Towards a liquid-state theory for active matter

Abstract

In equilibrium, the collective behaviour of particles interacting via steep, short-ranged potentials is well captured by the virial expansion of the free energy at low density. Here, we extend this approach beyond equilibrium to the case of active matter with self-propelled particles. Given that active systems do not admit any free-energy description in general, our aim is to build the dynamics of the coarse-grained density from first principles without any equilibrium assumption. Starting from microscopic equations of motion, we obtain the hierarchy of density correlations, which we close with an ansatz for the two-point density valid in the dilute regime at small activity. This closure yields the nonlinear dynamics of the one-point density, with hydrodynamic coefficients depending explicitly on microscopic interactions, by analogy with the equilibrium virial expansion. This dynamics admits a spinodal instability for purely repulsive interactions, a signature of motility-induced phase separation. Therefore, although our approach should be restricted to dilute, weakly-active systems a priori, it actually captures the features of a broader class of active matter.

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References in corpus (24)

• Motility-Induced Phase Separation
• Physics of Microswimmers - Single Particle Motion and Collective Behavior
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Pressure is not a state function for generic active fluids
• Langevin Equation for the Density of a System of Interacting Langevin Processes
• A continuum theory of phase separation kinetics for active Brownian particles
• Physics of Active Emulsions
• Effective Interactions in Active Brownian Suspensions
• Statistical Mechanics of Active Ornstein Uhlenbeck Particles
• Towards a 'Thermodynamics' of Active Matter
• Distortion and destruction of colloidal flocks in disordered environments
• Active colloidal suspensions: Clustering and phase behavior
• Virial pressure in systems of active Brownian particles
• Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics
• Time-(ir)reversibility in active matter: from micro to macro
• Nonequilibrium dynamics of mixtures of active and passive colloidal particles
• Steady-state distributions of ideal active Brownian particles under confinement and forcing
• Run-and-tumble motion: field theory and entropy production
• Dissipation controls transport and phase transitions in active fluids: Mobility, diffusion and biased ensembles
• Phase separation and nucleation in mixtures of particles with different temperatures
• Active hard-spheres in infinitely many dimensions
• Field Theory of free Active Ornstein-Uhlenbeck Particles
• Theoretical approaches to the steady-state statistical physics of interacting dissipative units

Cited by in corpus (7)

• Non-reciprocity across scales in active mixtures
• Active phase separation: new phenomenology from non-equilibrium physics
• Field-Theory of Active Chiral Hard Disks: A First-Principles Approach to Steric Interactions
• Thermodynamic nature of irreversibility in active matter
• Towards kinetic equations of open systems of active soft matter
• Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation
• Microcanonical ensemble out of equilibrium