A new representation for chemical kinetics based on a sum over histories formulation is discussed. The description of the time-dependent chemistry of a reaction network is provided by chemical pathways defined at a molecular level. Using this methodology, the quantitative time evolution of the kinetics is described by enumerating the most important pathways followed by a chemical moiety such as a tagged atom. An explicit formula for the pathway probabilities is derived which takes the form of an integral over a time-ordered product. This expression has a simple and computationally efficient Monte Carlo representation which permits the method to be applied to a wide range of problems. For small reaction networks, the chemical pathways can be enumerated using graph theoretic methods. More complicated networks can be explored using random walks computed from a stochastic algorithm. The workings of the method are illustrated using a simple network of 20 chemical species which react via first-order kinetics. The application of the sum over histories representation to problems in surface catalysis and hydrogen combustion provide more realistic applications.

中文翻译：

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化学动力学的历史表示总和：基于化学途径的定量理论

讨论了基于历史公式求和的化学动力学的新表示。反应网络的时间依赖性化学描述由在分子水平定义的化学途径提供。使用这种方法，动力学的定量时间演变是通过列举最重要的途径来描述的，然后是化学部分，如标记原子。导出了路径概率的显式公式，该公式采用时间有序乘积的积分形式。该表达式具有简单且计算效率高的 Monte Carlo 表示，允许该方法应用于广泛的问题。对于小型反应网络，可以使用图论方法枚举化学途径。可以使用从随机算法计算的随机游走来探索更复杂的网络。使用通过一级动力学反应的 20 种化学物质的简单网络来说明该方法的工作原理。将历史求和表示应用于表面催化和氢燃烧中的问题提供了更现实的应用。