Physics – Computational Physics
Scientific paper
2005-10-06
Physics
Computational Physics
23 pages, 5 EPS pages, submitted to PRE
Scientific paper
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and elimination of degrees of freedom via the renormalization of transition rates of slow reactions. The method suggested in this work is more general than other approaches presented previously: it is not limited to a particular type of stochastic processes and can be applied to different types of processes describing fast dynamics, and also provides crossover to the case when separation of time scales is not well pronounced. We derive a family of exact fluctuation-dissipation relations which establish the connection between effective rates and the statistics of the reaction events in fast reaction channels. An illustration of the technique is provided. Examples show that renormalized transition rates exhibit in general non-exponential relaxation behavior with a broad range of possible scenarios.
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