  We present a theoretical treatment of energy transfer in a molecular motor
described in terms of overdamped Brownian motion on a multidimensional tilted
periodic potential. The tilt acts as a thermodynamic force driving the system
out of equilibrium and, for non-separable potentials, energy transfer occurs
between degrees of freedom. For deep potential wells, the continuous theory
transforms to a discrete master equation that is tractable analytically. We use
this master equation to derive formal expressions for the hopping rates, drift,
diffusion, efficiency and rate of energy transfer in terms of the thermodynamic
force. These results span both strong and weak coupling between degrees of
freedom, describe the near and far from equilibrium regimes, and are consistent
with generalized detailed balance and the Onsager relations. We thereby derive
a number of diverse results for molecular motors within a single theoretical
framework.
