K. J. Challis, Michael W. Jack
A general theory of molecular-scale energy transfer promises to yield insights into the mechanisms of molecular machines and to unify a diverse range of experiments and phenomenological models. We progress towards a general theory by deriving analytic solutions to Brownian motion on a multi-dimensional tilted periodic free-energy potential. Analogous to the tight-binding model of quantum mechanics, we consider the limit of deep potential wells and show that the continuous theory transforms to a discrete master equation describing hopping between localized (meta-)stable states. For non-separable potentials the master equation describes energy transfer between degrees of freedom and we derive expressions for the efficiency and rate of energy transfer valid beyond the near-equilibrium limit. Our predictions are consistent with non-equilibrium fluctuation theorems and the Onsager relations and provide an opportunity to experimentally test the theory.
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http://arxiv.org/abs/1208.5818
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