Rearranged Stochastic Heat Equations with an Entropy Gradient Structure

Francois Delarue; Rhoss Likibi Pellat

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arXiv · 2607.13849

Rearranged Stochastic Heat Equations with an Entropy Gradient Structure

Francois Delarue·Rhoss Likibi Pellat

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Abstract

We extend a previously introduced one-dimensional diffusion model on the space of probability measures, defined via the rearranged stochastic heat equation by, penalizing the dynamics with an additional entropy-driven gradient-descent term. By means of a splitting argument, we prove that despite the opposite effects of rearrangement and entropy minimization, the resulting penalized stochastic heat equation is well defined. We study several properties of the associated dynamics and show, in particular, that solutions admit a density satisfying a corrected version of the Dean--Kawasaki equation. The smoothing properties established for the stochastic heat equation are shown to persist.

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BibTeX RIS

Francois Delarue, Rhoss Likibi Pellat. 2026-07-15. Rearranged Stochastic Heat Equations with an Entropy Gradient Structure. https://arxiv.org/abs/2607.13849

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