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I'll pretend you don't mean "sustained" to allow me to type something. Does this qualify?

Put a bowl of water down at room temperature, wait for one molecule to "evaporate", and I think you did it? Unfortunately they are now no longer at the same temperature.

Temperature is an average. You can still take advantage of the fact that there will be much lower and higher temperatures present. Also, what about Peltier effect? Same temperature when it starts.

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Yes. If you try to design any device to capture all the molecules like that and extract their energy, you'll find that just as often your device dislodges a water molecule the other way, back into the pool and losing energy. Thus although You aren't the first to invent the Brownian ratchet.

The device shown in the OP appears to allow for a sustained thermally-driven energy transfer one way or the other depending on the bit value ou are sending.

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