The effect of hopping energy relaxation on the diffusion-limited reaction A+B→0 is considered. The main effect of the relaxation is to make the diffusion constant a decreasing function of time. We find that fluctuation effects radically alter the decay law predicted from the rate-equation approach, as is already known to be the case for diffusion in thermal equilibrium. New long-time behavior is predicted for the concentration of reacting particles as compared to the thermal equilibrium case.

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