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I have read and I think that I agree with the idea that if we have to choose probability distribution for an unknown system then it is a good idea to choose a distribution that has the least bias.

I understand why Boltzmann chose to assume equal probability distribution because for me, intuitively, it means the least bias possible for the guess of the distribution.

But apparently, when we do statistical mechanics we usually maximize Gibbs entropy subject to some constraints on average values of macroscopic parameters. I am interested in the intuition behind how one would develop this approach and maybe how one would go from Boltzmann's hypothesis to Gibbs hypothesis.

When I read similar questions online I get explanations using information theory and Shannon's entropy which are extremely interesting and give a lot of insight. But I am also wondering about how did people came up with this definition and how did they justify it before Shannon's papers.

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  • $\begingroup$ Of possible interest related to this, the "Magic Square" of Stat. Mech scribd.com/document/61030166/Magic-Square $\endgroup$ – Carl Witthoft Jul 22 at 14:17
  • $\begingroup$ @CarlWitthoft Thank you for the link! But I am not really interested in Gibbs thermodynamic potential but in the Gibbs entropy and philosophy behind it (from Gibbs perspective) $\endgroup$ – HydrodynamicsPlease Jul 25 at 22:55
  • $\begingroup$ According to wikipedia, it seems Boltzmann considered it in 1866 - potentially page 22? - related to phase densities. Landau-Lifschitz presents an argument for it pages 11 to 25. I haven't read Gibbs treatise to know more his original arguments, but I would look there. $\endgroup$ – user73236 Nov 22 at 10:17

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