Coexistence of active Brownian discs: Van der Waals theory and analytical results

TL;DR

This paper develops a van der Waals theoretical framework for active Brownian discs, deriving an effective free energy that predicts phase coexistence and matches numerical results, extending equilibrium concepts to active matter.

Contribution

It formulates a van der Waals theory for active particles, providing analytical expressions for phase coexistence and interfacial properties in active matter systems.

Findings

Analytical derivation of effective free energy for active discs.

Good agreement between theory and numerical phase coexistence densities.

Discussion of interfacial tension and relation to Cahn-Hilliard models.

Abstract

At thermal equilibrium, intensive quantities like temperature and pressure have to be uniform throughout the system, restricting inhomogeneous systems composed of different phases. The paradigmatic example is the coexistence of vapor and liquid, a state that can also be observed for active Brownian particles steadily driven away from equilibrium. Recently, a strategy has been proposed that allows to predict phase equilibria of active particles [Phys. Rev. E \textbf{97}, 020602(R)(2018)]. Here we elaborate on this strategy and formulate it in the framework of a van der Waals theory for active discs. For a given equation of state, we derive the effective free energy analytically and show that it yields coexisting densities in very good agreement with numerical results. We discuss the interfacial tension and the relation to Cahn-Hilliard models.