论文标题
预测两个物种反应系统的固定概率电流的特性，而无需求解fokker-planck方程
Predicting properties of the stationary probability currents for two-species reaction systems without solving the Fokker-Planck equation
论文作者
论文摘要
我们得出了估计固定概率电流$ \ vec {j} _s $的拓扑方法的方法，而无需求解FPE而无需求解FPE。选择这些方法使它们在某些范围内变得精确，例如无限的系统大小或扩散矩阵中物种之间的耦合消失。这些方法对$ \ vec {j} _s $的固定点进行了预测，及其与平稳概率分布的极端和对流场的固定点的关系，这与系统的确定性漂移有关。此外，他们预测了$ \ vec {j} _s $的旋转感，围绕固定概率分布的极值。即使这些方法不能被证明是有效的，但具有不同旋转意义的区域之间的边界线以令人惊讶的精度获得。我们使用简单的反应系统说明和测试了这些方法，其中两个物种之间仅具有一个耦合项，以及从文献中获得的一些通用反应网络。我们还使用它来研究由于推导fokker-planck方程所涉及的近似值，在反应系统中发生的非物理概率电流的形状。
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.
