Mechanical Energy Flow and Dynamic Maintenance in Prebiotic Vesicles: A Minimal Non-Equilibrium Model

The emergence of life may be approached not only as a chemical problem but also as a problem of maintaining organized matter away from thermodynamic equilibrium. Inspired by Prigogine's framework of dissipative structures, we developed a minimal numerical model of a prebiotic fatty-acid vesicle exposed to continuous mechanical fluctuations from its environment. The model couples environmental mechanical forcing, membrane tension, tension-dependent fatty-acid incorporation, membrane-material loss, mechanical relaxation, and energy dissipation. A distinct transition between three dynamical regimes emerged: membrane decay, dynamic maintenance, and net membrane growth. For the baseline parameter set, a critical forcing amplitude of approximately (F_c = 0.3735) produced essentially zero net membrane growth (ΔA ≈ 0.004). Below this threshold membrane losses exceeded incorporation, whereas above it incorporation exceeded losses. Robustness tests showed that the decay–maintenance–growth transition persisted after variations in membrane loss rate, fatty-acid incorporation rate, and fatty-acid availability. Introducing Kelvin–Voigt viscoelasticity produced a pronounced frequency dependence of the maintenance threshold. Increasing forcing frequency increased both the mechanical amplitude and dissipated energy required to maintain the vesicle. The model does not demonstrate a mechanism for the origin of life. Rather, it demonstrates a physically plausible principle: an open membrane system can possess a dynamic maintenance regime in which continuous environmental energy flow compensates structural losses and preserves organization without requiring thermodynamic equilibrium.