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arXiv · 2506.22093

A gradient flow that is none: Heat flow with Wentzell boundary condition

Marie Bormann·Léonard Monsaingeon·D. R. Michiel Renger·Max von Renesse
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Abstract

We establish a representation of the heat flow with Wentzell boundary conditions on smooth domains as gradient descent dynamics for the entropy in a suitably extended Otto manifold of probability measures with additional boundary parts. Yet it is shown that for weak boundary diffusion, the associated Fokker-Planck dynamics cannot be recovered from any entropy-driven metric JKO-Wasserstein scheme, at least if the underlying point metric satisfies certain natural regularity assumptions. This discrepancy is illustrated in competing large-deviation heuristics in the Sanov and Schilder regimes.

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Marie Bormann, Léonard Monsaingeon, D. R. Michiel Renger, Max von Renesse. 2025-06-27. A gradient flow that is none: Heat flow with Wentzell boundary condition. https://arxiv.org/abs/2506.22093

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