradient
models. Our purpose is to provide the physics community, as well as member of
the mathematical community not specialized in the mathematical derivation of
scaling limits of lattice gases, some key elements in defining microscopic models
and deriving their hydrodynamic limit.

doi:10.61102/1024-2953-mprf.2024.30.1.002

Keywords: Particle systems, Hydrodynamic limits, Active matter, Phase transitions, lattice gases

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