基于梯度结构的详细平衡化学反应系统建模
Modeling of chemical reaction systems with detailed balance using gradient structures
摘要：
我们考虑空间均相化学反应系统的各种建模水平，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，我们限制我们的研究的情况下，微观系统满足详细的平衡条件。后者使我们能够丰富系统的梯度结构，即演变是由梯度流方程。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的联系。在演化$Γ$ -梯度流收敛的意义下研究了大体积的极限。此外，我们使用的梯度结构，以获得混合模型耦合不同的建模水平。
英文摘要：
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.
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