Thermal noise can facilitate energy conversion by a ratchet system

Molecular motors in biological systems are expected to use ambient fluctuation. In a recent paper [Phys. Rev. Lett. 80, 5251 (1998)], it was shown that the following question was unanswered: Can thermal noise facilitate energy conversion by ratchet system? We consider it using stochastic energetics, and show that there exist systems where thermal noise helps the energy conversion.