Editing Maxwell–Boltzmann distribution (section)

== Relaxation to the 2D Maxwell–Boltzmann distribution ==
For particles confined to move in a plane, the speed distribution is given by

<math display="block">P(s < |\mathbf{v}| < s {+} ds) = \frac{ms}{k_\text{B}T}\exp\left(-\frac{ms^2}{2k_\text{B}T}\right) ds  </math>

This distribution is used for describing systems in equilibrium. However, most systems do not start out in their equilibrium state. The evolution of a system towards its equilibrium state is governed by the [[Boltzmann equation]]. The equation predicts that for short range interactions, the equilibrium velocity distribution will follow a Maxwell–Boltzmann distribution. To the right is a [[molecular dynamics]] (MD) simulation in which 900&nbsp;[[Hard spheres|hard sphere]] particles are constrained to move in a rectangle. They interact via [[Elastic collision|perfectly elastic collisions]]. The system is initialized out of equilibrium, but the velocity distribution (in blue) quickly converges to the 2D Maxwell–Boltzmann distribution (in orange).