Active interface polarization as a state function

Sophie Hermann,Matthias Schmidt

doi:10.1103/physrevresearch.2.022003

Abstract

We prove three exact sum rules that relate the polarization of active Brownian particles to their one-body current: (i) The total polarization vanishes, provided that there is no net flux through the boundaries, (ii) at any planar wall the polarization is determined by the magnitude of the bulk current, and (iii) the total interface polarization between phase-separated fluid states is rigorously determined by the gas-liquid current difference. This result precludes the influence of the total interface polarization on active bulk coexistence and questions the proposed coupling of interface to bulk.

Highlights

We prove three exact sum rules that relate the polarization of active Brownian particles to their one-body current: (i) The total polarization vanishes, provided that there is no net flux through the boundaries, (ii) at any planar wall the polarization is determined by the magnitude of the bulk current, and (iii) the total interface polarization between phase-separated fluid states is rigorously determined by the gas-liquid current difference
In many of these cases, the spontaneous polarization occurs in the absence of any explicit torques that act on the particles: No external torques occur when all external fields depend and act on position only, and no internal torques arise when the particles are spheres
In equilibrium systems of spheres, the absence of torques implies local isotropy, and the emergence of nonzero local polarization is a genuine effect of nonequilibrium, as characterized by a nonzero spatially and orientationally resolved local one-body current J

Summary

Active interface polarization as a state function

Sophie Hermann and Matthias Schmidt * Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany (Received 25 January 2020; accepted 10 March 2020; published 3 April 2020). In equilibrium systems of spheres, the absence of torques implies local isotropy, and the emergence of nonzero local polarization is a genuine effect of nonequilibrium, as characterized by a nonzero spatially and orientationally resolved local one-body current J Important examples of these nonequilibrium situations include the spontaneous orientational ordering of ABPs against gravity in the sedimentation profile at large altitudes [4,5,6,7], the ordering upon adsorption against a (hard) wall [10,11,12,13], and the spontaneous polarization of the free interface between phase-separated active gas and liquid phases [13,14,15,16,17].

SOPHIE HERMANN AND MATTHIAS SCHMIDT

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