Pressure and phase equilibria in interacting active brownian spheres

Area of Science:

• Physics
• Soft Matter Physics
• Statistical Mechanics

Background:

• Active Brownian particles exhibit unique collective behaviors like motility-induced phase separation (MIPS).
• Understanding the mechanical pressure in these systems is key to characterizing their phase behavior.

Purpose of the Study:

• To derive a microscopic expression for the mechanical pressure (P) in a system of spherical active Brownian particles at density (ρ).
• To relate this pressure to bulk correlation functions and analyze its dependence on particle-wall interactions and system density.

Main Methods:

• Derivation of an exact microscopic expression for mechanical pressure.
• Analysis of pressure in relation to bulk correlation functions evaluated far from a bounding wall.
• Investigation of contributions from particle interactions, including those driving MIPS and direct contributions from passive systems.

Main Results:

• Mechanical pressure (P) is a state function, independent of specific particle-wall interactions.
• Interactions contribute two distinct terms to the pressure: one related to MIPS-driving slowdown and another from direct particle interactions.
• Pressure is equal in coexisting phases, a characteristic of equilibrium systems.

Conclusions:

• The derived pressure expression provides a fundamental tool for studying active matter systems.
• The results demonstrate that densities at coexistence in active Brownian particle systems do not follow a Maxwell construction on pressure.
• This work clarifies the thermodynamic and statistical mechanical underpinnings of MIPS.