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Collective operation of quantum heat machines via coherence recycling, and coherence induced reversibility

Collective behavior where a set of elements interact and generate effects that are beyond the reach of the individual non interacting elements, are always of great interest in physics. Quantum collective effects that have no classical analogue are even more intriguing. In this work we show how to construct collective quantum heat machines and explore their performance boosts with respect to regular machines. Without interactions between the machines the individual units operate in a stochastic, non-quantum manner. The construction of the collective machine becomes possible by introducing two simple quantum operations: coherence extraction and coherence injection. Together these operations can harvest coherence from one engine and use it to boost the performance of a slightly different engine. For weakly driven engines we show that the collective work output scales quadratically with the number of engines rather than linearly. Eventually, the boost saturates and the scaling becomes linear. Nevertheless, even in saturation, work is still significantly boosted compared to individual operation. To study the reversibility of the collective machine we introduce the 'entropy pollution' measure. It is shown that there is a regime where the collective machine is N times more reversible while producing N times more work, compared to the individual operation of N units. Moreover, the collective machine can even be more reversible than the most reversible unit in the collective. This high level of reversibility becomes possible due to a special symbiotic mechanism between engine pairs.