The “isothermal” compressibility of active matter

• Published in: The Journal of chemical physics 2021-01, Vol.154 (1), p.014902-014902
• Main Authors: Dulaney, Austin R., Mallory, Stewart A., Brady, John F.
• Format: Article
• Language: English
• Subjects: Brownian motion; Chemical potential; Compressibility; Critical point; Equivalence; Phase separation; Response functions; Stability criteria; Structure factor
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/5.0029364

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.