期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 307, 期 3, 页码 791-815出版社
SPRINGER
DOI: 10.1007/s00220-011-1328-4
关键词
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资金
- EPSRC [EP/I003746/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/I003746/1] Funding Source: researchfish
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.
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