What is the best source -in terms of quality- that would explain the argument that uses computations concepts to demonstrate that the Maxwell's Demon does not break the second law of thermodynamics? I have an impression that this argument has some flaw, because all the sources I know use natural language. However, I would like some source that demonstrates formally.
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1$\begingroup$ Lienhard Pagel in his book "Information ist Energie" gives a quantum mechanical analysis of Maxwell's Demon. He uses his information concept instead of a pure computation concept. If I remember correctly, he explains it both in natural language and with formulas and computations. $\endgroup$– Thomas KlimpelCommented Dec 9, 2017 at 23:10
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1$\begingroup$ May be these two blog entries of Scott Aaronson are of interest: scottaaronson.com/blog/?p=1818 scottaaronson.com/blog/?p=762 $\endgroup$– LamineCommented Dec 10, 2017 at 15:07
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A good place to start looking at these ideas is this paper, though it talks about the (related) idea of information and thermodynamics. It relates fundamental computational tasks (eg. editing a bit) to fundamental thermodynamic tasks (eg. energy extraction). Following the links within the paper should give reasonable access to literature on the subject. Also, see this paper.
EDIT - There is also discussion regarding this on Scott Aaronson's blog https://www.scottaaronson.com/blog/?p=3327. See the comments section too.
References -
1. The Hot Bit 1 : The Szilard-Landauer Correspondence, M Gopalkrishnan - arXiv preprint arXiv:1311.3533, 2013
2. The Thermodynamics of Computation — a Review, C. Bennet - International Journal of Theoretical Physics 21.12 (1982): 905-940.
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1$\begingroup$ Can you please give the references of the papers you cite so your answer remains valid even if the link does not work anymore? $\endgroup$– holfCommented Dec 10, 2017 at 8:29
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$\begingroup$ Good point. Added the references. $\endgroup$ Commented Dec 10, 2017 at 9:34