Eur. Phys. J. Plus (2015) 130: 91
https://doi.org/10.1140/epjp/i2015-15091-7

Regular Article

Axiomatic foundations of entropic theorems for hard-sphere systems

¹ Department of Mathematics and Geosciences, University of Trieste, Via Valerio 12, 34127, Trieste, Italy
² Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, CZ-74601, Opava, Czech Republic

^* e-mail: claudiocremaschini@gmail.com

Received: 5 March 2015
Revised: 7 April 2015
Accepted: 9 April 2015
Published online: 12 May 2015

Abstract

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.