Analytic continuation of asymptotic formulas and axiomatics of thermodynamics and semithermodynamics (Q1907457)

We deal with mathematical axioms and theorems related to phenomenological thermodynamics. By using the geometric quantization procedure, we approach statistical physics much ``closer'' than in conventional phenomenological (axiomatic) thermodynamics. An analogy can be drawn by considering classical mechanics either as the limit of quantum mechanics or, traditionally, as an independent ``phenomenological'' discipline. The analogy with the present paper becomes complete if, in addition, we resort to the ``Bohr-Sommerfeld-Keller-Maslov theory'' of semiclassical geometric quantization.