Phys. Rev. Lett. 96, 210602 (2006) [4 pages]Path Summation Formulation of the Master EquationReceived 23 February 2006; published 1 June 2006 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. © 2006 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.96.210602
DOI:
10.1103/PhysRevLett.96.210602
PACS:
05.40.−a, 02.50.−r
See AlsoComment: O. Flomenbom, J. Klafter, and R. J. Silbey, Comment on “Path Summation Formulation of the Master Equation”, Phys. Rev. Lett. 97, 178901 (2006). Reply: Sean X. Sun, Sun Replies:, Phys. Rev. Lett. 97, 178902 (2006). |
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