I think you've gotten some very good information. I've thought about a device such as you have described for years, run the numbers, and decided it might be possible, although not necessarily practical.

With real-world idealized efficiencies and a COP of 4.5 or so I managed to design the world's most complex coffee warmer that is, there would be just about enough leftover energy to brew a cup of coffee.

That was making the assumption that the engineering problems could be solved.

And idealized efficiencies could be maintained, Not a Particularly Realistic Assumption.

Problem 1. Several posts have mentioned that the efficiency of a heat pump is inversely proportional to the temperature difference between condenser and evaporator. I haven't bothered to look up performance tables but I'm going to guess that a 50° differential is the maximum that you can maintain the necessary COP, and I am probably being excessively optimistic.

Utilizing your 55° source temperature then precludes using an expendable working fluid such as water. Find some way to make a heat pump work efficiently with a Delta T of 200° and your machine is potentially practical.

Utilizing existing technologies you are limited to non-expendable working fluids i.e. refrigerants.

Problem 2. To utilize a captured working fluid will necessitate the use of a large heat exchanger and low ambient temperatures again doable however it will add complexity and expense.

The only way I see the system functioning is to have two separate circuits, your heat concentration circuit i.e. the heat pump, and for lack of a better term a boiler circuit.

There will be no metering device in the circuit used to drive your recovery engine, to get any useful work you will have to maintain a pressure differential via a separate condenser.

There will be additional parasitic load such as injection pumps, condenser fans etc.

Perhaps with a COP of 8 it might be possible to build a working machine.

While I agree religion and science do not necessarily belong in the same discussion, the philosophy expressed is sound. A lot of hard engineering i.e. a lot of hard work will be required to develop such a machine, a practical machine such as that would be a benefit to all.

I definitely disagree that you have not been offered a considerable amount of useful information.

It's far too early in the morning for me to start cracking numbers again, however if you could explain how you would solve my basic problems, and provide some numbers to go with it I would be more than happy to offer my meager assistance as I'm sure many others would in this endeavor.