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Recently it has been shown that in the quantum regime an additional quantum irreversibility occurs that is linked to decoherence into the energy basis. Here we employ quantum trajectories to construct distributions for classical heat and quantum heat exchanges, and show that the heat footprint of quantum irreversibility differs markedly from the classical case. We also quantify how quantum irreversibility reduces the amount of work that can be extracted from a state with coherences. Our results show that decoherence leads to both entropic and energetic footprints which both play an important role in the optimization of controlled quantum operations at low temperature.<\/jats:p>","DOI":"10.1038\/s42005-020-0356-9","type":"journal-article","created":{"date-parts":[[2020,5,19]],"date-time":"2020-05-19T10:04:11Z","timestamp":1589882651000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Energetic footprints of irreversibility in the quantum regime"],"prefix":"10.1038","volume":"3","author":[{"given":"M. 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