The "isothermal" compressibility of active matter

Area of Science:

• Soft Matter Physics
• Statistical Mechanics
• Active Matter

Background:

• Active Brownian particles exhibit unique collective behaviors like motility-induced phase separation (MIPS).
• Understanding the thermodynamic-like properties of active matter is crucial for predicting phase transitions.
• Traditional thermodynamic concepts may not directly apply to non-equilibrium active systems.

Purpose of the Study:

• To investigate the mechanical compressibility as a thermodynamic-like response function for active Brownian particle suspensions.
• To determine if mechanical compressibility can predict the critical point of MIPS.
• To establish the relationship between mechanical compressibility and the static structure factor in active systems.

Main Methods:

• Calculating mechanical compressibility from active pressure, which includes collision and swim pressures.
• Relating mechanical compressibility to the static structure factor using an active thermodynamic compressibility equation.
• Analyzing the behavior of compressibility above and within the coexistence region of the phase diagram.

Main Results:

• The mechanically defined compressibility accurately predicts the critical point for MIPS, consistent with mechanical stability criteria.
• Mechanical compressibility is equivalent to the static structure factor, mirroring behavior in equilibrium systems.
• Compressibility functions as a thermodynamic-like response function even at high activity levels.

Conclusions:

• Mechanical compressibility serves as a valid thermodynamic-like response function for active Brownian particle systems.
• The inclusion of swim pressure in compressibility is essential for accurately describing phase behavior and interfaces.
• The phase interface plays a critical role in defining the active chemical potential, particularly in the coexistence region.