An environment far from equilibrium is thought to be a necessary condition for the origin and persistence of life. In this context we report open-flow simulations of a non-enzymic proto-metabolic system, in which hydrogen peroxide acts both as oxidant and driver of thermochemical cycling. We find that a Gaussian perturbed input produces a non-Boltzmann output fluctuation distribution around the mean oscillation maximum. Our main result is that net biosynthesis can occur under fluctuating cyclical but not steady drive. Consequently we may revise the necessary condition to "dynamically far from equilibrium".