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.
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.
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.