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If I have a bit and I do not know what the current value is, is it possible to use less energy than $E_b = k_b T \ln(2)$ so that if the bit value is already equal to what you want, you don't waste energy by setting it?

My guess is no: "observation/sampling" + "making a decision" would still involve a logic operation which would require the flipping of at least 1 bit.

Bob
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In real life, erasing an already erased bit need not dissipate energy. Consider dynamic RAM, where a "1" is a charged capacitor, but a "0" is discharged. Erase by draining charge from the capacitor through a resistor. If it's "1", you dissipate its energy, but if it's "0" you (on average) dissipate no energy (there is some transfer of energy from the capacitor to the resistor ("kTC noise"), but its direction is random).

I believe the Landauer limit is statistical, assuming maximum entropy of the medium before erasure.

John Doty
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