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@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.
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