I have some questions about energy emitted when one bit of information is processed.

Landauer's principle states the minimum possible amount of energy required to erase one bit of information is k T ln2 Considering this,

  • How this formula is found? In terms of energy and memory unit, what is the processing cost per bit for normal and reverse operations respectively?
  • $\begingroup$ Cross-posted: physics.stackexchange.com/q/401968/24498. Please do not post the same question on multiple sites. Each community should have an honest shot at answering without anybody's time being wasted. $\endgroup$ – D.W. Apr 25 '18 at 20:37
  • $\begingroup$ I'm voting to close this question because it was cross-posted on Physics.SE and answered there. $\endgroup$ – D.W. Apr 25 '18 at 20:37
  • $\begingroup$ @D.W. I initially posted this question at here but no replies have happened so I decided to post it on Physics.SE as it is somewhat related to it. Actually it has got answers there so you can close this one. $\endgroup$ – Onur A. Apr 25 '18 at 22:51
  • $\begingroup$ I realize that. For future reference, please don't do that -- we don't want to have multiple copies of the same post on multiple SE sites (see the link in my original comment). If you decide you want to post it on a different site, please delete the copy here before posting elsewhere. I realize there's no way you could have known that; so I'm letting you know for the future. Thanks for your understanding! $\endgroup$ – D.W. Apr 25 '18 at 23:32

(This is a cross-posted answer from Physics Stack Exchange)

The simple answer would be: consider a physical system that can be in two states. Its thermodynamic entropy is $k_B \log(2)$ due to this. When you erase the bit, then you have a definite microstate and the entropy is zero. Since entropy cannot decrease it has to go somewhere, and this means it needs to be transferred to the environment that has temperature T, giving us a cost $k_B T\log(2)$.

This is the simplified version of a slightly dodgy derivation (note how I facilely equated thermodynamic entropy with information entropy without justification and did not specify how erasure happened or the entropy got moved around). Once can do this more rigorously, like in this paper.

Also, it is worth pointing out it is a misconception that the cost has to be paid in energy. If you have an empty computer memory you can just swap the erased bit for a fresh zero reversibly. But empty computer memory is in a sense a heat reservoir at absolute zero but with very limited capacity (it will eventually run out). It is possible to show that the cost can be paid using other conserved quantities like spin. It is just that in practice we tend to move entropy around by dumping it as waste heat in a cool outside heat bath.

(Landauer's original paper)


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