SELF-REPLICATION AS A UNIVERSAL PRINCIPLE: LOGISTIC DYNAMICS AND AUTOCATALYSIS IN COSMOLOGY AND IN LIVING SYSTEMS

This paper treats self-replication as a principle operating independently of substrate and sets out a programme for testing it. The starting point is the established fact that self-reproduction is not a privilege of biology but is described within non-equilibrium thermodynamics, molecular self-organization, statistical physics and systems chemistry. The formal basis is substantially strengthened relative to the previous version. Previously the common core of the two instantiations was taken to be exponential growth with a characteristic replication frequency; that basis is insufficient, since the exponential form is the most widespread in all of natural science and by itself does not distinguish a common mechanism from a structural analogy. Here it is shown that the evolution equation for the Hubble parameter in the cosmological self-replication model transforms identically into Ḣ = (Γ/2)·H·(1 − H/H∞), that is, into the Verhulst equation — the canonical logistic model of population growth in a resource-limited environment, in which the role of the carrying capacity is played by the limiting value H∞ = Γ/3. Furthermore, the requirement that the cosmological solution be non-singular yields the condition Γ′(H_max) > 3, which is precisely the definition of autocatalytic positive feedback. The commonality of the two instantiations therefore rests not on a coincidence of functional form but on a coincidence of the structure of the dynamics and of the type of feedback. The paper is programmatic; the identity of mechanism remains a hypothesis, and the condition for its falsification is stated explicitly.