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. ISSN 0010-3616

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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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of 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
Date:	November 2011
Volume:	Vol.307
Number:	No.3
Page Range:	pp. 791-815
Identification Number:	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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URI:	http://wrap.warwick.ac.uk/id/eprint/39907

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