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Collective behavior where a set of elements interact and generate effectsthat are beyond the reach of the individual non interacting elements, arealways of great interest in physics. Quantum collective effects that have noclassical analogue are even more intriguing. In this work we show how toconstruct collective quantum heat machines and explore their performance boostswith respect to regular machines. Without interactions between the machines theindividual units operate in a stochastic, non-quantum manner. The constructionof the collective machine becomes possible by introducing two simple quantumoperations: coherence extraction and coherence injection. Together theseoperations can harvest coherence from one engine and use it to boost theperformance of a slightly different engine. For weakly driven engines we showthat the collective work output scales quadratically with the number of enginesrather than linearly. Eventually, the boost saturates and the scaling becomeslinear. Nevertheless, even in saturation, work is still significantly boostedcompared to individual operation. To study the reversibility of the collectivemachine we introduce the 'entropy pollution' measure. It is shown that there isa regime where the collective machine is N times more reversible whileproducing N times more work, compared to the individual operation of N units.Moreover, the collective machine can even be more reversible than the mostreversible unit in the collective. This high level of reversibility becomespossible due to a special symbiotic mechanism between engine pairs.

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