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Condensed Matter > Statistical Mechanics
Title: A Dean-Kawasaki equation for reaction diffusion systems driven by Poisson noise
(Submitted on 3 Apr 2024 (v1), last revised 12 Apr 2024 (this version, v2))
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.
Submission history
From: Richard Spinney [view email][v1] Wed, 3 Apr 2024 05:48:40 GMT (41kb)
[v2] Fri, 12 Apr 2024 09:19:20 GMT (42kb)
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