随机非线性动力学中快变量的消去
Elimination of fast variables in stochastic nonlinear kinetics
摘要：
涉及少量变量的简化化学方案通常足以说明促成反应的主要物质浓度的确定性演变。然而，它的预测是值得怀疑的，例如在荧光相关光谱（FCS）或在爆炸系统中使用的小系统，涉及强非线性，如自催化步骤。我们精确的动力学标准定义的准稳态近似和消除确定性动力学中的快速浓度的有效域。设计两个不同的三变量模型收敛到同一个两变量模型，我们表明，慢变量的波动的方差和协方差不正确的预测的两变量模型，即使在一个大的系统大小的限制。在含有少量分子的介观体系中，简化方案的更显著的弱点被发现。比较了两种随机方法的结果，指出了Langevin方程相对于主方程的不足。我们的结论是描述的波动和它们的耦合与非线性的确定性动力学逃脱减少化学方案。
英文摘要：
A reduced chemical scheme involving a small number of variables is often sufficient to account for the deterministic evolution of the concentrations of the main species contributing to a reaction. However its predictions are questionable in small systems used for example in fluorescence correlation spectroscopy (FCS) or in explosive systems involving strong nonlinearities such as autocatalytic steps. We make precise dynamical criteria defining the validity domain of the quasi-steady-state approximation and the elimination of a fast concentration in deterministic dynamics. Designing two different three-variable models converging toward the same two-variable model, we show that the variances and covariance of the fluctuations of the slow variables are not correctly predicted by the two-variable model, even in the limit of a large system size. The more striking weaknesses of the reduced scheme are figured out in mesoscaled systems containing a small number of molecules. The results of two stochastic approaches are compared and the shortcomings of the Langevin equations with respect to the master equation are pointed out. We conclude that the description of the fluctuations and their coupling with nonlinearities of deterministic dynamics escape reduced chemical schemes.
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