A Minimal Thermodynamically Consistent Chemical Oscillator

What the math gives to ML

The paper presents a thermodynamically consistent reaction network with a supercritical Hopf bifurcation controlled by a chemostat concentration. Its transferable mechanism is the Hopf normal form, which produces a predictable transition from a stable fixed point to a bounded oscillation, with square-root amplitude growth above threshold and a measurable relaxation rate. This can be transferred to recurrent neural networks and state-space models by replacing unconstrained recurrent channels with explicitly saturating oscillator channels. The resulting architecture offers a falsifiable stability and long-horizon prediction mechanism rather than relying only on learned recurrent weights.