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Steady diffusion in a drift field: A comparison of large-deviation techniques and multiple-scale analysis
Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
Number of Authors: 2
2017 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, no 3, 032140Article in journal (Refereed) Published
Abstract [en]

A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while the effective diffusion has two terms. One is of the equilibrium type and satisfies an Einstein relation with the effective mobility while the other is quadratic in the applied force. In this contribution we present two new methods to obtain these results, on the one hand using large deviation techniques and on the other by a multiple-scale analysis, and compare the two. We consider both systems with discrete internal states and continuous internal states. We show that the auxiliary equations in the multiple-scale analysis can also be derived in second-order perturbation theory in a large deviation theory of a generating function (discrete internal states) or generating functional (continuous internal states). We discuss that measuring the two components of the effective diffusion give a way to determine kinetic rates from only first and second moments of the displacement in steady state.

Place, publisher, year, edition, pages
2017. Vol. 96, no 3, 032140
Keyword [en]
Brownian motion, Diffusion, Non-equilibrium fluctuations, Large deviation & rare event statistics, Markovian processes, Biological physics, Statistical physics
National Category
Physical Sciences Mathematics
Identifiers
URN: urn:nbn:se:su:diva-148073DOI: 10.1103/PhysRevE.96.032140ISI: 000411991200001OAI: oai:DiVA.org:su-148073DiVA: diva2:1152600
Available from: 2017-10-25 Created: 2017-10-25 Last updated: 2017-10-25Bibliographically approved

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