[peppercorn]

The 'working fluid' in heat engine can operate through either an open- or closed- cycle.
A car engine is an open-cycle just like your design with 'batches' of air being first drawn-in and then, in a closed 'phase', having it's temperature, and hence density, changed.

The critical aspect is that with a spark-ignition (or a Diesel) engine the change in temp. is by many hundreds of degrees C - which causes an awful lot of (near)instantaneous pressure increase.

I'd say your design is more like a direst-injection spark-engine, only one where the fuel isn't lit.  A spray of petrol will slightly lower the pressure in the cylinder in the same way as cold water would (only more so).
I could also give the example of the condensing stage on a steam engine, which can suck a piston along as the steam returns to water.  And just to separate the issue from the confusion of chemical fuel let's say the steam is raised by a solar collector.

Also I don't see what role entropy plays here? - Are  you saying that because, local to your machine (ie. taking only part of the whole system that includes the solar heating of the atmosphere) there is a lower entropy state due to the work extracted by the piston, for the now more humid air that before? ... This is likely true, but that doesn't mean the drop in entropy is where the work comes from.

[Ape Hunter]

We know that a great degree of energy is produced by a Hydrogen bomb. Even without utilizing the same process used within the bomb, certainly Hydrogen can cause quite an explosion within your automobile engine's combustion chambers

Water is basically comprised of explosive elements... Oxygen makes quite a "bang" also

[peppercorn]

Oxygen makes quite a "bang" also

But not with anything hanging about in any great concentration in the Earth's atmosphere.

Water is basically comprised of explosive elements...

...that have already been 'banged'. What's your point exactly?

[rosy]

We know that a great degree of energy is produced by a Hydrogen bomb. Even without utilizing the same process used within the bomb, certainly Hydrogen can cause quite an explosion within your automobile engine's combustion chambers

Water is basically comprised of explosive elements... Oxygen makes quite a "bang" also

To suggest that we can get chemical energy from water because elemental hydrogen and oxygen are chemically reactive is exactly equivalent to suggesting that we can get energy by burning carbon dioxide because coal burns. Chemistry doesn't work like that.

[wolfekeeper (OP)]

It's like when water flows down hill. Once it reaches the bottom it can go no lower, you can no longer get hydroelectric power from it.

Similarly the hydrogen has rolled to the bottom of the oxygen atom's valley. It can't go any lower, and can no longer give you any energy.

Only if you can find a lower valley, for example, if you react it with sodium, sodium attracts the oxygen more strongly than the hydrogen, so it can replace it, and give you lots of heat as it gives up the potential energy.