Lifetime of small systems controlled by autocatalytic reactions

Details Lifetime of small systems controlled by autocatalytic reactions Lifetime of small systems controlled by autocatalytic reactions

2004-07-05

arxiv.org/abs/cond-mat/0407106v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 7 figures

Scientific paper

By using the point model of reaction kinetics we have studied the stochastic properties of the lifetime of small systems controlled by autocatalytic reaction A+X -> X+X -> A+X, X -> B. Assuming that a system is living only when the number of autocatalytic particles is larger than zero but smaller than a positive integer N, we have calculated the probability of the lifetime provided that the number of substrate particles A is kept constant by a suitable reservoir, and the end-products B do not take part in the reaction. We have shown that the density function of the lifetime is strongly asymmetric and in certain cases it has a well-defined minimum at the beginning of the process. It has been also proven that the extinction probability of systems of this type is exactly 1.

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