Theory of Capillary Tension and Interfacial Dynamics of Motility-Induced Phases

TL;DR

This paper develops a theoretical framework for understanding the interfacial dynamics of motility-induced phases in active matter, revealing how nonequilibrium surface tension and interfacial fluctuations differ from equilibrium fluids.

Contribution

It derives a microscopic theory for active interfaces, identifying nonequilibrium surface tension contributions and linking interfacial stiffness to particle persistence length.

Findings

Interfacial stiffness scales linearly with particle persistence length.

Active surface tension includes nonconservative force contributions.

Large-wavelength interface behavior follows Boltzmann statistics.

Abstract

The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the last decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces arbitrarily far from equilibrium. In this work, beginning from microscopic particle dynamics that break time-reversal symmetry, we systematically derive the interfacial dynamics of coexisting motility-induced phases. Doing so allows us to identify the athermal energy scale that excites interfacial fluctuations and the nonequilibrium surface tension that resists these excitations. Our theory identifies that, in contrast to equilibrium fluids, this active surface tension contains contributions arising from nonconservative forces which act to suppress interfacial fluctuations and, crucially, is distinct from the mechanical surface tension of Kirkwood and Buff. We find that the interfacial stiffness scales linearly with the intrinsic persistence length of the constituent active particle trajectories, in agreement with simulation data. We demonstrate that at wavelengths much larger than the persistence length, the interface obeys surface area minimizing Boltzmann statistics with our derived nonequilibrium interfacial stiffness playing an identical role to that of equilibrium systems.