Active Ornstein-Uhlenbeck particles

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Show simple item record López Bonilla, Luis Francisco 2020-11-17T11:26:41Z 2020-11-17T11:26:41Z 2019-08-06
dc.identifier.bibliographicCitation Bonilla, L. L. (2019). Active Ornstein-Uhlenbeck particles. Physical Review E, 100(2), 022601.
dc.identifier.issn 1539-3755
dc.description.abstract Active Ornstein-Uhlenbeck particles (AOUPs) are overdamped particles in an interaction potential subject to external Ornstein-Uhlenbeck noises. They can be transformed into a system of underdamped particles under additional velocity dependent forces and subject to white noise forces. There has been some discussion in the literature on whether AOUPs can be in equilibrium for particular interaction potentials and how far from equilibrium they are in the limit of small persistence time. By using a theorem on the time reversed form of the AOUP Langevin-Ito equations, I prove that they have an equilibrium probability density invariant under time reversal if and only if their smooth interaction potential has zero third derivatives. In the limit of small persistence Ornstein-Uhlenbeck time t, a Chapman-Enskog expansion of the Fokker-Planck equation shows that the probability density has a local equilibrium solution in the particle momenta modulated by a reduced probability density that varies slowly with the position. The reduced probability density satisfies a continuity equation in which the probability current has an asymptotic expansion in powers of t. Keeping up to O(t) terms, this equation is a diffusion equation, which has an equilibrium stationary solution with zero current. However, O(t²) terms contain fifth- and sixth-order spatial derivatives and the continuity equation no longer has a zero current stationary solution. The expansion of the overall stationary solution now contains odd terms in the momenta, which clearly shows that it is not an equilibrium.
dc.description.sponsorship This work has been supported by the FEDER/Ministerio de Ciencia, Innovación y Universidades- Agencia Estatal de Investigación Grant No. MTM2017-84446-C2-2-R. I thank Jonathan Goodman and John Neu for fruitful discussions, and Russel Caflisch for hospitality during a sabbatical stay at the Courant Institute.
dc.format.extent 13
dc.language.iso eng
dc.publisher American Physical Society
dc.rights © 2019 American Physical Society.
dc.title Active Ornstein-Uhlenbeck particles
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2017-84446-C2-2-R
dc.type.version publishedVersion
dc.identifier.publicationissue 2
dc.identifier.publicationtitle Physical Review E
dc.identifier.publicationvolume 100
dc.identifier.uxxi AR/0000024736
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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