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Extracting work from stochastic pumps

The efficiency at maximum power output of stochastic pumps, systems driven away from equilibrium by a periodic variation of parameters, is investigated by studying simple models in which the driving consists of abrupt jumps of system parameters. The models are chosen to differ by qualitative aspects of the dynamics, namely the degree of directionality and cycle control. The behaviour at maximum power output is found to depend on the choice of parameters used to maximize the output. For a natural choice, in which the external force and the period of the driving are varied to increase the power output, numerical and analytical results suggest that the efficiency at maximum power output is at most 1/2.