Towards a liquidstate theory for active matter
Abstract
In equilibrium, the collective behaviour of particles interacting via steep, shortranged 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 selfpropelled particles. Given that active systems do not admit any freeenergy description in general, our aim is to build the dynamics of the coarsegrained 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 twopoint density valid in the dilute regime at small activity. This closure yields the nonlinear dynamics of the onepoint 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 motilityinduced phase separation. Therefore, although our approach should be restricted to dilute, weaklyactive systems a priori, it actually captures the features of a broader class of active matter.
 Publication:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.12155
 arXiv:
 arXiv:2301.12155
 Bibcode:
 2023arXiv230112155L
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Statistical Mechanics
 EPrint:
 2 figures