This paper is reasonably accessible, and talks about the Information Theoretic approach to Statistical Mechanics. It is written using Quantum Mechanics, because Classical Statistical Mechanics is conceptually harder. But, the same results apply in both cases.
Balian, R. (2005). Information in statistical physics. Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics, 36(2), 323–353. doi:doi: DOI: 10.1016/j.shpsb.2005.02.001