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  Status of the Principle of Maximum Entropy

+ 4 like - 0 dislike

Jaynes' principle of maximum entropy is a powerful tool in non-equilibrium statistical mechanics, but it relies on so called subjective probabilities, information entropy and other things, which could leave a foul taste in the mouth of non-Bayesian physicists. However, I have heard that there are other "frequentist" theories, which could come to the same results, f.e. large deviation theory.

Could someone explain or point out theories or papers which derive the maximum entropy principle within the context of "classical" probability theory?

asked Jul 26, 2014 in Mathematics by hhagenstroem (80 points) [ no revision ]

1 Answer

+ 4 like - 0 dislike

A non-subjective account of statistical mechanics close to the treatment with large deviation theory (which is just a more abstract version of it) is given in Part II of my online book 

Classical and Quantum Mechanics via Lie algebras, http://arxiv.org/abs/0810.1019

At the end (in Sections 10.6 and 10.7), one also finds a short discussion of the subjective, information theoretic treatment and its deficiencies. 

A survey that treats statistical mechanics directly in terms of large deviations is given in (reference [80] of the book, referenced on p.208) 

R.S. Ellis. An overview of the theory of large deviations and applications to statistical
mechanics. Scand. Actuarial J, 1:97–142, 1995.

A more recent survey is:

H. Touchette, The large deviation approach to statistical mechanics, Phys. Rep. 478 (2009), 1-69.

answered Jul 26, 2014 by Arnold Neumaier (15,787 points) [ revision history ]
edited Jul 28, 2014 by Arnold Neumaier

Thanks! The comments in your book as well as Touchette's review were helpful.

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