Couldn't you use the thermal mass of the hot water tank?
My concern was efficiency. It's much more efficient to dump heat into 60 degree dirt than a 110-140 degree water tank. I shouldn't have said reservoir, I should have said 'sink'.
You use the panels on the roof to provide the heat to power the system, a radiation system to dump the waste heat into the ground, then use the cold water to cool the house.
In the wintertime, start up the geothermal heat pump*, supplimented by the roof panels. The fact you've been dumping heat down there all summer is a bonus.
Why not just go with one of the absorption systems that is already on the market instead of trying to reinvent the wheel?
Because considering these sorts of system is fun?
Is there anything sized for residential systems? I know this cycle is used in big industrial applications, but I wasn't aware of any small, pump-less systems commercially available.
I haven't found any.
*Yes, you'll use electricity, but not much of it overall.