How does the act of erasing information increase the total entropy of the system? This goes by the name Landauer's principle. Some details are here. Can anyone shed more light on this?
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$\begingroup$ Erasing information decreases the system's entropy, and this process requires energy. The Landauer's principle states that there is a theoretical limit on minimal energy required to erase information. $\endgroup$– kludgApr 6, 2021 at 5:41
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It means that if you lose information from your system, that information must have been transferred to the system's surroundings. This shows up as an increase in the entropy in the surroundings. This is directly related to the 2nd law of thermodynamics which says the entropy of an isolated system is always increasing. See Wikipedia: Entropy in thermodynamics and information theory for more details.
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$\begingroup$ w.r.t. quantum computation it might be interesting to mention that loosing information implies that the according operation is not reversible anymore, hence can not be described by a unitary. $\endgroup$– FleeepJun 21, 2019 at 14:09
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$\begingroup$ That's right, a whole discussion on decoherence would be interesting. I don't think I'll have the time in the near future but feel free to add an answer if you have time - it would certainly add to my rather short reply! $\endgroup$– bRost03Jun 21, 2019 at 14:15