Who has proved Boltzmann's H-theorem (which tells that entropy of a closed system grows as the system approaches thermal equilibrium) for the kinetic equation with Landau collisions operator? One proof is provided by F. Hinton in 1st volume of "Basic plasma physics" (edited by Sudan and Galeev) but I wonder if Hinton was the first.

UPDATE: I asked same question on https://www.researchgate.net/post/Who_was_first_to_prove_the_Boltzman_H-theorem_for_the_Landau_kinetic_equation and was answered that a derivation was provided by N.Bogolubov but I don't believe in that.

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    $\begingroup$ Out of curiosity, why don't you believe the claim that said derivation existed? $\endgroup$ – HDE 226868 Jan 15 '16 at 0:22

Much to my dismay, the first proof of a global solution to the Boltzmann equation was not published until 2010. The paper was:

Gressman, P.T., and R.M. Strain "Global classical solutions of the Boltzmann equation with long-range interactions," Proc. Natl. Academy Sci. 107, pp. 5744-5749, 2010.

Apparently, all previous proofs had been for local interactions. I should note that Cédric Villani was awarded the 2010 Math Fields Medal for his work on this topic and the generation of entropy, specifically in a collisionless medium like a plasma. There was work by Lev Landau, of course, but others worked on this subject long before Villani like Roald Sagdeev and Mikhail Malkov. Yet I am not sure if they provided proofs since Villani was given the Fields Medal for his work on the topic.

Regardless, Villani has some very detailed and good material on his website http://cedricvillani.org including a book that has some very detailed notes and, I believe, some history on the subject in which you are interested.

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  • $\begingroup$ I disagree. Hinton in Basic Plasma Physics (osti.gov/scitech/biblio/6846853) gave a proof of H-thereon using Landau's integral of collisions. $\endgroup$ – Igor Kotelnikov Jan 14 '16 at 14:26
  • $\begingroup$ @IgorKotelnikov - Unfortunately, I cannot access that book electronically but I see that Galeev was one of the authors, correct? I believe he worked very closely with Sagdeev (might have even been his advisor or one of his students, I do not recall which way that went...). I mentioned these works to Malkov and his reaction was very similar to yours. Unfortunately, I do not understand the math well enough to determine whether Hinton's proof was sufficient to argue it did first what the references I cited did later... $\endgroup$ – honeste_vivere Jan 14 '16 at 17:40
  • $\begingroup$ Hinton's paper in 1st volume of Basic Plasma Physics has the proof I mentined above. Hinton's paper was publisged earlier than that by Gressman, P.T., and R.M. Strain and he did not mentioned any previous proofs. So, to the moment I think that Hinton was the first who prooved H-theorem for Landau's integral of equations. $\endgroup$ – Igor Kotelnikov Jan 15 '16 at 3:07

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