Yes, it can be used, but the definite article (the) should be dropped in that case:
Such mapping enabled the use of classical statistical mechanics' tools.
Using the phrase classical statistical mechanics without a definite article makes it a name for the theory (I've seen it capitalized), and since mechanics ends in
-s and wouldn't be pronounced with an extra syllable /-əz/ in the possessive,
mechanics' gets a solo apostrophe, according to orthodox apostrophic theories.
That's if and only if you want to make it possessive in writing, note. In speech
mechanics' can't be distinguished from
mechanics anyway, since apostrophes are always silent. And yet somehow we all manage to understand either version in speech and only notice a problem in writing. Amazing.
Whereas leaving the definite article in makes the classical statistical mechanics just one of several statistical mechanicses, or of several other kinds of mechanics, all unspecified, which is precisely what you want to avoid when you invoke a classical theory to explain something. Especially if you are interested in the tools and not the theories.