We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document}Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.

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使用梯度结构进行具有详细平衡的化学反应系统建模


我们考虑空间均匀化学反应系统的各种建模级别，即化学主方程、化学朗之万动力学和反应速率方程。在整个过程中，我们将我们的研究限制在微观系统满足详细平衡条件的情况。后者允许我们用梯度结构丰富系统，即演化由梯度流方程给出。我们提出了由详细平衡稳态的相对熵驱动的相关梯度结构之间出现的联系。从进化意义上研究大体积的限制 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document}伽马梯度流的收敛。此外，我们使用梯度结构来导出用于耦合不同建模级别的混合模型。