论文标题
使用梯度结构对具有详细平衡的化学反应系统建模
Modeling of chemical reaction systems with detailed balance using gradient structures
论文作者
论文摘要
我们考虑了用于空间均匀化学反应系统的各种建模水平，即化学主方程，化学兰格文动力学和反应速率方程。在整个过程中，我们将研究限制为微观系统满足详细的余量条件的情况。后者使我们能够用梯度结构丰富系统，即演变由梯度流动方程给出。我们介绍了由详细稳态稳态的相对熵驱动的相关梯度结构之间的链接。从进化$γ$ - 梯度流的进化$γ$结合的意义上研究了大量的极限。此外，我们使用梯度结构来得出混合模型，以耦合不同的建模水平。
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 $Γ$-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.
