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arXiv · 2510.17497

Non-Markovian heat flows on directed hypergraphs

Delio Mugnolo
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Abstract

We introduce a semigroup framework for Laplacians on directed hypergraphs, extending the classical heat flow models on graphs and establishing hypergraphs as prototypical models for non-Markovian diffusion. We apply spectral surgery methods to derive eigenvalue bounds, thus describing large-time behaviour of the heat flow. Unlike on standard graphs, heat flows on directed hypergraphs may lose positivity and/or $\infty$-contractivity, yet can recover them eventually or asymptotically under specific combinatorial configurations: examples based on duals of oriented graph and realisations of the Fano plane illustrate these phenomena. Our approach combines combinatorial, order-theoretic and linear-algebraic methods.

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Delio Mugnolo. 2025-10-20. Non-Markovian heat flows on directed hypergraphs. https://arxiv.org/abs/2510.17497

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