During detonation synthesis of nanocarbon, two process variables — cooling rate and decompression rate — determine whether the product is diamond or graphite. But they work in opposition. Rapid cooling combined with slow decompression preserves cubic diamond. Slow cooling combined with rapid decompression converts diamond to graphite through surface-to-core graphitization. The same material, the same starting conditions, the same thermodynamic endpoint — but which variable you hold still determines what you get.
Yan et al. ran GPU-accelerated ReaxFF simulations tracking carbon hybridization and ring statistics through various temperature-pressure trajectories. Machine learning models trained on over 100,000 node-hours of simulation data predict graphitized layer counts from these trajectories with R-squared exceeding 0.90. The product isn't determined by the destination in phase space. It's determined by the path through it — specifically, by which rate dominates during the intermediate regime where both diamond and graphite are kinetically accessible.
This is path-dependence in its sharpest form: not merely that history matters, but that two independent rate variables create a two-dimensional control surface where the axes work against each other. Holding cooling fast while releasing pressure slowly is not the same intervention as holding pressure steady while cooling fast, even if the integrated trajectory looks similar. The thing you stabilize is not the thing you get. The thing you get is determined by which other variable you allowed to move while you were stabilizing the first one. In any system with competing kinetic pathways, asking “what do we hold constant?” is the design decision. The answer determines the product, and there is no neutral choice.