2020
DOI: 10.1103/physrevresearch.2.022003
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Active interface polarization as a state function

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 polariza… Show more

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Cited by 25 publications
(41 citation statements)
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References 31 publications
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“…Efficient methods such as force sampling [54] render this a standard task. PFT has been applied to the bulk and interfacial behavior of active Brownian particles [46][47][48][49][50]. Here, the positionand orientation-resolved one-body fields have proven to be appropriate variables.…”
Section: Introductionmentioning
confidence: 99%
“…Efficient methods such as force sampling [54] render this a standard task. PFT has been applied to the bulk and interfacial behavior of active Brownian particles [46][47][48][49][50]. Here, the positionand orientation-resolved one-body fields have proven to be appropriate variables.…”
Section: Introductionmentioning
confidence: 99%
“…No such spontaneous polarization occurs in bulk. The interface polarization is a state function of the coexisting phases [53] as verified both experimentally [66] and numerically [67]. The total swim force that acts on V is (p g swim − p l swim )Ae, where p b swim = γsJ b /(2D rot ), with J b the bulk current in the forward direction ω and D rot indicating the rotational diffusion constant.…”
Section: Motility Induced Phase Separationmentioning
confidence: 75%
“…It vanishes, M tot = 0, as there is no net flux through the boundaries in steady state (see (10) in Ref. [53]). Combination of all integrals yields the relation…”
Section: Active Sedimentationmentioning
confidence: 99%
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“…The phenomenological equation of motion (23) of DDFT does not capture the full non-equilibrium dynamics of many-particle systems. Important physical effects such as drag [59], viscosity [58,75] and structural non-equilibrium forces [59,[76][77][78][79][80][81][82]82] are absent. PFT provides a formally exact method for including such effects and for calculating the full current in a non-equilibrium system [52]; see Ref.…”
Section: Power Functional Theorymentioning
confidence: 99%