An equation used in the study of a collection of particles in nonequilibrium statistical mechanics, particularly their transport properties. The Boltzmann equation describes a quantity called the distribution function, f, which gives a mathematical description of the state and how it is changing. The distribution function depends on a position vector r, a velocity vector v, and the time t; it thus provides a statistical statement about the positions and velocities of the particles at any time. In the case of one species of particle being present, Boltzmann's equation can be written ∂f/∂t+a.(∂f/∂v)+v.(∂f/∂r) = (∂f/∂t)coll, where a is the acceleration of bodies between collisions and (∂f/∂t)coll is the rate of change of f(r,v,t) due to collisions. The Boltzmann equation can be used to calculate transport coefficients, such as conductivity. The equation was proposed by Ludwig Boltzmann in 1872.
∂f/∂t+a.(∂f/∂v)+v.(∂f/∂r) = (∂f/∂t)coll
Subjects: Chemistry — Physics.