A Dean-Kawasaki equation for reaction diffusion systems driven by Poisson noise

Richard E. Spinney; Richard G. Morris

doi:10.1088/1751-8121/ad9efd

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arXiv · 2404.02487

A Dean-Kawasaki equation for reaction diffusion systems driven by Poisson noise

Richard E. Spinney·Richard G. Morris

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Abstract

We derive a stochastic partial differential equation that describes the fluctuating behaviour of reaction-diffusion systems of N particles, undergoing Markovian, unary reactions. This generalises the work of Dean [J. Phys. A: Math. and Gen., 29 (24), L613, (1996)] through the inclusion of random Poisson fields. Our approach is based on weak interactions, which has the dual benefit that the resulting equations asymptotically converge (in the N to infinity limit) on a variation of a McKean- Vlasov diffusion, whilst still being related to the case of Dean-like strong interactions via a trivial rescaling. Various examples are presented, alongside a discussion of possible extensions to more complicated reaction schemes.

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BibTeX RIS

Richard E. Spinney, Richard G. Morris. 2024-04-03. A Dean-Kawasaki equation for reaction diffusion systems driven by Poisson noise. https://doi.org/10.1088/1751-8121/ad9efd

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