On biological individuation.

In this paper, we understand the emergence of life as a pure individuation process. Individuation already occurs in open thermodynamics systems near equilibrium. We understand such open systems, as already recursively characterized (R₁) by the relation between their internal properties, and their boundary conditions. Second, global properties emerge in such physical systems. We interpret this change as the fact that their structure is the recursive result of their operations (R₂). We propose a simulation of the emergence of life in Earth by a mapping (R) through which (R₁R₂) operators are applied to themselves, so that R_N = (R₁R₂)_N. We suggest that under specific thermodynamic (open systems out of equilibrium) and chemical conditions (autocatalysis, kinetic dynamic stability), this mapping can go up to a limit characterized by a fixed-point equation: [Formula: see text]. In this equation, ([Formula: see text]) symbolizes a regime of permanent resonance characterizing the biosphere, as open from inside, by the recursive differential relation between the biosphere and all its holobionts. As such the biosphere is closed on itself as a pure differential entity. ([Formula: see text]) symbolizes the regime of permanent change characterizing the emergence of evolution in the biosphere. As such the biosphere is closed on itself, by the principle of descent with modifications, and by the fact that every holobiont evolves in a niche, while evolving with it.