论文标题
使用梯度结构的反应扩散主方程的流体动力极限的途径
A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures
论文作者
论文摘要
反应扩散主方程（RDME）是一种基于晶格的随机模型，用于空间分辨的细胞过程。它通常被解释为与空间连续反应扩散模型的近似值，该模型在无限大群的极限下可以通过反应 - 扩散部分微分方程（RDPDES）来描述。分析和理解反应扩散动力学不同数学模型之间的关系是一个稳定兴趣的研究主题。在这项工作中，我们探索了使用梯度结构的RDME流体动力极限的途径。具体而言，我们详细介绍了[J.中引入的一种方法。 Maas，A。Mielke：使用梯度结构进行详细平衡的化学反应系统建模。 J. Stat。物理。 （181），2257-2303（2020）]在混合良好的反应网络中，表明一旦与适当的极限过程进行补充，它可以应用于具有扩散的空间扩展系统。在详细平衡的假设下，我们写下了RDME的梯度结构，并使用该方法为其流体动力极限（即相应的RDPDE）产生梯度结构。
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 (RDPDEs). 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, A. Mielke: Modeling of chemical reactions systems with detailed balance using gradient structures. J. Stat. Phys. (181), 2257-2303 (2020)] 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 to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE.
