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.