By modelling heat engines as driven multi-partite system we show that their dissipation can be expressed in terms of the lag (relative entropy) between the perturbed state of each partition and their equilibrium state, and the correlations that build up among the partitions. We illustrate the rich interplay between correlations and lags with a two-qubit device driven by a quantum gate. ; Comment: 5 pages, 3 figures. This paper resulted from extensive rewriting and splitting in two of arXiv:1510.06183, now withdrawn