That refrigerator would still use energy compressing the refrigerant. That's Work=F*x energy which won't go to zero with a massless frictionless motor. Or do y

That refrigerator would still use energy compressing the refrigerant. That's Work=F*x energy which won't go to zero with a massless frictionless motor. Or do you mean you also have a generator to recover the energy from the temperature differences it creates? So it's not really doing refrigerating because you're using all the cooling power to run the motor?