arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2004.03966cond-mat.stat-mech
收藏

不解Fokker-Planck方程时两组分反应系统定态几率流的预测性质

Predicting properties of the stationary probability currents for two-species reaction systems without solving the Fokker-Planck equation

Marc Mendler, Barbara Drossel

发表信息：
Phys. Rev. E 102, 022208 (2020)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

我们推导出的方法估计的拓扑结构的平稳概率流$\vec{j}_s$的两个物种的福克-普朗克方程（FPE），而不需要解决的FPE。这些方法被选择为使得它们在某些限制下变得精确，例如无限大的系统尺寸或扩散矩阵中物种之间的耦合消失。该方法对$\vec{j}_s$的不动点及其与平稳概率分布极值和对流场不动点的关系进行了预测，对流场不动点与系统的确定性漂移有关。此外，他们还预测了$\vec{j}_s$围绕固定概率分布极值的旋转方向。即使这些方法不能被证明是有效的远离极值，具有不同的旋转方向的区域之间的边界线获得了令人惊讶的精度。我们说明和测试这些方法使用简单的反应系统，只有一个耦合项之间的两个物种，以及一些通用的反应网络从文献中。我们也用它来研究非物理的概率流的形状发生在反应系统中的细致平衡，由于在推导福克-普朗克方程的近似。

英文摘要：

We derive methods for estimating the topology of the stationary probability current $\vec{j}_s$ of the two-species Fokker-Planck equation (FPE) without the need to solve the FPE. These methods are chosen such that they become exact in certain limits, such as infinite system size or vanishing coupling between species in the diffusion matrix. The methods make predictions about the fixed points of $\vec{j}_s$ and their relation to extrema of the stationary probability distribution and to fixed points of the convective field, which is related to the deterministic drift of the system. Furthermore, they predict the rotation sense of $\vec{j}_s$ around extrema of the stationary probability distribution. Even though these methods cannot be proven to be valid away from extrema, the boundary lines between regions with different rotation sense are obtained with surprising accuracy. We illustrate and test these method using simple reaction systems with only one coupling term between the two species as well as a few generic reaction networks taken from literature. We use it also to investigate the shape of non-physical probability currents occurring in reaction systems with detailed balance due to the approximations involved in deriving the Fokker-Planck equation.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑