Title:
Deterministic approach to the kinetic theory of gases
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.