The most costly step in carbon capture from flue gas streams is regeneration of the pure CO2 stream from the sorbent, because of the high temperatures required by conventional systems. This work presents an entropy generation analysis of the new Endex calcium looping method, in which regeneration is driven directly by the heat of carbonation and pressure-swing is used to reduce the temperature of calcination. Entropy generation rates for the important subprocesses in the control volume are computed and visualised over the expedient parameter space. The performance of the system is optimised in two ways: by minimising the total entropy generation rate per mole of CO2 captured, and by maximising the capture efficiency. The tradeoff between these two objectives is highlighted.