On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems

@article{30099,
   author = {Tessarotto, Massimo and Cremaschini, Claudio and Mond, Michael and Asci, Claudio and Soranzo, Alessandro and Tironi, Gino},
   article_number = {3},
   doi = {http://dx.doi.org/10.1007/s10701-018-0144-5},
   keywords = {Boltzmann equation; Hard-sphere classical dynamical system; Boltzmann H-theorem; Master kinetic equation},
   language = {eng},
   issn = {0015-9018},
   journal = {Foundations of Physics},
   title = {On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems},
   url = {https://link.springer.com/article/10.1007%2Fs10701-018-0144-5},
   volume = {48},
   year = {2018}
}

TY  - JOUR
ID  - 30099
AU  - Tessarotto, Massimo - Cremaschini, Claudio - Mond, Michael - Asci, Claudio - Soranzo, Alessandro - Tironi, Gino
PY  - 2018
TI  - On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems
JF  - Foundations of Physics
VL  - 48
IS  - 3
SP  - 271-294
EP  - 271-294
SN  - 00159018
KW  - Boltzmann equation
KW  - Hard-sphere classical dynamical system
KW  - Boltzmann H-theorem
KW  - Master kinetic equation
UR  - https://link.springer.com/article/10.1007%2Fs10701-018-0144-5
L2  - https://link.springer.com/article/10.1007%2Fs10701-018-0144-5
N2  - The problem is posed of the prescription of the so-called Boltzmann-Grad limit operator (L_{BG}) for the N-body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. It is proved, that, despite the non-commutative property of the operator L_{BG}, the Boltzmann equation can nevertheless be uniquely determined. In particular, consistent with the claim of Uffink and Valente (Found Phys 45:404, 2015) that there is 'no time-asymmetric ingredient' in its derivation, the Boltzmann equation is shown to be time-reversal symmetric. The proof is couched on the "ab initio" axiomatic approach to the classical statistical mechanics recently developed (Tessarotto et al. in Eur Phys J Plus 128:32, 2013). Implications relevant for the physical interpretation of the Boltzmann H-theorem and the phenomenon of decay to kinetic equilibrium are pointed out.
ER  - 

TESSAROTTO, Massimo, Claudio CREMASCHINI, Michael MOND, Claudio ASCI, Alessandro SORANZO a Gino TIRONI. On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems. \textit{Foundations of Physics}. 2018, roč.~48, č.~3, s.~271-294. ISSN~0015-9018. Dostupné z: https://dx.doi.org/10.1007/s10701-018-0144-5.