  A Brownian Motor is a nanoscale or molecular device that combines the effects
of thermal noise, spatial or temporal asymmetry, and directionless input energy
to drive directed motion. Because of the input energy, Brownian motors function
away from thermodynamic equilibrium and concepts such as linear response
theory, fluctuation dissipation relations, and detailed balance do not apply.
The {\em generalized} fluctuation-dissipation relation, however, states that
even under strongly thermodynamically non-equilibrium conditions the ratio of
the probability of a transition to the probability of the time-reverse of that
transition is the exponent of the change in the internal energy of the system
due to the transition. Here, we derive an extension of the generalized
fluctuation dissipation theorem for a Brownian motor for the ratio between the
probability for the motor to take a forward step and the probability to take a
backward step.
