Is a Stirling Cycle Engine Still Valid with an Open Cold Reservoir?

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Let's say that I have a stirling motor designed in such a way that the cold reservoir is always at standard temperature and pressure (or at least very close to it).

So, if I were to put a hole in the cold reservoir there should be no effect on the engine running, but it might exchange air with the outside world (due to diffusion or turbulence or something) -- in fact, the cold reservoir could just be an opening to the ambient air.

Would the resulting engine still qualify as a stirling cycle engine?
 
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