Chemical potential in active systems: predicting phase equilibrium from bulk equations of state?

Abstract

We derive a microscopic expression for a quantity $\mu$ that plays the role of chemical potential of Active Brownian Particles (ABPs) in a steady state in the absence of vortices. We show that $\mu$ consists of (i) an intrinsic chemical potential similar to passive systems, which depends on density and self-propulsion speed, but not on the external potential, (ii) the external potential, and (iii) a newly derived one-body swim potential due to the activity of the particles. Our simulations on active Brownian particles show good agreement with our Fokker-Planck calculations, and confirm that $\mu (z)$ is spatially constant for several inhomogeneous active fluids in their steady states in a planar geometry. Finally, we show that phase coexistence of ABPs with a planar interface satisfies not only mechanical but also diffusive equilibrium. The coexistence can be well-described by equating the bulk chemical potential and bulk pressure obtained from bulk simulations for systems with low activity but requires explicit evaluation of the interfacial contributions at high activity.

arXiv commentAdded new results in Section 3.4 and updated Discussion and Conclusion

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• Statistical Mechanics of Active Ornstein Uhlenbeck Particles
• Classical dynamical density functional theory: from fundamentals to applications
• Generalized Thermodynamics of Phase Equilibria in Scalar Active Matter
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• Time-(ir)reversibility in active matter: from micro to macro
• Active phase separation by turning toward regions of higher density
• Autonomous engines driven by active matter: Energetics and design principles
• Power functional theory for many-body dynamics
• Microscopic Origins of the Swim Pressure and the Anomalous Surface Tension of Active Matter
• Active engines: Thermodynamics moves forward
• Mechanical Theory of Nonequilibrium Coexistence and Motility-Induced Phase Separation
• Thermodynamic cycles with active matter
• Linear response theory and Green-Kubo relations for active matter
• Noether's Theorem in Statistical Mechanics
• The Parental Active Model: a unifying stochastic description of self-propulsion
• Non-negative Interfacial Tension in Phase-Separated Active Brownian Particles
• Phase coexistence of active Brownian particles
• Collective forces in scalar active matter
• Thermodynamics of active field theories: Energetic cost of coupling to reservoirs
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• Disorder-Induced Long-Ranged Correlations in Scalar Active Matter
• Lamellar to micellar phases and beyond: when tactic active systems admit free-energy functionals
• Swimming to Stability: Structural and Dynamical Control via Active Doping
• How irreversible are steady-state trajectories of a trapped active particle?
• Predictive local field theory for interacting active Brownian spheres in two spatial dimensions
• Exact fluctuating hydrodynamics of active lattice gases -- Typical fluctuations
• Coexistence of active Brownian discs: Van der Waals theory and analytical results
• Disordered boundaries destroy bulk phase separation in scalar active matter
• Why Noether's Theorem applies to Statistical Mechanics
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• Pressure, surface tension and curvature in active systems: A touch of equilibrium
• From scalar to polar active matter: Connecting simulations with mean-field theory
• Adaptive Brownian Dynamics
• Active ideal sedimentation: Exact two-dimensional steady states
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• Inclusions, Boundaries and Disorder in Scalar Active Matter
• Polarization-Density Patterns of Active Particles in Motility Gradients
• Designing, Synthesizing and Modeling Active Fluids
• Tuning Nonequilibrium Phase Transitions with Inertia
• Isotropic-nematic transition of self-propelled rods in three dimensions
• Fluctuation profiles in inhomogeneous fluids
• Lack of an equation of state for the nonequilibrium chemical potential of gases of active particles in contact
• Phase separation of active Brownian particles in two dimensions: Anything for a quiet life
• Wetting dynamics by mixtures of fast and slow self-propelled particles
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• Long-range influence of a pump on a critical fluid
• Effective interactions in active Brownian particles
• Work to insert a particle into an active fluid