Path summation formulation of the master equation.
Path summation formulation of the master equation.
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主方程的路径求和公式。
DOI：
10.1103/physrevlett.96.210602
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发表时间：
2006
影响因子：
8.6
通讯作者：
Sun,SeanX
中科院分区：
文献类型：
--
作者：
Sun,SeanX
由动力学主方程描述的马尔可夫动力学在化学、物理和生物学中有着广泛的应用。对于任意数目的状态和路径长度，我们导出了离散状态空间中马尔可夫路径的概率的精确表达式。路径重复访问一组状态的总概率可以显式求和。状态之间的转移概率可以表示为连接状态的所有可能路径的总和。导出的路径概率满足涨落定理。路径可以是路径空间蒙特卡罗过程的起点，该过程可以用作分析复杂反应网络中的路径的替代算法。
Markovian dynamics, modeled by the kinetic master equation, has wide ranging applications in chemistry, physics, and biology. We derive an exact expression for the probability of a Markovian path in discrete state space for an arbitrary number of states and path length. The total probability of paths repeatedly visiting a set of states can be explicitly summed. The transition probability between states can be expressed as a sum over all possible paths connecting the states. The derived path probabilities satisfy the fluctuation theorem. The paths can be the starting point for a path space Monte Carlo procedure which can serve as an alternative algorithm to analyze pathways in a complex reaction network.