Work

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

Year: 2024

Type: article

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 (1996 J. Phys. A: Math. and Gen. 29 L613) 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 → ∞ 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.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/ad9efd

Authors: Richard E Spinney, Richard G Morris

Institutions: UNSW Sydney, EMBL Australia

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,165

Funder: EMBL Australia