WebHubTelescope: You again cite another book which is not about thermodynamics or statistical mechanics. And the author only cites image recovery as application of maximum [information] entropy. I already referred to information theory before.
You have extensible quoted this author in this thread about thermodynamics. In the same page that you quoted the author says: I do not know any thermodynamics.
In a first reading of the rest of that chapter, it seems that the author confounds different entropies: Boltzmann, Gibbs, Shannon, physical, informational… Maybe this explains why he does not understand why Shannon entropy is ignored for most applications on statistical mechanics and thermodynamics.
But at least he confirms what I have said in this thread: Jaynes ideas, MAXENT, MEP and similar ideas plays virtually no role in science (physics, chemistry, biology, geology…) and associated engineerings.
Sorry, I do not find any “deeper mathematical meaning of entropy” in the Azimuth blog.