The "isothermal" compressibility of active matter

TL;DR

This paper shows that the isothermal compressibility in active matter systems behaves like a thermodynamic response function, predicting phase separation and relating to structure factors, even far from equilibrium.

Contribution

It establishes a mechanical definition of compressibility for active particles that aligns with thermodynamic concepts and relates to phase behavior and structure.

Findings

Compressibility predicts motility-induced phase separation.

Active compressibility is equivalent to static structure factor.

Interface effects are crucial for phase coexistence understanding.

Abstract

We demonstrate that the mechanically-defined "isothermal" compressibility behaves as a thermodynamic-like response function for suspensions of active Brownian particles. The compressibility computed from the active pressure - a combination of the collision and unique swim pressures - is capable of predicting the critical point for motility induced phase separation, as expected from the mechanical stability criterion. We relate this mechanical definition to the static structure factor via an active form of the thermodynamic compressibility equation and find the two to be equivalent, as would be the case for equilibrium systems. This equivalence indicates that compressibility behaves like a thermodynamic response function, even when activity is large. Finally, we discuss the importance of the phase interface when defining an active chemical potential. Previous definitions of the active chemical potential are shown to be accurate above the critical point but breakdown in the coexistence region. Inclusion of the swim pressure in the mechanical compressibility definition suggests that the interface is essential for determining phase behavior.