Boltzmann chaos assumption

In statistical thermodynamics, Boltzmann chaos assumption or molecular chaos assumption postulates that during a two-body collision, between particles in an ideal gas system, there is no correlation of velocity. This assumption, outlined by Austrian physicist Ludwig Boltzmann in the 1870s, allowed for a molecular chaos view of particles in the gas phase, which thus fit the temperature-defined velocity distribution developed by Scottish physicist James Maxwell in 1859. [1]

A key insight applied by Boltzmann was to determine the collision term resulting solely from two-body collisions between particles that are assumed to be uncorrelated prior to the collision. This assumption was referred to by Boltzmann as the 'Stosszahl Ansatz', and is now known as the Boltzmann chaos assumption or 'molecular chaos assumption'. The Boltzmann chaos assumption, roughly speaking, postulates the non-correlation of velocities of particles which are about to collide. [2]

1. Boltzmann, Ludwig. (1964). Lectures on Gas Theory (pgs. 9, 74). New York: Dover.
2. Villani, Cédric. (2003). Topics in Optimal Transportation (pg. 224). AMS Bookstore.

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