2004/07/05 by L. Pal, Pal, L.
Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0407106
8 pages, 7 figures
arxiv created 2004/07/05 · arxiv updated 2009/12/01
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.