Axiomatic foundations of entropic theorems for hard-sphere systems

Following the recent establishment of an exact kinetic theory describing the statistical behavior of the Boltzmann-Sinai Classical Dynamical System and realized by the Master kinetic equation, in this paper the problem is posed of the construction of related appropriate entropic theorems. The same equation is proved to warrant, in particular, an exact constant H-theorem, referred to here as Master constant H-theorem, which holds for the 1-body (i.e., kinetic) Boltzmann-Shannon entropy. The relationship with the customary Boltzmann H-theorem holding for the Boltzmann equation and the physical origin of the related phenomenon of macroscopic irreversibility are investigated.