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In this short note, we consider a system of two rotors, one of whichinteracts with a Langevin heat bath. We show that the system relaxes to itsinvariant measure (steady state) no faster than a stretched exponential$\exp(-c t^{1/2})$. This indicates that the exponent $1/2$ obtained earlier bythe present authors and J.-P. Eckmann for short chains of rotors is optimal.

On the relaxation rate of short chains of rotors interacting with Langevin thermostats