Ive read a few courses on statistical mechanics, and while their textual explanations and example choices differ, the flow of information from microscopy to macroscopy seems the same, and reading between the lines you can see some mathematical construct. Has statistical mechanics been formalized in the sense that say analysis has been formalized (down to quantifiers, sets, functions,...) more rigorously? Where can one find a formal axiomatic approach to statistical mechanics as opposed to an introductory descriptory approach?
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