I investigate the mechanisms driving spontaneous functional complexification in nonequilibrium reaction-diffusion systems. A fully bidirectional coupling is constructed between a Gray-Scott Turing pattern and an Eigen quasispecies equation. Through systematic variable-decoupling experiments—enforcing spatial homogeneity, switching off environmental feedback, and toggling between private and public-good fitness functions—the causal roles of private fitness, spatial patterns, and environmental feedback are isolated. Ten independent statistical replicates demonstrate that under the private fitness scheme the mean functionality rises from approximately 0. 34 to 0. 89 (final-state values all converge to 0. 8929), whereas the strict public-good control groups (one- and two-dimensional) remain stationary at approximately 0. 33 (all converge to 0. 3302, independent-samples t-test p<<0. 001), exhibiting no functional improvement. Nonequilibrium thermodynamic analysis reveals that the total entropy production rate increases from approximately 0. 008 to 0. 035 during the functional jump, confirming that dissipation drives complexity; at late times the inhibitor concentration drops below the numerical cutoff threshold (~10^-94), the chemical reaction term vanishes, and entropy production decays to zero, indicating that the system relaxes into a diffusion-maintained equilibrium state. Extensive scans over fitness landscape parameters, mutation rates, and environmental parameters delineate the boundaries within which the private-fitness advantage holds. Additional single-run observations of periodic environmental inversions, spontaneous rise without a seed, and long-term post-peak decay exhibit qualitatively intriguing trends whose statistical significance requires confirmation through repeated experiments. All scripts and data are publicly available at https: //doi. org/10. 5281/zenodo. 19978912.
Shutong Hou (Thu,) studied this question.