Path summation formulation of the master equation |
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Authors: | Sun Sean X |
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Affiliation: | Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA. |
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Abstract: | 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. |
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