In the
kinetic theory of gases in
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, the molecular chaos hypothesis (also called ''Stosszahlansatz'' in the writings of
Paul Ehrenfest) is the assumption that the velocities of colliding particles are uncorrelated, and independent of position. This means the probability that a pair of particles with given velocities will collide can be calculated by considering each particle separately and ignoring any correlation between the probability for finding one particle with velocity and probability for finding another velocity in a small region .
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and li ...
introduced this approximation in 1867 although its origins can be traced back to his first work on the kinetic theory in 1860.
The assumption of molecular chaos is the key ingredient that allows proceeding from the
BBGKY hierarchy to
Boltzmann's equation, by reducing the 2-particle distribution function showing up in the collision term to a product of 1-particle distributions. This in turn leads to Boltzmann's
H-theorem
In classical statistical mechanics, the ''H''-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency to decrease in the quantity ''H'' (defined below) in a nearly-ideal gas of molecules.
L. Boltzmann,Weitere Studien über das Wä ...
of 1872, 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
Loschmidt's paradox, also known as the reversibility paradox, irreversibility paradox or ', is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics. This puts the time reversal symmetry of (al ...
). 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.
Though the ''Stosszahlansatz'' is usually understood as a physically grounded hypothesis, it was recently highlighted that it could also be interpreted as a heuristic hypothesis. This interpretation allows using the
principle of maximum entropy in order to generalize the ''ansatz'' to higher-order distribution functions.
References
Philosophy of thermal and statistical physics
Statistical mechanics
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