I've now, more or less abandoned all prior vestiges of past heat engine theory where alternating hot and cold, or hot and cold "reservoirs" or whatever are necessary in favor of a "pure" kinetic theory of heat. I.e. so-called "heat" is transfer of kinetic energy. Nothing to compel a "flow" from hot to cold. True, the generally disordered random collisions result in a gradual "spreading out" of energy but that "spreading out" is not assisted or facilitated by the presence of "cold"
The gas particles, in other words, should have a clear unfettered path between heat source where kinetic energy transfers into the engine and piston, where kinetic energy transfers out of the engine.
In a reciprocating engine this necessitates a "pulsed" heat input, to drive the piston, alternating with periods of no heat input so as to allow the return of the piston between pulses.
My theory is then, that a heat "sink" imparts no benefit, only an obstacle or side path that has the effect of bleeding off supposed "excess" kinetic energy or "waste heat".
In other words, there is no intrinsic "waste heat" only mismanaged or miss directed kinetic energy.
As a "proof of concept" of sorts, consider this situation.
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A mostly thermally insulated vacuum chamber containing one gas atom. There is one or two relatively small membranes where "heat" transfer may take place.
When the particle collides with a membrane, heat (kinetic energy) is imparted to it. It then bounces around unfettered until it happens to collide with a microscopic paddle wheel equipped with a ratchet that allows movement in one direction only.
On average there should be a tendency for the paddle wheel to turn and lift the attached external weight.
In other words, the particle picks up "heat" ( kinetic energy ) at a membrane, then in time imparts that energy to the ratchet.
Now a lot can go wrong. Maybe the gas molecule hits the ratchet twice, loosing all it's energy and stops, or possibly it collides with the membrane in such a way as loose all it's energy, leaving it to float aimlessly about inside the chamber.
Introducing a second molecule should compensate for such occurrences. Possibly a third, and a fourth etc.
Statistically there should still be a more or less direct transfer of energy from the heat input "membrane" to the ratchet, to effect external work output.
The point here is that there is only one "reservoir"
What would introducing a "cold" "sink" accomplish?
This would actually be just a LESS HOT membrane that would tend to absorb kinetic energy from the gas mecules in the chamber without giving any back.
The paddle wheel itself is the target "sink". (Absorber of kinetic energy) Having an additional low energy sink just reduces efficiency.
Practically speaking however, where heat sensitive magnets are in use, a cooling jacket is necessary to avoid damage to the magnets, but that speaks to poor design. The magnets could be positioned out of harms way.
Would a regenerator added into the picture be if any benefit in this paddle wheel arangement, vacuum chamber setup?
I don't see any benefit to introducing a regenerator into the picture.
I don't think that a "scaled up" version of the above box engine is necessary. I think a Stirling engine, generally, is already a scaled up version in principle, but this has not been generally recognized.