Adams, Stefan, Dirr, Nicolas P.  ORCID: https://orcid.org/0000-0003-3634-7367, Peletier, 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
307
(3)
, pp. 791-815.
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: | Article |
|---|---|
| Date Type: | Publication |
| Status: | Published |
| Schools: | Schools > Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Publisher: | Springer |
| ISSN: | 0010-3616 |
| Last Modified: | 18 Oct 2022 13:13 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/13082 |
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