A Dean-Kawasaki equation for reaction diffusion systems driven by Poisson noise
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909453320716288 |
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| author | Spinney, Richard E. Morris, Richard G. |
| author_facet | Spinney, Richard E. Morris, Richard G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02487 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Dean-Kawasaki equation for reaction diffusion systems driven by Poisson noise Spinney, Richard E. Morris, Richard G. Statistical Mechanics Probability 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. |
| title | A Dean-Kawasaki equation for reaction diffusion systems driven by Poisson noise |
| topic | Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2404.02487 |