Optimizing the classical heat engine

A pair of systems at different temperatures is a classic environment for a heat engine, which produces work during the relaxation to a common equilibrium. It is generally believed that a direct interaction between the two systems will always decrease the amount of the obtainable work, due to inevitable dissipation. Here a situation is reported where, in some time window, work can be gained due the direct coupling, while dissipation is relevant only for much larger times. Thus, the amount of extracted work increases, at the cost of a change of the final state.