2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/24346By 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 1.8 pages, 7 figuresStatistical MechanicsDisordered Systems and Neural Networkstext