The greatest physical barrier in the origin of life is overcoming the thermodynamic pull towards hydrolytic death to establish a self-maintaining dissipative structure. This paper formulates the emergence of self-replicating molecular systems as a mathematically necessary nonequilibrium phase transition dictated by spatial geometry. First, we prove that the traditional "primordial soup" model is physically precluded; spontaneous polymerization in an open 3D ocean is strictly forbidden by an insurmountable entropy barrier and the complete attenuation of thermal noise. We demonstrate that initiating the phase transition requires "dimensional reduction" onto a 2D membrane and the modular assembly of short fragments to generate finite probability noise. Furthermore, leveraging an exact mathematical isomorphism with the overdamped Langevin dynamics of cosmic inflation, we prove that amplifying this thermal noise to surpass deterministic decay strictly demands an ultra-small micro-compartment. Thus, the phase transition is absolutely governed by pushing the Surface-to-Volume (S/V) ratio to its physical upper limit. Strikingly, the exact physical conditions mandated by this thermodynamic transition—short fragment modularity and spatial confinement—inadvertently provide the collective systemic redundancy necessary to overcome Eigen’s informational error threshold. Ultimately, pushing the S / V ratio to its physical upper limit serves as the universal geometric equation that rescues matter from both thermodynamic and informational death, driving the spontaneous onset of Darwinian evolution.
ikutoshi miyamoto (Sat,) studied this question.
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