Perpetual Engine

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Recently, after reading the book Strugatsky brothers "Monday begins on Saturday." Found a interesting thing, Maxwell Demon, . Which creates a temperature difference. (For details, look in google). There is also a Stirling engine that operates on the difference in temperatures. Could not we will integrate them? Because modern technology allows a Maxwell demon using ion traps. It will also be a perpetual motion machine. Well, or efficiency will far exceed the efficiency of existing engines.