Irreversible operation in a stalled state of Feynman's ratchet

We consider the Langevin dynamics which describes the transducer of thermal fluctuation into mechanical work. In the frame of Feynman's ratchet, we prove that irreversibility is unavoidable in operating the transducer if the system is described by the conventional Langevin equation with two degrees of freedom, where the degrees correspond to two heat baths of different temperatures.