Correlation of subsystems at the onset of a centre manifold organization

Abstract

A dissipative reactive system operating far from thermodynamic equilibrium has been considered. The phase-space contraction occurring beyond the dynamical instability is assumed to correspond to a locally attractive and locally invariant centre, manifold. Under these constraints a subsystem is not a virtual entity, but rather the decomposition of a system in an ensemble of interacting subsystems arises from the characteristic scaling relations which hold at the onset of a centre manifold and involve the control parameters of the system. This scaling defines the local volume to which fluctuations are confined. Thus the interaction of subsystems inducing organization on one another has been analyzed for the case where a temporal dissipative structure is substained within a centre manifold occurring beyond a hard-mode instability. We prove that the scaling laws define a coarse grained phase space compatible with the space of realizations of the random source term in the macroscopic dynamics. The time-evolution of the probability density in the coarse-grained phase space common to all subsystems is equivalent to the selection process described by Eigen's equations for a collection of self-reproducing macromolecular information carriers.