  Quantum statistical methods that are commonly used for the derivation of
classical thermodynamic properties are extended to classical mechanical
properties. The usual assumption that every real motion of a classical
mechanical system is represented by a sharp trajectory is not testable and is
replaced by a class of fuzzy models, the so-called maximum entropy (ME)
packets. The fuzzier are the compared classical and quantum ME packets, the
better seems to be the match between their dynamical trajectories. Classical
and quantum models of a stiff rod will be constructed to illustrate the
resulting unified quantum theory of thermodynamic and mechanical properties.
