Editing H-theorem (section)

== Boltzmann's ''H'' theorem ==

[[Image:Translational motion.gif|thumb|upright=1.3|In this mechanical model of a gas, the motion of the molecules appears very disorderly. Boltzmann showed that, assuming each collision configuration in a gas is truly random and independent, the gas converges to the [[Maxwell speed distribution]] even if it did not start out that way.]]

Boltzmann considered what happens during the collision between two particles. It is a basic fact of mechanics that in the elastic collision between two particles (such as hard spheres), the energy transferred between the particles varies depending on initial conditions (angle of collision, etc.).

Boltzmann made a key assumption known as the ''Stosszahlansatz'' ([[molecular chaos]] assumption), that during any collision event in the gas, the two particles participating in the collision have 1) independently chosen kinetic energies from the distribution, 2) independent velocity directions, 3) independent starting points. Under these assumptions, and given the mechanics of energy transfer, the energies of the particles after the collision will obey a certain new random distribution that can be computed.

Considering repeated uncorrelated collisions, between any and all of the molecules in the gas, Boltzmann constructed his kinetic equation ([[Boltzmann's equation]]). From this kinetic equation, a natural outcome is that the continual process of collision causes the quantity ''H'' to decrease until it has reached a minimum.