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From a large-deviations principle to the Wasserstein gradient flow : a new micro-macro passage
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Adams, S. (Stefan), Dirr, Nicolas, Peletier, M. A. (Mark A.) and Zimmer, Johannes (2011) From a large-deviations principle to the Wasserstein gradient flow : a new micro-macro passage. Communications in Mathematical Physics, Vol.307 (No.3). pp. 791-815. doi:10.1007/s00220-011-1328-4 ISSN 0010-3616.
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Official URL: http://dx.doi.org/10.1007/s00220-011-1328-4
Abstract
We study the connection between a system of many independent Brownian particles on one hand and the deterministic diffusion equation on the other. For a fixed time step h > 0, a large-deviations rate functional J h characterizes the behaviour of the particle system at t = h in terms of the initial distribution at t = 0. For the diffusion equation, a single step in the time-discretized entropy-Wasserstein gradient flow is characterized by the minimization of a functional K h . We establish a new connection between these systems by proving that J h and K h are equal up to second order in h as h → 0. This result gives a microscopic explanation of the origin of the entropy-Wasserstein gradient flow formulation of the diffusion equation. Simultaneously, the limit passage presented here gives a physically natural description of the underlying particle system by describing it as an entropic gradient flow.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Large deviations, Mathematical physics | ||||
Journal or Publication Title: | Communications in Mathematical Physics | ||||
Publisher: | Springer | ||||
ISSN: | 0010-3616 | ||||
Official Date: | November 2011 | ||||
Dates: |
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Volume: | Vol.307 | ||||
Number: | No.3 | ||||
Page Range: | pp. 791-815 | ||||
DOI: | 10.1007/s00220-011-1328-4 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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