Comparison of thermodynamic characteristics in the ordinary quantum and classical approaches

► Some old problems (on the behavior of thermodynamics characteristics for h tending to zero), which go back to E. Wigner and J.G. Kirkwood, and A. Wehrl, are solved. ► The statistical sum in the quantum and classical approaches is compared. ► The same goes for the energy and entropy without the demand of Planck's constant h being small. ► A fundamental principle, which allows us to derive Gibbs-type formulas rigorously, is proposed. ► Game-theoretic analogies, which appear, are also discussed.