It all depends. I believe the IMA has stop/start shutdown technology, so that helps.

Also, remember that engine speed and fuel used are not always "in sync" - so the motor could be providing torque and power in a queue, supplimenting what the engine can do at "idle" in terms of RPM and fuel usage.

Different technology, but as an example, during warmup, my Prius will run at about 1100 rpm ALL the time until you get above a certain speed / acceleration, or warmup ends. During this time, the power available from the engine is either used for motion while being supplimented by the battery/motor (if needed) , or charging, . It's quite easy to run the battery down in warmup mode if you don't exceed 30mph or so (after which, the engine bursts into normal mode ).

The Jazz effectivly freewheels down hills without using petrol but charging the battery thus when the motor is assisting the petrol engine it is not always using power derived inefficiently. I get the impression that on occasions like a downhill run the valves are locked open and the petrol is switched off. The transition back to normal running goes unnoticed without any jerking.

The Jazz effectivly freewheels down hills without using petrol but charging the battery thus when the motor is assisting the petrol engine it is not always using power derived inefficiently

That's a perpetual motion argument. The charging of the battery is not 'free'; it comes from the expense of momentum which then has to be regained. Of course, if you wanted to slow down anyway, then you're quids in, but if you didn't, then you're worse off.

Valves are invariably closed when cylinders are 'decativated'. Otherwise, the engine still functions as an air pump with the associated losses-and you cool the catalytic converter so it miay not immediately function when the engine commences firing again.

Would they not have the exhaust valves open to stop pumping losses, or am I missing something?