Relaxation dynamics in Dyson’s model for the origin of metabolism

This paper discusses some aspects of the dynamical evolution of the system described by Dyson’s model for the origin of metabolism. First, the mean number of mutation events required to observe the origin of metabolism in the model is calculated. This number can span a large range depending upon the values of some critical parameters. Second, the dynamics of the relaxation to equilibrium is investigated by computing the correlation function of an on-off random function that defines the instantaneous state of the system. It was found that the dynamics of the system is well described by a double or a stretched exponential relaxation. © 1996 The American Physical Society.