Adiabatic operation of a molecular machine

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Abstract
Operation of a molecular machine is often thought of as a “far from equilibrium” process in which energy released by some high free energy fuel molecule or by light is used to drive a nonequilibrium “power stroke” to do work on the environment. Here we discuss how a molecular machine can be operated arbitrarily close to chemical equilibrium and still perform significant work at an appreciable rate: micrometer per second velocities against piconewton loads. As a specific example, we focus on a motor based on a three-ring catenane similar to that discussed by Leigh [Leigh DA, Wong JKY, Dehez F, Zerbetto F (2003) Nature 424:174–179]. The machine moves through its working cycle under the influence of external modulation of the energies of the states, where the modulation is carried out slowly enough that the state probabilities obey a Boltzmann equilibrium distribution at every instant. The mechanism can be understood in terms of the geometric phase [Berry MV (1990) Phys Today 43(12):34–40] in which the system moves adiabatically around a closed loop in parameter space, completing, on average, nearly one-half mechanical cycle each time it does so. Because the system is very close to equilibrium at every instant, the efficiency can approach 100%.

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