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FOURIER ANALYSIS AND THE KINETIC THEORY OF GASES

Published online by Cambridge University Press:  16 December 2011

József Beck
Affiliation:
Mathematics Department, Rutgers University New Brunswick, New Jersey, U.S.A. (email: jbeck@math.rutgers.edu)
Corresponding
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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 force is acting on them, (4) there is no collision between the particles, (5) the collisions against the walls of the container are according to the law of elastic collision, we deduce from Newtonian mechanics two basic probabilistic limit laws about particle-counting. The first one is a global central limit theorem, and the second one is a local Poisson law. The key fact is that we can prove the “realistic limit”: first the time interval is fixed and the number of particles tends to infinity (where the density particle/volume remains a fixed constant), and then, in the second step, the time tends to infinity.

Type
Research Article
Copyright
Copyright © University College London 2012

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