Molecular chaos

In the kinetic theory of gases in physics, molecular chaos is the assumption that the velocities of colliding particles are uncorrelated, and independent of position. James Clerk Maxwell introduced this approximation in 1867.^[1] This assumption, also called in the writings of Ludwig Boltzmann the Stosszahlansatz (collision number hypothesis), makes many calculations tractable.

In particular, the assumption of molecular chaos was a key element, although initially unrecognised, in Boltzmann's H-theorem of 1872,^[2] which attempted to use kinetic theory to show that the entropy of a gas prepared in a state of less than complete disorder must inevitably increase, as the gas molecules are allowed to collide.

This drew the objection from Loschmidt that it should not be possible to deduce an irreversible process from time-symmetric dynamics and a time-symmetric formalism: something must be wrong (Loschmidt's paradox).

The resolution (1895) of this paradox is that the velocities of two particles after a collision are no longer truly uncorrelated. By asserting that it was acceptable to ignore these correlations in the population at times after the initial time, Boltzmann had introduced an element of time asymmetry through the formalism of his calculation.

References

1. Maxwell, J. C. (1867). "On the Dynamical Theory of Gases". Philosophical Transactions of the Royal Society of London 157: 49. doi:10.1098/rstl.1867.0004.
2. L. Boltzmann, "Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen." Sitzungsberichte Akademie der Wissenschaften 66 (1872): 275-370.
   English translation: Boltzmann, L. (2003). "Further Studies on the Thermal Equilibrium of Gas Molecules". The Kinetic Theory of Gases. History of Modern Physical Sciences 1. pp. 262–349. doi:10.1142/9781848161337_0015. ISBN 978-1-86094-347-8.