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02-Mar-2019 14:25

As far as I can tell, he is mostly interested in the issue of Bayesian statistics (i.e. Although he's now a statistician and not a physicist, he does have a Ph D in physics and it looks like a serious argument to me.

(I haven't read enough Jaynes to say how closely Shalizi's assumptions model Jaynes's ideas, but I think you should at least give his arxiv paper a close read.)@Matt Reece : But apparently, Section IIB is only a criticism of Jaynes' elementary approach to the second principle of thermodynamics.

On the other hand, given the recipe for statistical evolution of a system, the question of whether or not MAXENT methods are necessary at all arises, as Grad said: [MAXENT] has not yet been connected in any way with dynamics.

It can only be looked upon as an ad hoc recipe whose accuracy must be empirically determined.

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But I am much less enamored of the whole probability theory catfight (I would like to understand it better). This contains a clear statement of his result and section IIB in particular contains arguments about how applying a "maximum entropy" procedure doesn't reproduce the expected results of stat mech.

My preferred reference (never published, I think): Where do we stand on maximum entropy?

@JoséFigueroa-O' Farrill: I personally find Jaynes' continuous diatribe against detractors of his brand of probability theory annoying; for instance here it seriously dilutes what is otherwise a great set of applications of the methodology, which I believe stands on its own without the abstract dialectic.

Personally I see it as morally dimensional analysis, writ large.

Yvan pointed out that there is a problem with classical hamiltonian systems because they have an (uncountable) underlying configuration space, and there are technical problems with defining entropy on them.

One main strength (and limitation) of Jaynes' approach is that it applies regardless of the underlying dynamics (at least as a foundation of statistical mechanics).