Maas Jan, Mielke Alexander
Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria.
WIAS Berlin, Mohrenstraße 39, 10117 Berlin, Germany.
J Stat Phys. 2020;181(6):2257-2303. doi: 10.1007/s10955-020-02663-4. Epub 2020 Nov 6.
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 -convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.
我们考虑空间均匀化学反应系统的各种建模层次，即化学主方程、化学朗之万动力学和反应速率方程。在整个研究过程中，我们将研究限制在微观系统满足细致平衡条件的情况下。后者使我们能够用梯度结构丰富系统，即演化由梯度流方程给出。我们展示了由细致平衡稳态的相对熵驱动的相关梯度结构之间产生的联系。从梯度流的演化 - 收敛意义上研究大体积极限。此外，我们利用梯度结构推导用于耦合不同建模层次的混合模型。
