Universal Inductive Engine: A Memory Coupled Reaction Diffusion Framework for the Emergence of Biological Organization

How does lifeless chemistry become a living system? We argue that the answer lies not in any particular molecule, but in a physical mechanism that is already present on the prebiotic Earth: the power-law temporal memory of disordered mineral surfaces. When this memory couples to autocatalytic chemistry driven out of equilibrium by hydrothermal flow, a threshold is crossed above which transient chemistry becomes persistent, localized, heritable, and subject to Darwinian selection. We present UIE : a first-principles field-theoretic framework, grounded in non-equilibrium reaction-diffusion partial differential equations with temporal memory.

Results include: the complete derivation of the renormalization group (RG) flow equation for the memory kernel; the exact result for the IR fixed point; the derivation of the birth-rate power law from the Gamma stationary distribution; the prediction of a reproductively sterile protocell regime; the generalization to arbitrary N component disordered chemical networks; the dimensional mapping to physical prebiotic chemistry; and the derivation of the Free Energy Principle from the MSRJD action with fractional exponent identification.

Update: I emphasize that the framework developed here still does not constitute a theory of biological evolution or Darwinian selection. The memory term introduced in the dynamics can be formally represented as an auxiliary field, rendering the system Markovian in an extended state space. Consequently, the phenomena described here are best interpreted as history-dependent self-organization in non-equilibrium systems.