TY - JOUR

T1 - On the Boltzmann–Grad Limit for Smooth Hard-Sphere Systems

AU - Tessarotto, Massimo

AU - Cremaschini, Claudio

AU - Mond, Michael

AU - Asci, Claudio

AU - Soranzo, Alessandro

AU - Tironi, Gino

N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - The problem is posed of the prescription of the so-called Boltzmann–Grad limit operator (LBG) 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 LBG, 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.

AB - The problem is posed of the prescription of the so-called Boltzmann–Grad limit operator (LBG) 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 LBG, 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.

KW - Boltzmann H-theorem

KW - Boltzmann equation

KW - Hard-sphere classical dynamical system

KW - Master kinetic equation

UR - http://www.scopus.com/inward/record.url?scp=85042218780&partnerID=8YFLogxK

U2 - 10.1007/s10701-018-0144-5

DO - 10.1007/s10701-018-0144-5

M3 - Article

AN - SCOPUS:85042218780

VL - 48

SP - 271

EP - 294

JO - Foundations of Physics

JF - Foundations of Physics

SN - 0015-9018

IS - 3

ER -