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

Massimo Tessarotto, Claudio Cremaschini, Michael Mond, Claudio Asci, Alessandro Soranzo, Gino Tironi

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish
Pages (from-to)271-294
Number of pages24
JournalFoundations of Physics
Issue number3
StatePublished - 1 Mar 2018


  • Boltzmann H-theorem
  • Boltzmann equation
  • Hard-sphere classical dynamical system
  • Master kinetic equation

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Philosophy
  • History and Philosophy of Science


Dive into the research topics of 'On the Boltzmann–Grad Limit for Smooth Hard-Sphere Systems'. Together they form a unique fingerprint.

Cite this