Deterministic approach to the kinetic theory of gases

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Abstract

In the so-called Bernoulli model of the kinetic theory of gases, where (1) the particles are dimensionless points, (2) they are contained in a cube container, (3) no attractive or exterior forces are acting on them, (4) there is no collision between the particles, (5) the collision against the walls of the container are according to the law of elastic reflection, we deduce from Newtonian mechanics two local probabilistic laws: a Poisson limit law and a central limit theorem. We also prove some global law of large numbers, justifying that "density" and "pressure" are constant. Finally, as a byproduct of our research, we prove the surprising super-uniformity of the typical billiard path in a square.

Original languageEnglish (US)
Pages (from-to)160-269
Number of pages110
JournalJournal of Statistical Physics
Volume138
Issue number1
DOIs
StatePublished - Feb 1 2010

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Elastic reflection
  • Fourier analysis
  • Large billiard systems
  • Parseval's formula
  • Poisson limit law
  • Typical billiard path in a square and in a cube

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