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A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures

  • The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations. Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas and A. Mielke, J. Stat. Phys., 181 (2020), pp. 2257–2303] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method in order to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE.
Author:Alberto MontefuscoORCiD, Christof SchütteORCiD, Stefanie WinkelmannORCiD
Document Type:Article
Parent Title (English):SIAM Journal on Applied Mathematics
First Page:837
Last Page:861
Date of first Publication:2023/04/28
ArXiv Id:http://arxiv.org/abs/2201.02613
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