Boltzmann equation

Summary

The Boltzmann equation describes a dilute gas through the density $f(t, x, v)$ of particles at position $x$ with velocity $v$. Particles move freely in straight lines and change velocity only in binary collisions, which the collision operator accounts for. It links the motion of individual molecules with the equations of fluid dynamics. Boltzmann's H-theorem shows that a certain entropy cannot decrease, which explains the approach to equilibrium.