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The goal here is to keep a bit of information $b$ at the temperature $T$ during a time $\delta t$.

I don't know if this question makes a lot of sense, considering the diversity of ways to encode information.

But is there a way to generalize all this techniques in term of state and particle?

Then could we obtain a lower bound on the energy we need to spend to keep this information unaltered.

It's a question very open, so don't hesitate to reformulate the problem in a way understandable for you. And I hope it's not a off-topic.

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The minimum amount of energy required to erase 1 bit of information is $kT\log{2}$ (Landauer limit)

If an object is isolated, then it never reaches thermal equilibrium, and no energy is required to support such state (and the information stored in it). In practice, however, quantum decoherence takes place, and the system loses all information about its initial state. Energy required to keep state coherent may vary for different cases.

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  • $\begingroup$ Is there no any minimal amount required among all cases? $\endgroup$ – Ievgeni Aug 20 at 15:13

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