# Lifetime of small systems controlled by autocatalytic reactions

Source: [Lifetime of small systems controlled by autocatalytic reactions](<https://www.sota2.com/research/paper/68fa1e607a2b558e2932205c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T14:57:13.366Z

Authors: L. Pal

Published: 2004-07-05T16:29:54.000Z

## Abstract

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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0407106>)

[PDF](<https://arxiv.org/pdf/cond-mat/0407106.pdf>)