In the

kinetic theory of gases Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to: * Kinetic theory, describing a gas as particles in random motion * Kinetic energy, the energy of an object that it possesses due to its motion Art and enter ...

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 Paul Ehrenfest (18 January 1880 – 25 September 1933) was an Austrian theoretical physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition a ...

) 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 ligh ...

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 In statistical physics, the BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, sometimes called Bogoliubov hierarchy) is a set of equations describing the dynamics of a system of a large number of interacting particles. The equ ...

Boltzmann's equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lerne ...

, 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 Johann Josef Loschmidt (15 March 1821 – 8 July 1895), who referred to himself mostly as Josef Loschmidt (omitting his first name), was a notable Austrian scientist who performed ground-breaking work in chemistry, physics (thermodynamics, optics ...

that it should not be possible to deduce an

irreversible process In science, a process that is not reversible is called irreversible. This concept arises frequently in thermodynamics. All complex natural processes are irreversible, although a phase transition at the coexistence temperature (e.g. melting of ic ...

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 The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one with largest entropy, in the context of precisely stated prior data (such as a proposition ...

in order to generalize the ''ansatz'' to higher-order distribution functions.

References

Philosophy of thermal and statistical physics Statistical mechanics {{statisticalmechanics-stub