Dynamical patterns and nonreciprocal effective interactions in an active-passive mixture through exact hydrodynamic analysis

TL;DR

This paper introduces an exactly solvable model of active-passive particle mixtures, revealing how nonreciprocal interactions lead to complex dynamical patterns and phase behaviors in nonequilibrium systems.

Contribution

It provides an exact hydrodynamic analysis of active-passive mixtures, uncovering nonreciprocal effective interactions and novel phase separation phenomena.

Findings

Exact hydrodynamic equations derived for the mixture

Identification of nonreciprocal couplings between species

Discovery of a phase diagram with active phase separation

Abstract

The formation of dynamical patterns is one of the most striking features of nonequilibrium physical systems. Recent work has shown that such patterns arise generically from forces that violate Newton's third law, known as nonreciprocal interactions. These nonequilibrium phenomena are challenging for modern theories. Here, we introduce a model mixture of active (self-propelled) and passive (diffusive) particles amenable to exact mathematical analysis. We exploit state-of-the-art methods to derive exact hydrodynamic equations for the particle densities, which reveal effective nonreciprocal couplings between the active and passive species. We study the resulting collective behavior, including the linear stability of homogeneous states and phase coexistence in large systems. This reveals a novel phase diagram with the spinodal associated with active phase separation protruding through the associated binodal, heralding the emergence of dynamical steady states. We analyze these states in the thermodynamic limit of large system size, showing, for example, that sharp interfaces may travel at finite velocities, but traveling phase-separated states are forbidden. The model's mathematical tractability enables precise new conclusions beyond those available by numerical simulation of particle models or field theories.